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Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 592138 12 pageshttpdxdoiorg1011552013592138

Research ArticleApplication of a New Hybrid Fuzzy AHP Model tothe Location Choice

Chien-Chang Chou12 and Ker-Wei Yu3

1 Department of Shipping Technology National Kaohsiung Marine University 482 Chung-Chou 3rd RoadChi-Chin 805 Kaohsiung Taiwan

2 Choursquos Science Research Center Taiwan3Department of Marine Engineering National Kaohsiung Marine University Taiwan

Correspondence should be addressed to Ker-Wei Yu kwyumailnkmuedutw

Received 10 April 2013 Accepted 26 May 2013

Academic Editor Jer-Guang Hsieh

Copyright copy 2013 C-C Chou and K-W Yu This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

The purpose of this paper is to propose a new hybrid fuzzy Analytic Hierarchy Process (AHP) algorithm to deal with the decision-making problems in an uncertain andmultiple-criteria environment In this study the proposed hybrid fuzzy AHPmodel is appliedto the location choices of international distribution centers in international ports from the view of multiple-nation corporationsThe results show that the proposed new hybrid fuzzy AHP model is an appropriate tool to solve the decision-making problems inan uncertain and multiple-criteria environment

1 Introduction

Modern logistics service provided by the logistics provideremphasizes quick response to customer demand Howeverit is difficult to fit totally customer demands in a logisticssystem In particular in a global logistics system a lotof uncertainties and complexities exist A global logisticssystem includes two important roles One is the logisticsservice provider for example shipping carriers interna-tional ports and international distribution centers Anotheris the logistics service demander such as multinationalcorporations (MNCs) The international distribution centerwithin the international port is also one important part ofa global logistics system The shipping companies and themultiple-national corporation prefer to use high-efficiencyand high-service quality international logistics centers withinan international port Therefore it is an important andcomplex decision-making problem for shipping companiesandmultinational corporations to select a high-efficiency andhigh-service quality international logistics center within aninternational port

Due to a shift in the global center of manufacturing toAsia since 1980smajor international ports in theAsian regionhave been expanded rapidly Thus the shipping companies

and the multinational corporations focus on the locationchoice of international distribution centers inAsiaThemajorinternational ports in Asia include the ports of ShanghaiSingapore Hong Kong Shenzhen Busan Ningbo QingdaoGuangzhou Tianjin and Kaohsiung In the future thedemand for cargoes in Asia will further increase In Table 1the container throughputs in 2010 for the worldrsquos top 20container ports including the ports of Shanghai SingaporeHong Kong Shenzhen Busan Ningbo Guangzhou Qing-dao Dubai Rotterdam Tianjin Kaohsiung Antwerp KlangHamburg Los Angeles Tanjung Pelepas Long Beach Xia-men and Laem Chabang are 29069 28430 23611 2250914180 13146 12545 12012 11613 11145 10086 9181 84838146 7900 7831 6603 6263 5824 and 5640 thousandTEUs respectively The rankings and the volumes for thesemajor international ports from 2006 to 2010 are also shownin Table 1

Many international distribution centers at major Asianports have been established in the recent years such asWaigaoqiao Bond Logistics Park in the port of ShanghaiHong Kong International Distribution Center in the port ofHong Kong Kaohsiung Yes Logistics Zone in the port ofKaohsiung Schwartz Logistics Hub in the port of ShenzhenBusan Logistics Park in the port of Busan and Keppel

2 Mathematical Problems in Engineering

Table 1 The container throughputs and the rankings for the worldrsquos top 20 container ports (unit thousand TEUs)

2010 2009 2008 2007 2006 Name of port 2010 2009 2008 2007 20061 2 2 2 3 Shanghai 29069 25002 27780 26150 217202 1 1 1 1 Singapore 28430 25866 29918 27935 247923 3 3 3 2 Hong Kong 23611 20925 24248 23881 235394 4 4 4 4 Shenzhen 22509 18250 21400 21090 184685 5 5 5 5 Busan 14180 11980 13452 13261 120386 8 8 11 13 Ningbo 13146 10502 10933 9360 71407 6 7 12 15 Guangzhou 12545 11190 11001 9200 66568 9 10 10 11 Qingdao 12012 10260 10020 9462 77029 7 6 6 8 Dubai 11613 11150 11830 11000 892310 10 9 7 7 Rotterdam 11145 9800 10784 10791 969011 11 14 17 17 Tianjin 10086 8700 8500 7102 595012 12 12 8 6 Kaohsiung 9181 8581 9676 10256 977413 13 13 14 14 Antwerp 8483 7309 8663 8176 701814 14 15 16 16 Klang 8146 7300 7973 7118 632615 15 11 9 9 Hamburg 7900 7010 9737 9890 886116 16 16 13 10 Los Angeles 7831 6748 7849 8355 846917 17 18 18 19 Tanjung Pelepas 6603 6000 5600 5500 477018 18 17 15 12 Long Beach 6263 5067 6487 7312 728919 19 22 22 22 Xiamen 5824 4680 5034 4627 401820 20 21 21 21 Laem Chabang 5640 4640 5130 4640 4123Source Chou et al [1]

Distripark in the port of Singapore Therefore it is veryimportant for the shipping companies and the multinationalcorporations to evaluate the environment among these majorinternational logistics centers in different nations in orderto design and implement an appropriate global logisticssystem It is also a complexmultiple-criteria decision-making(MCDM) problem under uncertain environment AHP isan appropriate approach to solve complex multiple-criteriadecision-making problem Fuzzy sets theory method hasbeen widely applied to the uncertain decision-making prob-lem in the real world Thus this paper combines AHP andfuzzy sets theory and then proposes a new hybrid fuzzy AHPmodel for the location choice of international logistics centerswithin the international ports from the perspective of multi-nation corporations

2 Literature Review

21 Environmental Evaluation Approaches Environmentevaluation approaches including the resource-based view(RBV) traditional strength-weakness-opportunity-threat(SWOT) and quantitative SWOT such as the external factorevaluation matrix (EFE) internal factor evaluation matrix(IFE) and competitive profile matrix (CPM) have beenwidely used The traditional SWOT analytical method iscommonly applied to marketing strategy analysis [2ndash4] TheSWOT analytical method is able to help the decision makerof the enterprises evaluate qualitatively their competitivenessand can be used as a foundation of the development ofstrategies [5] The quantitative SWOT such as externalfactor evaluation matrix (EFE) internal factor evaluationmatrix (IFE) and competitive profile matrix (CPM) aim

at analyzing statistical data differing from the traditionalSWOT analytical method [3 6] The disadvantage of theabove approaches is that they cannot evaluate the qualitativeand quantitative criteria simultaneously Therefore thispaper proposes a new hybrid approach which integratesAHPmethod to carry out a complete evaluation of qualitativeand quantitative criteria simultaneously and to evaluate thecompetitive environmental relationships between the severalinternational distribution center locations within the portsin the asian region

Erol and Ferrell Jr [7] use fuzzy Quality Function De-ployment (QFD) to convert qualitative information intoquantitative parameters and then combine this data withother quantitative data to multiobjective mathematical pro-gramming model Mikhailov and Tsvetinov [8] proposea fuzzy AHP approach for tackling the uncertainty andimprecision of the service evaluation process Ronza et al[9] present a quantitative risk analysis approach to porthydrocarbon logistics Because risk is an uncertain criterionit is not easy for a decision maker to measure exactly thevalue of risk Chang and Huang [4] present a quantita-tive strengthweaknessopportunitythreat (SWOT) analysismethod for assessing the competing strengths of majorports in East Asia Yong [10] uses a fuzzy TOPSIS modelto solve the problem of plant location choice Onut andSoner [11] propose an AHPTOPSIS approach for solvingtransshipment site selection problem under fuzzy environ-ment Tahera et al [12] develop a fuzzy logic approach fordealing with qualitative quality characteristics of a processChen et al [13] combine fuzzy AHP with MultidimensionScaling (MDS) in identifying the preference similarity ofalternatives Chou et al [14] present a new fuzzy multiple

Mathematical Problems in Engineering 3

Lminus1A1(h)c1 b1

h

a1 d1

LA1(x)RA1(x)

Rminus1A1(h)

A1

1

Figure 1 Trapezoidal fuzzy number 1198601= (1198881 1198861 1198871 1198891)

attributes decision-making (MADM) approach for solvingfacility location selection problem by using objective andsubjective attributes Lee and Lin [15] use a fuzzy quan-titative SWOT procedure for environment evaluation ofinternational distribution centers in Pacific Asian region Leeet al [16] introduce a fuzzy AHP and Balanced Score Card(BSC) approach for evaluating performance of IT departmentin the manufacturing industry in Taiwan Chou [17] usesfuzzy MCDM approach for dealing with quantitative andqualitative criteria in a process of location choice Chou [18]deals with objective data and subjective ratings by fuzzy logicChou [19] analyzes the competitive relationship betweenthe ports of Hong Kong Shanghai and Kaohsiung by thesensitivity analysis

In the past although many researchers proposed a lot offuzzy approaches for example fuzzy QFD MADM AHPTOPSIS BSC SWOT and MCDM few presented a hybridqualitativequantitative fuzzy AHP model for dealing withboth objective data and subjective criteria simultaneously inthe decision-making process

22 Fuzzy AHP Despite of its wide application to variousdecision-making problems the conventional AHP approachmay not fully reflect a style of human thinking Thus thefuzzy AHP approach is proposed to overcome the disadvan-tage of the conventional AHP The fuzzy AHP approach is asystematic method for the alternative choice and justificationproblems that combines the concept of fuzzy sets theory [20]and the hierarchical structure analysis [21]

Fuzzy AHP approach has been widely applied to manydecision-making problems For example Chang [22] devel-oped a fuzzy extent analysis for AHP and the approach isrelatively easier in computational procedure than the otherfuzzy AHP approaches Kuo et al [23] presented a fuzzyAHP method for the location choice of a convenience storeKurttila et al [5] combined AHP with SWOT to provide anew hybrid method for a forest certification case Stewartet al [24] combined AHP method with SWOT to present anew approach for improving the usability of AHP in strategicmanagement Kahraman et al [25] applied fuzzy AHP toselect the location of facility Zhang et al [26] combined fuzzyAHP with MCDM to deal with an MCDM decision-makingproblem The results show that the proposed hybrid methodwas a useful way to deal with MCDM decision-makingproblems Erensal et al [27] determined key capabilities

in technology management by using fuzzy AHP Chan andKumar [28] proposed a model for global supplier develop-ment considering risk factors by using fuzzy AHP Bozburaand Beskese [29] determined the priorities of organizationalcapital measurement indicators by using fuzzy AHP Bozburaet al [30] used fuzzy AHPmethod to determine the prioritiesof human capital measurement indicators Lee and Lin [15]developed a fuzzy quantified SWOTprocedure that integratesMCDM concept and fuzzy AHP method for the locationchoice of international distribution centers

3 Methodology

31 Fuzzy Sets Theory Fuzzy sets theory is initially intro-duced by Zadeh [20] A fuzzy number is defined as followsSuppose 119860

1= (1198881 1198861 1198871 1198891) is a trapezoidal fuzzy number

in Figure 1 The membership function of 1198601and the fuzzy

arithmetic operations on fuzzy numbers are shown as follows

1198911198601(119909) =

(119909 minus 1198881)

(1198861minus 1198881) 119888

1le 119909 le 119886

1

1 1198861le 119909 le 119887

1

(119909 minus 1198891)

(1198871minus 1198891) 119887

1le 119909 le 119889

1

0 otherwise

(1)

Suppose 1198601= (1198881 1198861 1198871 1198891) and 119860

2= (1198882 1198862 1198872 1198892) are

two trapezoidal fuzzy numbers

(a) Addition operation on A1and A

2

1198601oplus 1198602= (1198881+ 1198882 1198861+ 1198862 1198871+ 1198872 1198891+ 1198892) (2)

(b) Subtraction operation on 1198601and 119860

2

1198601Θ1198602= (1198881minus 1198892 1198861minus 1198872 1198871minus 1198862 1198891minus 1198882) (3)

(c) Multiplication operation on 1198601and 119903

119903 otimes 1198601= (119903119888

1 1199031198861 1199031198871 1199031198891) (4)

(d) Division operation on 1198601and 119903

1198601

119903= (

1198881

1199031198861

1199031198871

1199031198891

119903) (5)

Chou [31] proposed the canonical representation of atriangular fuzzy number 119884 = (119888 119886 119887)

119875 (119884) =1

6(119888 + 4119886 + 119887) (6)

32 AHP Theory Saaty [21] initially proposed the AnalyticHierarchy Process (AHP) which is a multiple-attributedecision-making tool for solving complex multiple-criteriadecision-making problems AHP methodology has someadvantages One of the most important advantages of theAHP is based on the pairwise comparison Another is that


the AHP calculates the inconsistency index which is the ratioof the decision makerrsquos inconsistency on the criteria Thecomputational procedures for AHP are listed as follows

Let us consider the criteria 1198621 119862

119894 119862

119895 119862

119899

someone level in the hierarchy One wishes to find theirweights of importance119882

1 119882

119894 119882

119895 119882

119899 on some

elements in the next level Allow 119886119894119895 119894 119895 = 1 2 119899 to be

the importance strength of 119862119894when compared with 119862

119895 In

generally we can represent the comparative importance scaleof criteria as shown in Table 2 The matrix of these numbers119886119894119895is denoted by 119861

119861 =

[[[[[[[

[

1198861111988612sdot sdot sdot 119886

1119895sdot sdot sdot 119886

1119899

11988611989411198861198942sdot sdot sdot 119886

119894119895sdot sdot sdot 119886

119894119899

11988611989911198861198992sdot sdot sdot 119886

119899119895sdot sdot sdot 119886

119899119899

]]]]]]]

]119899times119899

(7)

where 119886119895119894= 1119886

119894119895 that is 119861 is reciprocal If onersquos judgment

is perfect in all comparisons then 119886119894119896= 119886119894119895sdot 119886119895119896for all 119894 119895 119896

and one calls the matrix 119861 consistent An obvious case of aconsistent matrix 119861 is its elements

119886119894119895=119908119894

119908119895

119894 119895 = 1 2 119899 (8)

Thus when the matrix 119861 is multiplied by the vectorformed by each weighting 119908 = (119908

1 1199082 119908

119899)119879 one gets

119861119908 =

[[[[[[[[[[[[[[[[[

[

1199081

1199081

1199081

1199082

sdot sdot sdot1199081

119908119895


119908119899

1199082

1199081

1199082

1199082


119908119895


119908119899

119908119894

1199081

119908119894

1199082

119908119894

119908119895

119908119894

119908119899

119908119899

1199081

119908119899

1199082


119908119895


119908119899

]]]]]]]]]]]]]]]]]

]119899times119899

[[[[[[[[[

[

1199081

1199082

119908119895

119908119899

]]]]]]]]]

]119899times1

= 119899

[[[[[[[[[

[

1199081

1199082

119908119895

119908119899

]]]]]]]]]

]

= 119899119908

(9)

Because 119886119894119895is the subjective ratings given by the decision

maker there must be a distance between it and the actualvalues 119908

119894119908119895 Thus 119861119908 = 119899119908 cannot be calculated directly

Therefore Saaty suggested using the maximum eigenvalue120582max = (1119899)(119908

1015840

11199081+ 1199081015840

21199082+ sdot sdot sdot + 119908

1015840

119899119908119899) of the solution

of matrix 119861 to replace 119899 then

119861119908 = 120582max119908 (10)

By this method one can obtain the characteristic vectorreferred to as the priority vector Besides Saaty suggestedthe consistency index (CI = (120582max minus 119899)(119899 minus 1)) and theconsistency rate (CR = CIRI) to test the consistency of theintuitive judgment In general it is satisfactory and acceptedif the value of CI is about 01 and the value of CR is less than01

33 Proposed Hybrid Fuzzy AHP Approach The proposedhybrid fuzzy AHP approach to solving both quantitativedata and qualitative ratings simultaneously in process of thelocation selection is introduced in this sectionThe proposedhybrid fuzzy AHP approach involves 11 steps shown asfollows

Step 1 Construct a hierarchical analysis structure in Table 3These criteria in the hierarchical analysis structure can bedivided into two categories objective and subjective criteriaThe objective criteria are defined in monetary or quantitativeterms The subjective criteria are defined in linguistic termsrepresented by fuzzy numbers

Step 2 Introduce linguistic variables for importance weightof criteria Terms of linguistic variables for importanceweight of criteria could be called ldquoequally importantrdquoldquoweakly importantrdquo ldquostrongly importantrdquo ldquodemonstrablyimportantrdquo ldquoabsolutely importantrdquo and so forth Theselinguistic variables can be expressed in fuzzy numbers suchas ldquoequally importantrdquo = (1 1 1) ldquoweakly importantrdquo =(2 3 4) ldquostrongly importantrdquo = (4 5 6) ldquodemonstrablyimportantrdquo = (6 7 8) and ldquoabsolutely importantrdquo = (9 9 9)Their reciprocals are considered as ldquoweakly unimportantrdquo =(14 13 12) ldquostrongly unimportantrdquo= (16 15 14)ldquodemonstrably unimportantrdquo = (18 17 16) and ldquoabso-lutely unimportantrdquo= (19 19 19)

Step 3 Introduce linguistic variables for ratings of alternativelocations Terms of linguistic variables for ratings of alter-native locations could be called ldquovery poorrdquo ldquopoorrdquo ldquofairrdquoldquogoodrdquo ldquovery goodrdquo and so forth These linguistic variablescan be expressed in fuzzy numbers such as ldquovery poorrdquo =(00 10 20) ldquopoorrdquo = (10 20 30) ldquofair = (20 30 40)rdquoldquogoodrdquo = (30 40 50) ldquovery goodrdquo = (50 50 50) and soforth

Step 4 Determine the importance weights of criteria by thedecision maker Assume there areN candidate locations (119860

1

1198602 119860119899 119860

119873) 119868 evaluation criteria (119862

1 1198622 119862119894 119862

119868)

and J subcriteria (1198621198941 1198621198942 119862119894119895 119862

119894119869) under criteria i where

1 le 119899 le 119873 1 le 119894 le 119868 1 le 119895 le 119869 119894= (119888119894 119886119894 119887119894) and

119894119895=

(119888119894119895 119886119894119895 119887119894119895) are the fuzzy importance weights given by the

decision maker to criteria 119862119894and subcriteria 119862

119894119895 respectively

Step 5 Defuzzify the weights of criteria and subcriteriaThencalculate the normalized weights According to (6) proposedby Chou [31] we can obtain the representation of fuzzynumbers

119894and

119894119895as follows

119875 (119894) =

1

6(119888119894+ 4119886119894+ 119887119894)


Table 2 Comparative importance scale of criteria

Scale Definition Description(1 1 1) Equally important EI The importance of both comparative alternatives is equal(1 2 3) Intermediate values IV Need to compromise between EI and WI(2 3 4) Weakly important WI Experience and judgment weakly tend to prefer one alternative(3 4 5) Intermediate values IV Need to compromise between WI and SI(4 5 6) Strongly important SI Experience and judgment strongly tend to prefer one alternative(5 6 7) Intermediate values IV Need to compromise between SI and DI(6 7 8) Demonstrably important DI Experience and judgment demonstrably tend to prefer one alternative(7 8 9) Intermediate values IV Need to compromise between DI and AI(9 9 9) Absolutely important AI Experience and judgment absolutely tend to prefer one alternative

Table 3 A hierarchical analysis structure

Criteria and subcriteria Weight RatingGeographical condition (C1) 01527

Closeness to the importexport area (C11) 03333 (50 50 50)Proximity of the feeder port (C12) 01111 (42 42 42)Closeness to main navigation route (C13) 01111 (50 50 50)Frequency of ship calls (C14) 01111 (46 48 50)Delivery time (C15) 03333 (30 40 50)

Cost (C2) 04394Transportation cost (C21) 03543 (20 30 40)Operation cost (C22) 01921 (20 30 40)Land cost (C23) 01921 (20 30 40)Labor cost (C24) 01921 (20 30 40)Port charge (C25) 00694 (10 10 10)

Economy (C3) 00824Volume of import cargoes (C31) 02607 (44 46 46)Volume of export cargoes (C32) 01720 (42 44 46)Volume of transshipment cargoes (C33) 01976 (49 49 50)Economic growth (C34) 01720 (50 50 50)Trade variables (C35) 01976 (30 40 50)

Government (C4) 00757Private ownership of enterprise (C41) 01131 (50 50 50)Efficiency of customs (C42) 03055 (50 50 50)Efficiency of government department (C43) 02453 (50 50 50)Type of cooperation of enterprise and government (C44) 01226 (30 40 50)Political stability (C45) 02135 (30 40 50)

Investment conditions (C5) 00785Tax break and preferential treatment (C51) 02500 (20 30 40)Law on investment restrictions (C52) 02500 (50 50 50)Social stability (C53) 01250 (30 40 50)Land availability and expansion possibility (C54) 02500 (00 10 20)Labor quality (C55) 01250 (50 50 50)

Infrastructure and efficiency (C6) 01714Port facilities (C61) 01057 (50 50 50)Loading and discharging facilities (C62) 02164 (49 49 50)Intermodal link (C63) 03096 (30 40 50)Cargo handling efficiency (C64) 02043 (47 49 50)Computer information system (C65) 01640 (30 40 50)


119875 (119894119895) =

1

6(119888119894119895+ 4119886119894119895+ 119887119894119895)

(11)

The normalized weights of criteria 119862119894and subcriteria 119862

119894119895are

given by

119882119894=

119875 (119894)

sum119868

119894=1119875 (119894)

119882119894119895=

119875 (119894119895)

sum119869

119895=1119875 (119894119895)

(12)

where sum119868119894=1119882119894= 1 sum119869

119895=1119882119894119895= 1

The weight vector is therefore formed as follows

119882 = [1198821times119882111198821times11988212 119882

1times1198821119895 119882

119894times1198821198941

119882119894times1198821198942 119882

119894times119882119894119895 119882

119868times1198821198681

119882119868times1198821198682 119882

119868times119882119868119869]

= [119882111119882112 119882

11119895 119882

11989411989411198821198941198942 119882

119894119894119895

11988211986811986811198821198681198682 119882

119868119868119869]

(13)

Step 6 Calculate the maximum eigenvalue (120582max ) the con-sistency index (CI) and the consistency rate (CR) for AHPmodel to test the consistency of the intuitive judgment

Step 7 The decision maker assesses alternatives under sub-jective criteria Let

119894119895119899= (119888119894119895119899 119886119894119895119899 119887119894119895119899) be the fuzzy ratings

given by the decision maker to alternative 119860119899under subjec-

tive subcriteria 119862119894119895

Step 8 Assess alternatives under objective criteria Let 119900119894119895119899=

(119888119900

119894119895119899 119886119900

119894119895119899 119887119900

119894119895119899) be the fuzzy quantity given to alternative A

119899

under objective sub-criteria C119894119895 The objective criteria are

determined in various units and must be transformed intodimensionless indices (or ratings) to ensure compatibilitywith the linguistic ratings of subjective criteria The alterna-tive with the minimum cost (or maximum benefit) shouldhave the highest rating By (14) and (15) we can transformfuzzy quantities for objective subcriteria into fuzzy ratings

119894119895119899=

119900

119894119895119899

max119894119887119900

119894119895119899

times 5 (14)

where max119894119887119900

119894119895119899 gt 0 and

119894119895119899denotes the transformed fuzzy

rating of objective fuzzy benefit 119900119894119895119899 119894119895119899

becomes largerwhen objective fuzzy benefit 119900

119894119895119899is larger

119894119895119899=

min119894119888119900

119894119895119899

119900

119894119895119899

times 5 (15)

where min119894119888119900

119894119895119899 gt 0 and


rating of objective fuzzy cost 119900119894119895119899 119894119895119899

becomes smaller whenobjective fuzzy cost 119900

119894119895119899is larger

Step 9 Construct a fuzzy rating matrix based on fuzzyratingsThe fuzzy ratingmatrixM can be concisely expressedin matrix format

119872 =[[[

[

111

121

sdot sdot sdot 1198681198691

112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]

]

(16)

Step 10 Obtain the total fuzzy rating () based on the fuzzyrating matrix (119872) and weight vector (119882)

=

[[[[

[

111

121


112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]]

]

otimes

[[[[

[

119882111

119882112

119882119868119868119869

]]]]

]

=

[[[[

[

1

2

119873

]]]]

]

(17)

Step 11 Defuzzify the total fuzzy rating by (6) and then rankalternatives according to their total crisp ratings Finally wecan select easily the best alternative with the maximum totalcrisp ratings

119875 (119899) =

1

6(119888119899+ 4119886119899+ 119887119899) (18)

4 A Case Study

In this section the proposed hybrid fuzzy AHP approach isapplied to the location choice of international distributioncenters in the global logistics of the multinational corpora-tion A Taiwanese multinational corporation plans to selectan appropriate location of international distribution center atthe international transshipment port After initial screeningthree alternative port locations including the port 119860

1 the

port 1198602 and the port 119860

3are selected for further evaluation

The procedures for evaluation are shown as follows

Step 1 Constructing a hierarchical analysis structure isshown in Table 3 There are 6 criteria and 30 subcriteriain the hierarchical analysis structure summarized by Chou[19] These criteria in the hierarchical analysis structurecan be divided into two categories objective and subjectivecriteriaThe objective criteria include proximity of the feederport (119862

12) frequency of ship calls (119862

14) port charge (119862

25)

volumes of import containers (11986231) volumes of export

containers (11986232) volumes of transshipment containers (119862

33)


Table4Survey

dataforfuzzy

comparativ

eweightsfore

achcriterio

n

Criteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Cr

iteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 1geographical

XC 2

cost

C 1geographical

XC 3

econo

my

C 1geographical

XC 4

governm

ent

C 1geographical

XC 5

investm

ent

C 1geographical

XC 6

infrastr

ucture

andeffi

ciency

C 2cost

XC 3

econo

my

C 2cost

XC 4

governm

ent

C 2cost

XC 5

investm

ent

C 2cost

XC 6

infrastr

ucture

andeffi

ciency

C 3econo

my

XC 4

governm

ent

C 3econo

my

XC 5

investm

ent

C 3econo

my

XC 6

infrastr

ucture

andeffi

ciency

C 4governm

ent

XC 5

investm

ent

C 4governm

ent

XC 6

infrastr

ucture

andeffi

ciency

C 5investm

ent

XC 6

infrastr

ucture

andeffi

ciency


Table5Survey

dataforfuzzy

comparativ

eweightsfore

achsubcriterion

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 11impexparea

XC 1

2feeder

port

C 11impexparea

XC 1

3mainroute

C 11impexparea

XC 1

4fre

quency

C 11impexparea

XC 1

5delivery

C 12feeder

port

XC 1

3mainroute

C 12feeder

port

XC 1

4fre

quency

C 12feeder

port

XC 1

5delivery

C 13mainroute

XC 1

4fre

quency

C 13mainroute

XC 1

5delivery

C 14fre

quency

XC 1

5delivery

C 21transportcost

XC 2

2op

erationcost

C 21transportcost

XC 2

3land

cost

C 21transportcost

XC 2

4labo

rcost

C 21transportcost

XC 2

5po

rtcharge

C 22op

erationcost

XC 2

3land

cost

C 22op

erationcost

XC 2

4labo

rcost

C 22op

erationcost

XC 2

5po

rtcharge

C 23land

cost

XC 2

4labo

rcost

C 23land

cost

XC 2

5po

rtcharge

C 24labo

rcost

XC 2

5po

rtcharge

C 31volof

impo

rtX

C 32volof

expo

rtC 3

1volof

impo

rtX

C 33volof

tranship

C 31volof

impo

rtX

C 34econ

omy

C 31volof

impo

rtX

C 35tradev

ariable

C 32volof

expo

rtX

C 33volof

tranship

C 32volof

expo

rtX

C 34econ

omy

C 32volof

expo

rtX

C 35tradev

ariable

C 33volof

tranship

XC 3

4econ

omy

C 33volof

tranship

XC 3

5tradev

ariable

C 34econ

omy

XC 3

5tradev

ariable

C 41private

XC 4

2custo

ms

C 41private

XC 4

3government

C 41private

XC 4

4coop

eration

C 41private

XC 4

5po

litical

C 42custo

ms

XC 4

3government

C 42custo

ms

XC 4

4coop

eration

C 42custo

ms

XC 4

5po

litical

C 43government

XC 4

4coop

eration

C 43government

XC 4

5po

litical

C 44coop

eration

XC 4

5po

litical

C 51taxbreak

XC 5

2law

C 51taxbreak

XC 5

3socialsta

bility

C 51taxbreak

XC 5

4expansion

C 51taxbreak

XC 5

5labo

rquality

C 52law

XC 5

3socialsta

bility

C 52law

XC 5

4expansion

C 52law

XC 5

5labo

rquality

C 53socialsta

bility

XC 5

4expansion

C 53socialsta

bility

XC 5

5labo

rquality

C 54expansion

XC 5

5labo

rquality


Table5Con

tinued

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 6

1po

rtfacilities

XC 6

2loaddisc

harge

C 61po

rtfacilities

XC 6

3mod

allin

kC 6

1po

rtfacilities

XC 6

4cargohand

leC 6

1po

rtfacilities

XC 6

5inform

ation

C 62loaddisc

harge

XC 6

3mod

allin

kC 6

2loaddisc

harge

XC 6

4cargohand

leC 6

2loaddisc

harge

XC 6

5inform

ation

C 63mod

allin

kX

C 64cargohand

leC 6

3mod

allin

kX

C 65inform

ation

C 64cargohand

leX

C 65inform

ation


Table 6 Fuzzy ratings for alternatives under objective criteria

Objective criteria Fuzzy quantity Fuzzy ratingC12 Proximity of the feeder port (nautical mile)A1 (6356 6356 6356) (42 42 42)

A2 (5401 5401 5401) (50 50 50)

A3 (7288 7288 7288) (37 37 37)

C14 Frequency of ship calls (vesselweek)A1 (415 435 455) (46 48 50)

A2 (167 177 187) (18 19 21)

A3 (186 206 226) (21 23 25)

C25 Port charge ($USTEU)A1 (328 338 348) (10 10 10)

A2 (100 110 120) (27 30 33)

A3 (65 70 75) (43 46 50)

C31 Volumes of import containers (TEU)A1 (11599000 12041000 12064000) (44 46 46)

A2 (1887381 1906255 1925318) (07 07 07)

A3 (9042000 10860000 13075000) (35 42 50)

C32 Volumes of export containers (TEU)A1 (11002000 11475000 11958000) (42 44 46)

A2 (2116017 2158338 2201505) (08 08 08)

A3 (9042000 10860000 13075000) (35 42 50)

C33 Volume of transshipment containers (TEU)A1 (10000000 10150000 10300000) (49 49 50)

A2 (5406461 5647846 5710712) (26 27 28)

A3 (300000 400000 5000000) (01 02 02)

C61 Port facilities (length of wharf m)A1 (8530 8530 8530) (50 50 50)

A2 (7453 7453 7453) (44 44 44)

A3 (8387 8387 8387) (49 49 49)

C62 Loading and discharging facilities (crane)A1 (83 84 85) (49 49 50)

A2 (66 67 68) (39 39 40)

A3 (81 82 83) (48 48 49)

C64 Cargo handling efficiency (moveh)A1 (33 34 35) (47 49 50)

A2 (31 32 33) (44 46 47)

A3 (29 30 31) (41 43 44)

Source Hong Kong Maritime Industry Council website httpwwwmicgovhkPort of Kaohsiung website httpwwwkhbgovtwPort of Shanghai website httpwwwportshanghaicomcnContainerization International YearbookThe Institute of Transportation Ministry of Transportation and Communications Taiwan

port facilities (11986261) loading and unloading facilities (119862

62)

and cargo handling efficiency (11986264)The others are subjective

criteria The objective criteria are defined in quantitativeterms (eg nautical mile $US TEU) The subjective cri-teria are defined in linguistic terms represented by fuzzynumbers

Step 2 Present the linguistic variables and fuzzy numbers forcomparative importance weights of criteria

Step 3 Present the linguistic variables and fuzzy numbers forratings of alternatives

Step 4 Determine the fuzzy comparative importanceweightsof criteria and subcriteria by the decision maker in Tables 4and 5 respectively

Step 5 Defuzzify the fuzzyweights of criteria and subcriteriaThen calculate the normalized weights in Table 3



119860119908 =

[[[[[[[[[[[[[[[[[[[[

[

11

43 3 2

1

2

4 1 4 5 4 4

1

3

1

41 2 1

1

3

1

3

1

5

1

21 1 1

1

2

1

41 1 1

1

3

21

43 1 3 1

]]]]]]]]]]]]]]]]]]]]

]

[[[[[[[

[

01527

04394

00824

00757

00785

01714

]]]]]]]

]

=

[[[[[[[

[

09793

27574

05301

05055

04799

11449

]]]]]]]

]

120582max =1

6(09793

01527+27574

04394+05301

00824+05055

00757

+04799

00785+11449

01714) = 64331

CI =120582max minus 119899

119899 minus 1=64331 minus 6

6 minus 1= 008

CR = CIRI

=008

124= 007

(19)

Step 7 The decision maker assesses alternatives under sub-jective criteria For example the fuzzy ratings given by thedecision maker to the port 119860

1under subjective subcriteria

are shown in Table 3

Step 8 Assess alternatives under objective criteria The fuzzyquantities given to alternative under objective subcriteriaare listed in Table 6 The objective fuzzy quantities aredetermined in various units (eg nautical mile $US TEU)and must be transformed into dimensionless indices (orratings) to ensure compatibility with the linguistic ratingsof subjective criteria By (14) and (15) we can transformfuzzy quantities for objective subcriteria into fuzzy ratings inTable 6

Step 9 Construct a fuzzy rating matrix based on fuzzyratings

Step 10 Obtain the total fuzzy ratings based on the fuzzyrating matrix and the weight vector

Step 11 By (6) we can defuzzify the total fuzzy ratings and thetotal crisp ratings for the port 119860

1 the port 119860

2 and the port

1198603are 372 388 and 441 respectively Finally the decision

maker of Taiwanese multinational corporation selects easilythe port 119860

3with the maximum total crisp ratings as the best

location for international distribution center in the globallogistics system

5 Conclusions

The paper proposes a new hybrid fuzzy AHP model fordealing with both objective and subjective criteria in processof decision making simultaneously The proposed hybridfuzzy AHP model is applied to solve the location choiceproblem of international distribution center in the globallogistics of multinational corporation The results show thatthe proposed new hybrid fuzzy AHPmodel is an appropriateand more efficient approach to deal with both objective andsubjective criteria in process of decision making simultane-ously The hybrid fuzzy AHP model in this paper overcomesthe disadvantages of quantitative or qualitative approachesin the previous literature The proposed hybrid fuzzy AHPapproach can not only solve the problems of location choicebut also many other decision-making problems

Acknowledgment

This research work was partially supported by the NationalScience Council of Taiwan under Grant no NSC 101-2514-S-022-001

References

[1] C C Chou J F Ding T M Chang et al ldquoOperation man-agement of port logistics in the global supply chainrdquo AdvancedMaterials Research vol 706ndash708 pp 2087ndash2090 2013

[2] S J Chen and C L Hwang Fuzzy Multiple Attribute DecisionMaking Methods and Applications vol 375 of Lecture Notesin Economics and Mathematical Systems Springer Berlin Ger-many 1992

[3] F R David Strategic Management Prentice Hall Upper SaddleRiver NJ USA 7th edition 1998

[4] HChang andWHuang ldquoApplication of a quantification SWOTanalytical methodrdquoMathematical and Computer Modelling vol43 no 1-2 pp 158ndash169 2006

[5] M Kurttila M Pesonen J Kangas and M Kajanus ldquoUtilizingthe analytic hierarchy process (AHP) in SWOT analysismdashahybrid method and its application to a forest-certification caserdquoForest Policy and Economics vol 1 no 1 pp 41ndash52 2000

[6] F R David Strategic Management Concept and Cases PrenticeHall Upper Saddle River NJ USA 8th edition 2001

[7] I Erol andW G Ferrell Jr ldquoA methodology for selection prob-lems with multiple conflicting objectives and both qualitativeand quantitative criteriardquo International Journal of ProductionEconomics vol 86 no 3 pp 187ndash199 2003

[8] L Mikhailov and P Tsvetinov ldquoEvaluation of services usinga fuzzy analytic hierarchy processrdquo Applied Soft ComputingJournal vol 5 no 1 pp 23ndash33 2004

[9] A Ronza S Carol V Espejo J A Vılchez and J ArnaldosldquoA quantitative risk analysis approach to port hydrocarbonlogisticsrdquo Journal of Hazardous Materials vol 128 no 1 pp 10ndash24 2006

[10] D Yong ldquoPlant location selection based on fuzzy TOPSISrdquoInternational Journal of Advanced Manufacturing Technologyvol 28 no 7-8 pp 839ndash844 2006

[11] S Onut and S Soner ldquoTransshipment site selection using theAHP and TOPSIS approaches under fuzzy environmentrdquoWasteManagement vol 28 no 9 pp 1552ndash1559 2008


[12] K Tahera R N Ibrahim and P B Lochert ldquoA fuzzy logicapproach for dealing with qualitative quality characteristics ofa processrdquo Expert Systems with Applications vol 34 no 4 pp2630ndash2638 2008

[13] M F Chen G H Tzeng and C G Ding ldquoCombining fuzzyAHP with MDS in identifying the preference similarity ofalternativesrdquo Applied Soft Computing Journal vol 8 no 1 pp110ndash117 2008

[14] S Y Chou Y H Chang and C Y Shen ldquoA fuzzy simpleadditive weighting system under group decision-making forfacility location selection with objectivesubjective attributesrdquoEuropean Journal ofOperational Research vol 189 no 1 pp 132ndash145 2008

[15] K L Lee and S C Lin ldquoA fuzzy quantified SWOT procedurefor environmental evaluation of an international distributioncenterrdquo Information Sciences vol 178 no 2 pp 531ndash549 2008

[16] A H I Lee W Chen and C Chang ldquoA fuzzy AHP andBSC approach for evaluating performance of IT departmentin the manufacturing industry in Taiwanrdquo Expert Systems withApplications vol 34 no 1 pp 96ndash107 2008

[17] C C Chou ldquoAn integrated quantitative and qualitativeFMCDM model for location choicesrdquo Soft Computing vol 14no 7 pp 757ndash771 2010

[18] C C Chou ldquoA fuzzy logic approach to dealing with objectivedata and subjective ratingrdquo International Journal of InnovativeComputing Information and Control vol 6 no 5 pp 2199ndash2209 2010

[19] C Chou ldquoA combined mcdm and fuzzy mcdm approach toselecting the location of the distribution center in the hub portan empirical study on Hong Kong Shanghai and KaohsiungrdquoInternational Journal of Innovative Computing Information andControl vol 6 no 7 pp 3037ndash3051 2010

[20] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[21] T L Saaty The Analytic Hierarchy Process McGraw-Hill NewYork NY USA 1980

[22] D Chang ldquoApplications of the extent analysis method on fuzzyAHPrdquo European Journal of Operational Research vol 95 no 3pp 649ndash655 1996

[23] R J Kuo S C Chi and S S Kao ldquoDecision support system forlocating convenience store through fuzzy AHPrdquo Computers andIndustrial Engineering vol 37 no 1 pp 323ndash326 1999

[24] R A Stewart SMohamed andRDaet ldquoStrategic implementa-tion of ITIS projects in construction a case studyrdquoAutomationin Construction vol 11 no 6 pp 681ndash694 2002

[25] C Kahraman D Ruan and I Dogan ldquoFuzzy group decision-making for facility location selectionrdquo Information Sciences vol157 no 1ndash4 pp 135ndash153 2003

[26] C Zhang C B Ma and J D Xu ldquoA new fuzzy MCDMmethod based on trapezoidal fuzzy AHP and hierarchical fuzzyintegralrdquo in Fuzzy Systems and Knowledge Discovery vol 3614of Lecture Notes in Computer Science pp 466ndash474 2005

[27] Y C Erensal T Oncan and M L Demircan ldquoDeterminingkey capabilities in technologymanagement using fuzzy analytichierarchy process a case study of Turkeyrdquo Information Sciencesvol 176 no 18 pp 2755ndash2770 2006

[28] F T S Chan and N Kumar ldquoGlobal supplier developmentconsidering risk factors using fuzzy extended AHP-basedapproachrdquo Omega vol 35 no 4 pp 417ndash431 2007

[29] F T Bozbura and A Beskese ldquoPrioritization of organizationalcapital measurement indicators using fuzzy AHPrdquo International

Journal of Approximate Reasoning vol 44 no 2 pp 124ndash1472007

[30] F T Bozbura A Beskese and C Kahraman ldquoPrioritizationof human capital measurement indicators using fuzzy AHPrdquoExpert Systems with Applications vol 32 no 4 pp 1100ndash11122007

[31] C C Chou ldquoThe canonical representation of multiplicationoperation on triangular fuzzy numbersrdquo Computers and Math-ematics with Applications vol 45 no 10-11 pp 1601ndash1610 2003

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Table 1 The container throughputs and the rankings for the worldrsquos top 20 container ports (unit thousand TEUs)

2010 2009 2008 2007 2006 Name of port 2010 2009 2008 2007 20061 2 2 2 3 Shanghai 29069 25002 27780 26150 217202 1 1 1 1 Singapore 28430 25866 29918 27935 247923 3 3 3 2 Hong Kong 23611 20925 24248 23881 235394 4 4 4 4 Shenzhen 22509 18250 21400 21090 184685 5 5 5 5 Busan 14180 11980 13452 13261 120386 8 8 11 13 Ningbo 13146 10502 10933 9360 71407 6 7 12 15 Guangzhou 12545 11190 11001 9200 66568 9 10 10 11 Qingdao 12012 10260 10020 9462 77029 7 6 6 8 Dubai 11613 11150 11830 11000 892310 10 9 7 7 Rotterdam 11145 9800 10784 10791 969011 11 14 17 17 Tianjin 10086 8700 8500 7102 595012 12 12 8 6 Kaohsiung 9181 8581 9676 10256 977413 13 13 14 14 Antwerp 8483 7309 8663 8176 701814 14 15 16 16 Klang 8146 7300 7973 7118 632615 15 11 9 9 Hamburg 7900 7010 9737 9890 886116 16 16 13 10 Los Angeles 7831 6748 7849 8355 846917 17 18 18 19 Tanjung Pelepas 6603 6000 5600 5500 477018 18 17 15 12 Long Beach 6263 5067 6487 7312 728919 19 22 22 22 Xiamen 5824 4680 5034 4627 401820 20 21 21 21 Laem Chabang 5640 4640 5130 4640 4123Source Chou et al [1]

Distripark in the port of Singapore Therefore it is veryimportant for the shipping companies and the multinationalcorporations to evaluate the environment among these majorinternational logistics centers in different nations in orderto design and implement an appropriate global logisticssystem It is also a complexmultiple-criteria decision-making(MCDM) problem under uncertain environment AHP isan appropriate approach to solve complex multiple-criteriadecision-making problem Fuzzy sets theory method hasbeen widely applied to the uncertain decision-making prob-lem in the real world Thus this paper combines AHP andfuzzy sets theory and then proposes a new hybrid fuzzy AHPmodel for the location choice of international logistics centerswithin the international ports from the perspective of multi-nation corporations

2 Literature Review

21 Environmental Evaluation Approaches Environmentevaluation approaches including the resource-based view(RBV) traditional strength-weakness-opportunity-threat(SWOT) and quantitative SWOT such as the external factorevaluation matrix (EFE) internal factor evaluation matrix(IFE) and competitive profile matrix (CPM) have beenwidely used The traditional SWOT analytical method iscommonly applied to marketing strategy analysis [2ndash4] TheSWOT analytical method is able to help the decision makerof the enterprises evaluate qualitatively their competitivenessand can be used as a foundation of the development ofstrategies [5] The quantitative SWOT such as externalfactor evaluation matrix (EFE) internal factor evaluationmatrix (IFE) and competitive profile matrix (CPM) aim

at analyzing statistical data differing from the traditionalSWOT analytical method [3 6] The disadvantage of theabove approaches is that they cannot evaluate the qualitativeand quantitative criteria simultaneously Therefore thispaper proposes a new hybrid approach which integratesAHPmethod to carry out a complete evaluation of qualitativeand quantitative criteria simultaneously and to evaluate thecompetitive environmental relationships between the severalinternational distribution center locations within the portsin the asian region

Erol and Ferrell Jr [7] use fuzzy Quality Function De-ployment (QFD) to convert qualitative information intoquantitative parameters and then combine this data withother quantitative data to multiobjective mathematical pro-gramming model Mikhailov and Tsvetinov [8] proposea fuzzy AHP approach for tackling the uncertainty andimprecision of the service evaluation process Ronza et al[9] present a quantitative risk analysis approach to porthydrocarbon logistics Because risk is an uncertain criterionit is not easy for a decision maker to measure exactly thevalue of risk Chang and Huang [4] present a quantita-tive strengthweaknessopportunitythreat (SWOT) analysismethod for assessing the competing strengths of majorports in East Asia Yong [10] uses a fuzzy TOPSIS modelto solve the problem of plant location choice Onut andSoner [11] propose an AHPTOPSIS approach for solvingtransshipment site selection problem under fuzzy environ-ment Tahera et al [12] develop a fuzzy logic approach fordealing with qualitative quality characteristics of a processChen et al [13] combine fuzzy AHP with MultidimensionScaling (MDS) in identifying the preference similarity ofalternatives Chou et al [14] present a new fuzzy multiple


Lminus1A1(h)c1 b1

h

a1 d1

LA1(x)RA1(x)

Rminus1A1(h)

A1

1







3 Methodology





1198911198601(119909) =

(119909 minus 1198881)

(1198861minus 1198881) 119888

1le 119909 le 119886

1

1 1198861le 119909 le 119887

1

(119909 minus 1198891)

(1198871minus 1198891) 119887

1le 119909 le 119889

1

0 otherwise

(1)

Suppose 1198601= (1198881 1198861 1198871 1198891) and 119860

2= (1198882 1198862 1198872 1198892) are



2

1198601oplus 1198602= (1198881+ 1198882 1198861+ 1198862 1198871+ 1198872 1198891+ 1198892) (2)


2



119903 otimes 1198601= (119903119888

1 1199031198861 1199031198871 1199031198891) (4)


1198601

119903= (

1198881

1199031198861

1199031198871

1199031198891

119903) (5)


119875 (119884) =1

6(119888 + 4119886 + 119887) (6)





119894 119862

119895 119862

119899


1 119882

119894 119882

119895 119882

119899 on some



119895 In


119861 =

[[[[[[[

[

1198861111988612sdot sdot sdot 119886


1119899

11988611989411198861198942sdot sdot sdot 119886

119894119895sdot sdot sdot 119886

119894119899

11988611989911198861198992sdot sdot sdot 119886

119899119895sdot sdot sdot 119886

119899119899

]]]]]]]

]119899times119899

(7)

where 119886119895119894= 1119886




119886119894119895=119908119894

119908119895

119894 119895 = 1 2 119899 (8)


1 1199082 119908

119899)119879 one gets

119861119908 =

[[[[[[[[[[[[[[[[[

[

1199081

1199081

1199081

1199082


119908119895


119908119899

1199082

1199081

1199082

1199082


119908119895


119908119899

119908119894

1199081

119908119894

1199082

119908119894

119908119895

119908119894

119908119899

119908119899

1199081

119908119899

1199082


119908119895


119908119899

]]]]]]]]]]]]]]]]]

]119899times119899

[[[[[[[[[

[

1199081

1199082

119908119895

119908119899

]]]]]]]]]

]119899times1

= 119899

[[[[[[[[[

[

1199081

1199082

119908119895

119908119899

]]]]]]]]]

]

= 119899119908

(9)





1015840

11199081+ 1199081015840

21199082+ sdot sdot sdot + 119908

1015840

119899119908119899) of the solution


119861119908 = 120582max119908 (10)







1

1198602 119860119899 119860


1 1198622 119862119894 119862

119868)




119894119895=





119894and


119875 (119894) =

1

6(119888119894+ 4119886119894+ 119887119894)













119875 (119894119895) =

1

6(119888119894119895+ 4119886119894119895+ 119887119894119895)

(11)


119894119895are

given by

119882119894=

119875 (119894)

sum119868

119894=1119875 (119894)

119882119894119895=

119875 (119894119895)

sum119869

119895=1119875 (119894119895)

(12)

where sum119868119894=1119882119894= 1 sum119869

119895=1119882119894119895= 1


119882 = [1198821times119882111198821times11988212 119882

1times1198821119895 119882

119894times1198821198941

119882119894times1198821198942 119882

119894times119882119894119895 119882

119868times1198821198681

119882119868times1198821198682 119882

119868times119882119868119869]

= [119882111119882112 119882

11119895 119882

11989411989411198821198941198942 119882

119894119894119895

11988211986811986811198821198681198682 119882

119868119868119869]

(13)







(119888119900

119894119895119899 119886119900

119894119895119899 119887119900


119899



119894119895119899=

119900

119894119895119899

max119894119887119900

119894119895119899

times 5 (14)

where max119894119887119900

119894119895119899 gt 0 and




119894119895119899is larger

119894119895119899=

min119894119888119900

119894119895119899

119900

119894119895119899

times 5 (15)

where min119894119888119900

119894119895119899 gt 0 and




119894119895119899is larger


119872 =[[[

[

111

121


112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]

]

(16)


=

[[[[

[

111

121


112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]]

]

otimes

[[[[

[

119882111

119882112

119882119868119868119869

]]]]

]

=

[[[[

[

1

2

119873

]]]]

]

(17)


119875 (119899) =

1

6(119888119899+ 4119886119899+ 119887119899) (18)

4 A Case Study


1 the







25)



33)


Table4Survey

dataforfuzzy

comparativ

eweightsfore

achcriterio

n

Criteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Cr

iteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 1geographical

XC 2

cost

C 1geographical

XC 3

econo

my

C 1geographical

XC 4

governm

ent

C 1geographical

XC 5

investm

ent

C 1geographical

XC 6

infrastr

ucture

andeffi

ciency

C 2cost

XC 3

econo

my

C 2cost

XC 4

governm

ent

C 2cost

XC 5

investm

ent

C 2cost

XC 6

infrastr

ucture

andeffi

ciency

C 3econo

my

XC 4

governm

ent

C 3econo

my

XC 5

investm

ent

C 3econo

my

XC 6

infrastr

ucture

andeffi

ciency

C 4governm

ent

XC 5

investm

ent

C 4governm

ent

XC 6

infrastr

ucture

andeffi

ciency

C 5investm

ent

XC 6

infrastr

ucture

andeffi

ciency


Table5Survey

dataforfuzzy

comparativ

eweightsfore

achsubcriterion

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 11impexparea

XC 1

2feeder

port

C 11impexparea

XC 1

3mainroute

C 11impexparea

XC 1

4fre

quency

C 11impexparea

XC 1

5delivery

C 12feeder

port

XC 1

3mainroute

C 12feeder

port

XC 1

4fre

quency

C 12feeder

port

XC 1

5delivery

C 13mainroute

XC 1

4fre

quency

C 13mainroute

XC 1

5delivery

C 14fre

quency

XC 1

5delivery

C 21transportcost

XC 2

2op

erationcost

C 21transportcost

XC 2

3land

cost

C 21transportcost

XC 2

4labo

rcost

C 21transportcost

XC 2

5po

rtcharge

C 22op

erationcost

XC 2

3land

cost

C 22op

erationcost

XC 2

4labo

rcost

C 22op

erationcost

XC 2

5po

rtcharge

C 23land

cost

XC 2

4labo

rcost

C 23land

cost

XC 2

5po

rtcharge

C 24labo

rcost

XC 2

5po

rtcharge

C 31volof

impo

rtX

C 32volof

expo

rtC 3

1volof

impo

rtX

C 33volof

tranship

C 31volof

impo

rtX

C 34econ

omy

C 31volof

impo

rtX

C 35tradev

ariable

C 32volof

expo

rtX

C 33volof

tranship

C 32volof

expo

rtX

C 34econ

omy

C 32volof

expo

rtX

C 35tradev

ariable

C 33volof

tranship

XC 3

4econ

omy

C 33volof

tranship

XC 3

5tradev

ariable

C 34econ

omy

XC 3

5tradev

ariable

C 41private

XC 4

2custo

ms

C 41private

XC 4

3government

C 41private

XC 4

4coop

eration

C 41private

XC 4

5po

litical

C 42custo

ms

XC 4

3government

C 42custo

ms

XC 4

4coop

eration

C 42custo

ms

XC 4

5po

litical

C 43government

XC 4

4coop

eration

C 43government

XC 4

5po

litical

C 44coop

eration

XC 4

5po

litical

C 51taxbreak

XC 5

2law

C 51taxbreak

XC 5

3socialsta

bility

C 51taxbreak

XC 5

4expansion

C 51taxbreak

XC 5

5labo

rquality

C 52law

XC 5

3socialsta

bility

C 52law

XC 5

4expansion

C 52law

XC 5

5labo

rquality

C 53socialsta

bility

XC 5

4expansion

C 53socialsta

bility

XC 5

5labo

rquality

C 54expansion

XC 5

5labo

rquality


Table5Con

tinued

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 6

1po

rtfacilities

XC 6

2loaddisc

harge

C 61po

rtfacilities

XC 6

3mod

allin

kC 6

1po

rtfacilities

XC 6

4cargohand

leC 6

1po

rtfacilities

XC 6

5inform

ation

C 62loaddisc

harge

XC 6

3mod

allin

kC 6

2loaddisc

harge

XC 6

4cargohand

leC 6

2loaddisc

harge

XC 6

5inform

ation

C 63mod

allin

kX

C 64cargohand

leC 6

3mod

allin

kX

C 65inform

ation

C 64cargohand

leX

C 65inform

ation




A2 (5401 5401 5401) (50 50 50)

A3 (7288 7288 7288) (37 37 37)


A2 (167 177 187) (18 19 21)

A3 (186 206 226) (21 23 25)


A2 (100 110 120) (27 30 33)

A3 (65 70 75) (43 46 50)


A2 (1887381 1906255 1925318) (07 07 07)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (2116017 2158338 2201505) (08 08 08)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (5406461 5647846 5710712) (26 27 28)

A3 (300000 400000 5000000) (01 02 02)


A2 (7453 7453 7453) (44 44 44)

A3 (8387 8387 8387) (49 49 49)


A2 (66 67 68) (39 39 40)

A3 (81 82 83) (48 48 49)


A2 (31 32 33) (44 46 47)

A3 (29 30 31) (41 43 44)



62)









119860119908 =

[[[[[[[[[[[[[[[[[[[[

[

11

43 3 2

1

2

4 1 4 5 4 4

1

3

1

41 2 1

1

3

1

3

1

5

1

21 1 1

1

2

1

41 1 1

1

3

21

43 1 3 1

]]]]]]]]]]]]]]]]]]]]

]

[[[[[[[

[

01527

04394

00824

00757

00785

01714

]]]]]]]

]

=

[[[[[[[

[

09793

27574

05301

05055

04799

11449

]]]]]]]

]

120582max =1

6(09793

01527+27574

04394+05301

00824+05055

00757

+04799

00785+11449

01714) = 64331

CI =120582max minus 119899

119899 minus 1=64331 minus 6

6 minus 1= 008

CR = CIRI

=008

124= 007

(19)








1 the port 119860

2 and the port





5 Conclusions


Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Lminus1A1(h)c1 b1

h

a1 d1

LA1(x)RA1(x)

Rminus1A1(h)

A1

1







3 Methodology





1198911198601(119909) =

(119909 minus 1198881)

(1198861minus 1198881) 119888

1le 119909 le 119886

1

1 1198861le 119909 le 119887

1

(119909 minus 1198891)

(1198871minus 1198891) 119887

1le 119909 le 119889

1

0 otherwise

(1)

Suppose 1198601= (1198881 1198861 1198871 1198891) and 119860

2= (1198882 1198862 1198872 1198892) are



2

1198601oplus 1198602= (1198881+ 1198882 1198861+ 1198862 1198871+ 1198872 1198891+ 1198892) (2)


2



119903 otimes 1198601= (119903119888

1 1199031198861 1199031198871 1199031198891) (4)


1198601

119903= (

1198881

1199031198861

1199031198871

1199031198891

119903) (5)


119875 (119884) =1

6(119888 + 4119886 + 119887) (6)





119894 119862

119895 119862

119899


1 119882

119894 119882

119895 119882

119899 on some



119895 In


119861 =

[[[[[[[

[

1198861111988612sdot sdot sdot 119886


1119899

11988611989411198861198942sdot sdot sdot 119886

119894119895sdot sdot sdot 119886

119894119899

11988611989911198861198992sdot sdot sdot 119886

119899119895sdot sdot sdot 119886

119899119899

]]]]]]]

]119899times119899

(7)

where 119886119895119894= 1119886




119886119894119895=119908119894

119908119895

119894 119895 = 1 2 119899 (8)


1 1199082 119908

119899)119879 one gets

119861119908 =

[[[[[[[[[[[[[[[[[

[

1199081

1199081

1199081

1199082


119908119895


119908119899

1199082

1199081

1199082

1199082


119908119895


119908119899

119908119894

1199081

119908119894

1199082

119908119894

119908119895

119908119894

119908119899

119908119899

1199081

119908119899

1199082


119908119895


119908119899

]]]]]]]]]]]]]]]]]

]119899times119899

[[[[[[[[[

[

1199081

1199082

119908119895

119908119899

]]]]]]]]]

]119899times1

= 119899

[[[[[[[[[

[

1199081

1199082

119908119895

119908119899

]]]]]]]]]

]

= 119899119908

(9)





1015840

11199081+ 1199081015840

21199082+ sdot sdot sdot + 119908

1015840

119899119908119899) of the solution


119861119908 = 120582max119908 (10)







1

1198602 119860119899 119860


1 1198622 119862119894 119862

119868)




119894119895=





119894and


119875 (119894) =

1

6(119888119894+ 4119886119894+ 119887119894)













119875 (119894119895) =

1

6(119888119894119895+ 4119886119894119895+ 119887119894119895)

(11)


119894119895are

given by

119882119894=

119875 (119894)

sum119868

119894=1119875 (119894)

119882119894119895=

119875 (119894119895)

sum119869

119895=1119875 (119894119895)

(12)

where sum119868119894=1119882119894= 1 sum119869

119895=1119882119894119895= 1


119882 = [1198821times119882111198821times11988212 119882

1times1198821119895 119882

119894times1198821198941

119882119894times1198821198942 119882

119894times119882119894119895 119882

119868times1198821198681

119882119868times1198821198682 119882

119868times119882119868119869]

= [119882111119882112 119882

11119895 119882

11989411989411198821198941198942 119882

119894119894119895

11988211986811986811198821198681198682 119882

119868119868119869]

(13)







(119888119900

119894119895119899 119886119900

119894119895119899 119887119900


119899



119894119895119899=

119900

119894119895119899

max119894119887119900

119894119895119899

times 5 (14)

where max119894119887119900

119894119895119899 gt 0 and




119894119895119899is larger

119894119895119899=

min119894119888119900

119894119895119899

119900

119894119895119899

times 5 (15)

where min119894119888119900

119894119895119899 gt 0 and




119894119895119899is larger


119872 =[[[

[

111

121


112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]

]

(16)


=

[[[[

[

111

121


112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]]

]

otimes

[[[[

[

119882111

119882112

119882119868119868119869

]]]]

]

=

[[[[

[

1

2

119873

]]]]

]

(17)


119875 (119899) =

1

6(119888119899+ 4119886119899+ 119887119899) (18)

4 A Case Study


1 the







25)



33)


Table4Survey

dataforfuzzy

comparativ

eweightsfore

achcriterio

n

Criteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Cr

iteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 1geographical

XC 2

cost

C 1geographical

XC 3

econo

my

C 1geographical

XC 4

governm

ent

C 1geographical

XC 5

investm

ent

C 1geographical

XC 6

infrastr

ucture

andeffi

ciency

C 2cost

XC 3

econo

my

C 2cost

XC 4

governm

ent

C 2cost

XC 5

investm

ent

C 2cost

XC 6

infrastr

ucture

andeffi

ciency

C 3econo

my

XC 4

governm

ent

C 3econo

my

XC 5

investm

ent

C 3econo

my

XC 6

infrastr

ucture

andeffi

ciency

C 4governm

ent

XC 5

investm

ent

C 4governm

ent

XC 6

infrastr

ucture

andeffi

ciency

C 5investm

ent

XC 6

infrastr

ucture

andeffi

ciency


Table5Survey

dataforfuzzy

comparativ

eweightsfore

achsubcriterion

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 11impexparea

XC 1

2feeder

port

C 11impexparea

XC 1

3mainroute

C 11impexparea

XC 1

4fre

quency

C 11impexparea

XC 1

5delivery

C 12feeder

port

XC 1

3mainroute

C 12feeder

port

XC 1

4fre

quency

C 12feeder

port

XC 1

5delivery

C 13mainroute

XC 1

4fre

quency

C 13mainroute

XC 1

5delivery

C 14fre

quency

XC 1

5delivery

C 21transportcost

XC 2

2op

erationcost

C 21transportcost

XC 2

3land

cost

C 21transportcost

XC 2

4labo

rcost

C 21transportcost

XC 2

5po

rtcharge

C 22op

erationcost

XC 2

3land

cost

C 22op

erationcost

XC 2

4labo

rcost

C 22op

erationcost

XC 2

5po

rtcharge

C 23land

cost

XC 2

4labo

rcost

C 23land

cost

XC 2

5po

rtcharge

C 24labo

rcost

XC 2

5po

rtcharge

C 31volof

impo

rtX

C 32volof

expo

rtC 3

1volof

impo

rtX

C 33volof

tranship

C 31volof

impo

rtX

C 34econ

omy

C 31volof

impo

rtX

C 35tradev

ariable

C 32volof

expo

rtX

C 33volof

tranship

C 32volof

expo

rtX

C 34econ

omy

C 32volof

expo

rtX

C 35tradev

ariable

C 33volof

tranship

XC 3

4econ

omy

C 33volof

tranship

XC 3

5tradev

ariable

C 34econ

omy

XC 3

5tradev

ariable

C 41private

XC 4

2custo

ms

C 41private

XC 4

3government

C 41private

XC 4

4coop

eration

C 41private

XC 4

5po

litical

C 42custo

ms

XC 4

3government

C 42custo

ms

XC 4

4coop

eration

C 42custo

ms

XC 4

5po

litical

C 43government

XC 4

4coop

eration

C 43government

XC 4

5po

litical

C 44coop

eration

XC 4

5po

litical

C 51taxbreak

XC 5

2law

C 51taxbreak

XC 5

3socialsta

bility

C 51taxbreak

XC 5

4expansion

C 51taxbreak

XC 5

5labo

rquality

C 52law

XC 5

3socialsta

bility

C 52law

XC 5

4expansion

C 52law

XC 5

5labo

rquality

C 53socialsta

bility

XC 5

4expansion

C 53socialsta

bility

XC 5

5labo

rquality

C 54expansion

XC 5

5labo

rquality


Table5Con

tinued

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 6

1po

rtfacilities

XC 6

2loaddisc

harge

C 61po

rtfacilities

XC 6

3mod

allin

kC 6

1po

rtfacilities

XC 6

4cargohand

leC 6

1po

rtfacilities

XC 6

5inform

ation

C 62loaddisc

harge

XC 6

3mod

allin

kC 6

2loaddisc

harge

XC 6

4cargohand

leC 6

2loaddisc

harge

XC 6

5inform

ation

C 63mod

allin

kX

C 64cargohand

leC 6

3mod

allin

kX

C 65inform

ation

C 64cargohand

leX

C 65inform

ation




A2 (5401 5401 5401) (50 50 50)

A3 (7288 7288 7288) (37 37 37)


A2 (167 177 187) (18 19 21)

A3 (186 206 226) (21 23 25)


A2 (100 110 120) (27 30 33)

A3 (65 70 75) (43 46 50)


A2 (1887381 1906255 1925318) (07 07 07)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (2116017 2158338 2201505) (08 08 08)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (5406461 5647846 5710712) (26 27 28)

A3 (300000 400000 5000000) (01 02 02)


A2 (7453 7453 7453) (44 44 44)

A3 (8387 8387 8387) (49 49 49)


A2 (66 67 68) (39 39 40)

A3 (81 82 83) (48 48 49)


A2 (31 32 33) (44 46 47)

A3 (29 30 31) (41 43 44)



62)









119860119908 =

[[[[[[[[[[[[[[[[[[[[

[

11

43 3 2

1

2

4 1 4 5 4 4

1

3

1

41 2 1

1

3

1

3

1

5

1

21 1 1

1

2

1

41 1 1

1

3

21

43 1 3 1

]]]]]]]]]]]]]]]]]]]]

]

[[[[[[[

[

01527

04394

00824

00757

00785

01714

]]]]]]]

]

=

[[[[[[[

[

09793

27574

05301

05055

04799

11449

]]]]]]]

]

120582max =1

6(09793

01527+27574

04394+05301

00824+05055

00757

+04799

00785+11449

01714) = 64331

CI =120582max minus 119899

119899 minus 1=64331 minus 6

6 minus 1= 008

CR = CIRI

=008

124= 007

(19)








1 the port 119860

2 and the port





5 Conclusions


Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












119894 119862

119895 119862

119899


1 119882

119894 119882

119895 119882

119899 on some



119895 In


119861 =

[[[[[[[

[

1198861111988612sdot sdot sdot 119886


1119899

11988611989411198861198942sdot sdot sdot 119886

119894119895sdot sdot sdot 119886

119894119899

11988611989911198861198992sdot sdot sdot 119886

119899119895sdot sdot sdot 119886

119899119899

]]]]]]]

]119899times119899

(7)

where 119886119895119894= 1119886




119886119894119895=119908119894

119908119895

119894 119895 = 1 2 119899 (8)


1 1199082 119908

119899)119879 one gets

119861119908 =

[[[[[[[[[[[[[[[[[

[

1199081

1199081

1199081

1199082


119908119895


119908119899

1199082

1199081

1199082

1199082


119908119895


119908119899

119908119894

1199081

119908119894

1199082

119908119894

119908119895

119908119894

119908119899

119908119899

1199081

119908119899

1199082


119908119895


119908119899

]]]]]]]]]]]]]]]]]

]119899times119899

[[[[[[[[[

[

1199081

1199082

119908119895

119908119899

]]]]]]]]]

]119899times1

= 119899

[[[[[[[[[

[

1199081

1199082

119908119895

119908119899

]]]]]]]]]

]

= 119899119908

(9)





1015840

11199081+ 1199081015840

21199082+ sdot sdot sdot + 119908

1015840

119899119908119899) of the solution


119861119908 = 120582max119908 (10)







1

1198602 119860119899 119860


1 1198622 119862119894 119862

119868)




119894119895=





119894and


119875 (119894) =

1

6(119888119894+ 4119886119894+ 119887119894)













119875 (119894119895) =

1

6(119888119894119895+ 4119886119894119895+ 119887119894119895)

(11)


119894119895are

given by

119882119894=

119875 (119894)

sum119868

119894=1119875 (119894)

119882119894119895=

119875 (119894119895)

sum119869

119895=1119875 (119894119895)

(12)

where sum119868119894=1119882119894= 1 sum119869

119895=1119882119894119895= 1


119882 = [1198821times119882111198821times11988212 119882

1times1198821119895 119882

119894times1198821198941

119882119894times1198821198942 119882

119894times119882119894119895 119882

119868times1198821198681

119882119868times1198821198682 119882

119868times119882119868119869]

= [119882111119882112 119882

11119895 119882

11989411989411198821198941198942 119882

119894119894119895

11988211986811986811198821198681198682 119882

119868119868119869]

(13)







(119888119900

119894119895119899 119886119900

119894119895119899 119887119900


119899



119894119895119899=

119900

119894119895119899

max119894119887119900

119894119895119899

times 5 (14)

where max119894119887119900

119894119895119899 gt 0 and




119894119895119899is larger

119894119895119899=

min119894119888119900

119894119895119899

119900

119894119895119899

times 5 (15)

where min119894119888119900

119894119895119899 gt 0 and




119894119895119899is larger


119872 =[[[

[

111

121


112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]

]

(16)


=

[[[[

[

111

121


112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]]

]

otimes

[[[[

[

119882111

119882112

119882119868119868119869

]]]]

]

=

[[[[

[

1

2

119873

]]]]

]

(17)


119875 (119899) =

1

6(119888119899+ 4119886119899+ 119887119899) (18)

4 A Case Study


1 the







25)



33)


Table4Survey

dataforfuzzy

comparativ

eweightsfore

achcriterio

n

Criteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Cr

iteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 1geographical

XC 2

cost

C 1geographical

XC 3

econo

my

C 1geographical

XC 4

governm

ent

C 1geographical

XC 5

investm

ent

C 1geographical

XC 6

infrastr

ucture

andeffi

ciency

C 2cost

XC 3

econo

my

C 2cost

XC 4

governm

ent

C 2cost

XC 5

investm

ent

C 2cost

XC 6

infrastr

ucture

andeffi

ciency

C 3econo

my

XC 4

governm

ent

C 3econo

my

XC 5

investm

ent

C 3econo

my

XC 6

infrastr

ucture

andeffi

ciency

C 4governm

ent

XC 5

investm

ent

C 4governm

ent

XC 6

infrastr

ucture

andeffi

ciency

C 5investm

ent

XC 6

infrastr

ucture

andeffi

ciency


Table5Survey

dataforfuzzy

comparativ

eweightsfore

achsubcriterion

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 11impexparea

XC 1

2feeder

port

C 11impexparea

XC 1

3mainroute

C 11impexparea

XC 1

4fre

quency

C 11impexparea

XC 1

5delivery

C 12feeder

port

XC 1

3mainroute

C 12feeder

port

XC 1

4fre

quency

C 12feeder

port

XC 1

5delivery

C 13mainroute

XC 1

4fre

quency

C 13mainroute

XC 1

5delivery

C 14fre

quency

XC 1

5delivery

C 21transportcost

XC 2

2op

erationcost

C 21transportcost

XC 2

3land

cost

C 21transportcost

XC 2

4labo

rcost

C 21transportcost

XC 2

5po

rtcharge

C 22op

erationcost

XC 2

3land

cost

C 22op

erationcost

XC 2

4labo

rcost

C 22op

erationcost

XC 2

5po

rtcharge

C 23land

cost

XC 2

4labo

rcost

C 23land

cost

XC 2

5po

rtcharge

C 24labo

rcost

XC 2

5po

rtcharge

C 31volof

impo

rtX

C 32volof

expo

rtC 3

1volof

impo

rtX

C 33volof

tranship

C 31volof

impo

rtX

C 34econ

omy

C 31volof

impo

rtX

C 35tradev

ariable

C 32volof

expo

rtX

C 33volof

tranship

C 32volof

expo

rtX

C 34econ

omy

C 32volof

expo

rtX

C 35tradev

ariable

C 33volof

tranship

XC 3

4econ

omy

C 33volof

tranship

XC 3

5tradev

ariable

C 34econ

omy

XC 3

5tradev

ariable

C 41private

XC 4

2custo

ms

C 41private

XC 4

3government

C 41private

XC 4

4coop

eration

C 41private

XC 4

5po

litical

C 42custo

ms

XC 4

3government

C 42custo

ms

XC 4

4coop

eration

C 42custo

ms

XC 4

5po

litical

C 43government

XC 4

4coop

eration

C 43government

XC 4

5po

litical

C 44coop

eration

XC 4

5po

litical

C 51taxbreak

XC 5

2law

C 51taxbreak

XC 5

3socialsta

bility

C 51taxbreak

XC 5

4expansion

C 51taxbreak

XC 5

5labo

rquality

C 52law

XC 5

3socialsta

bility

C 52law

XC 5

4expansion

C 52law

XC 5

5labo

rquality

C 53socialsta

bility

XC 5

4expansion

C 53socialsta

bility

XC 5

5labo

rquality

C 54expansion

XC 5

5labo

rquality


Table5Con

tinued

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 6

1po

rtfacilities

XC 6

2loaddisc

harge

C 61po

rtfacilities

XC 6

3mod

allin

kC 6

1po

rtfacilities

XC 6

4cargohand

leC 6

1po

rtfacilities

XC 6

5inform

ation

C 62loaddisc

harge

XC 6

3mod

allin

kC 6

2loaddisc

harge

XC 6

4cargohand

leC 6

2loaddisc

harge

XC 6

5inform

ation

C 63mod

allin

kX

C 64cargohand

leC 6

3mod

allin

kX

C 65inform

ation

C 64cargohand

leX

C 65inform

ation




A2 (5401 5401 5401) (50 50 50)

A3 (7288 7288 7288) (37 37 37)


A2 (167 177 187) (18 19 21)

A3 (186 206 226) (21 23 25)


A2 (100 110 120) (27 30 33)

A3 (65 70 75) (43 46 50)


A2 (1887381 1906255 1925318) (07 07 07)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (2116017 2158338 2201505) (08 08 08)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (5406461 5647846 5710712) (26 27 28)

A3 (300000 400000 5000000) (01 02 02)


A2 (7453 7453 7453) (44 44 44)

A3 (8387 8387 8387) (49 49 49)


A2 (66 67 68) (39 39 40)

A3 (81 82 83) (48 48 49)


A2 (31 32 33) (44 46 47)

A3 (29 30 31) (41 43 44)



62)









119860119908 =

[[[[[[[[[[[[[[[[[[[[

[

11

43 3 2

1

2

4 1 4 5 4 4

1

3

1

41 2 1

1

3

1

3

1

5

1

21 1 1

1

2

1

41 1 1

1

3

21

43 1 3 1

]]]]]]]]]]]]]]]]]]]]

]

[[[[[[[

[

01527

04394

00824

00757

00785

01714

]]]]]]]

]

=

[[[[[[[

[

09793

27574

05301

05055

04799

11449

]]]]]]]

]

120582max =1

6(09793

01527+27574

04394+05301

00824+05055

00757

+04799

00785+11449

01714) = 64331

CI =120582max minus 119899

119899 minus 1=64331 minus 6

6 minus 1= 008

CR = CIRI

=008

124= 007

(19)








1 the port 119860

2 and the port





5 Conclusions


Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





















119875 (119894119895) =

1

6(119888119894119895+ 4119886119894119895+ 119887119894119895)

(11)


119894119895are

given by

119882119894=

119875 (119894)

sum119868

119894=1119875 (119894)

119882119894119895=

119875 (119894119895)

sum119869

119895=1119875 (119894119895)

(12)

where sum119868119894=1119882119894= 1 sum119869

119895=1119882119894119895= 1


119882 = [1198821times119882111198821times11988212 119882

1times1198821119895 119882

119894times1198821198941

119882119894times1198821198942 119882

119894times119882119894119895 119882

119868times1198821198681

119882119868times1198821198682 119882

119868times119882119868119869]

= [119882111119882112 119882

11119895 119882

11989411989411198821198941198942 119882

119894119894119895

11988211986811986811198821198681198682 119882

119868119868119869]

(13)







(119888119900

119894119895119899 119886119900

119894119895119899 119887119900


119899



119894119895119899=

119900

119894119895119899

max119894119887119900

119894119895119899

times 5 (14)

where max119894119887119900

119894119895119899 gt 0 and




119894119895119899is larger

119894119895119899=

min119894119888119900

119894119895119899

119900

119894119895119899

times 5 (15)

where min119894119888119900

119894119895119899 gt 0 and




119894119895119899is larger


119872 =[[[

[

111

121


112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]

]

(16)


=

[[[[

[

111

121


112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]]

]

otimes

[[[[

[

119882111

119882112

119882119868119868119869

]]]]

]

=

[[[[

[

1

2

119873

]]]]

]

(17)


119875 (119899) =

1

6(119888119899+ 4119886119899+ 119887119899) (18)

4 A Case Study


1 the







25)



33)


Table4Survey

dataforfuzzy

comparativ

eweightsfore

achcriterio

n

Criteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Cr

iteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 1geographical

XC 2

cost

C 1geographical

XC 3

econo

my

C 1geographical

XC 4

governm

ent

C 1geographical

XC 5

investm

ent

C 1geographical

XC 6

infrastr

ucture

andeffi

ciency

C 2cost

XC 3

econo

my

C 2cost

XC 4

governm

ent

C 2cost

XC 5

investm

ent

C 2cost

XC 6

infrastr

ucture

andeffi

ciency

C 3econo

my

XC 4

governm

ent

C 3econo

my

XC 5

investm

ent

C 3econo

my

XC 6

infrastr

ucture

andeffi

ciency

C 4governm

ent

XC 5

investm

ent

C 4governm

ent

XC 6

infrastr

ucture

andeffi

ciency

C 5investm

ent

XC 6

infrastr

ucture

andeffi

ciency


Table5Survey

dataforfuzzy

comparativ

eweightsfore

achsubcriterion

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 11impexparea

XC 1

2feeder

port

C 11impexparea

XC 1

3mainroute

C 11impexparea

XC 1

4fre

quency

C 11impexparea

XC 1

5delivery

C 12feeder

port

XC 1

3mainroute

C 12feeder

port

XC 1

4fre

quency

C 12feeder

port

XC 1

5delivery

C 13mainroute

XC 1

4fre

quency

C 13mainroute

XC 1

5delivery

C 14fre

quency

XC 1

5delivery

C 21transportcost

XC 2

2op

erationcost

C 21transportcost

XC 2

3land

cost

C 21transportcost

XC 2

4labo

rcost

C 21transportcost

XC 2

5po

rtcharge

C 22op

erationcost

XC 2

3land

cost

C 22op

erationcost

XC 2

4labo

rcost

C 22op

erationcost

XC 2

5po

rtcharge

C 23land

cost

XC 2

4labo

rcost

C 23land

cost

XC 2

5po

rtcharge

C 24labo

rcost

XC 2

5po

rtcharge

C 31volof

impo

rtX

C 32volof

expo

rtC 3

1volof

impo

rtX

C 33volof

tranship

C 31volof

impo

rtX

C 34econ

omy

C 31volof

impo

rtX

C 35tradev

ariable

C 32volof

expo

rtX

C 33volof

tranship

C 32volof

expo

rtX

C 34econ

omy

C 32volof

expo

rtX

C 35tradev

ariable

C 33volof

tranship

XC 3

4econ

omy

C 33volof

tranship

XC 3

5tradev

ariable

C 34econ

omy

XC 3

5tradev

ariable

C 41private

XC 4

2custo

ms

C 41private

XC 4

3government

C 41private

XC 4

4coop

eration

C 41private

XC 4

5po

litical

C 42custo

ms

XC 4

3government

C 42custo

ms

XC 4

4coop

eration

C 42custo

ms

XC 4

5po

litical

C 43government

XC 4

4coop

eration

C 43government

XC 4

5po

litical

C 44coop

eration

XC 4

5po

litical

C 51taxbreak

XC 5

2law

C 51taxbreak

XC 5

3socialsta

bility

C 51taxbreak

XC 5

4expansion

C 51taxbreak

XC 5

5labo

rquality

C 52law

XC 5

3socialsta

bility

C 52law

XC 5

4expansion

C 52law

XC 5

5labo

rquality

C 53socialsta

bility

XC 5

4expansion

C 53socialsta

bility

XC 5

5labo

rquality

C 54expansion

XC 5

5labo

rquality


Table5Con

tinued

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 6

1po

rtfacilities

XC 6

2loaddisc

harge

C 61po

rtfacilities

XC 6

3mod

allin

kC 6

1po

rtfacilities

XC 6

4cargohand

leC 6

1po

rtfacilities

XC 6

5inform

ation

C 62loaddisc

harge

XC 6

3mod

allin

kC 6

2loaddisc

harge

XC 6

4cargohand

leC 6

2loaddisc

harge

XC 6

5inform

ation

C 63mod

allin

kX

C 64cargohand

leC 6

3mod

allin

kX

C 65inform

ation

C 64cargohand

leX

C 65inform

ation




A2 (5401 5401 5401) (50 50 50)

A3 (7288 7288 7288) (37 37 37)


A2 (167 177 187) (18 19 21)

A3 (186 206 226) (21 23 25)


A2 (100 110 120) (27 30 33)

A3 (65 70 75) (43 46 50)


A2 (1887381 1906255 1925318) (07 07 07)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (2116017 2158338 2201505) (08 08 08)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (5406461 5647846 5710712) (26 27 28)

A3 (300000 400000 5000000) (01 02 02)


A2 (7453 7453 7453) (44 44 44)

A3 (8387 8387 8387) (49 49 49)


A2 (66 67 68) (39 39 40)

A3 (81 82 83) (48 48 49)


A2 (31 32 33) (44 46 47)

A3 (29 30 31) (41 43 44)



62)









119860119908 =

[[[[[[[[[[[[[[[[[[[[

[

11

43 3 2

1

2

4 1 4 5 4 4

1

3

1

41 2 1

1

3

1

3

1

5

1

21 1 1

1

2

1

41 1 1

1

3

21

43 1 3 1

]]]]]]]]]]]]]]]]]]]]

]

[[[[[[[

[

01527

04394

00824

00757

00785

01714

]]]]]]]

]

=

[[[[[[[

[

09793

27574

05301

05055

04799

11449

]]]]]]]

]

120582max =1

6(09793

01527+27574

04394+05301

00824+05055

00757

+04799

00785+11449

01714) = 64331

CI =120582max minus 119899

119899 minus 1=64331 minus 6

6 minus 1= 008

CR = CIRI

=008

124= 007

(19)








1 the port 119860

2 and the port





5 Conclusions


Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










119875 (119894119895) =

1

6(119888119894119895+ 4119886119894119895+ 119887119894119895)

(11)


119894119895are

given by

119882119894=

119875 (119894)

sum119868

119894=1119875 (119894)

119882119894119895=

119875 (119894119895)

sum119869

119895=1119875 (119894119895)

(12)

where sum119868119894=1119882119894= 1 sum119869

119895=1119882119894119895= 1


119882 = [1198821times119882111198821times11988212 119882

1times1198821119895 119882

119894times1198821198941

119882119894times1198821198942 119882

119894times119882119894119895 119882

119868times1198821198681

119882119868times1198821198682 119882

119868times119882119868119869]

= [119882111119882112 119882

11119895 119882

11989411989411198821198941198942 119882

119894119894119895

11988211986811986811198821198681198682 119882

119868119868119869]

(13)







(119888119900

119894119895119899 119886119900

119894119895119899 119887119900


119899



119894119895119899=

119900

119894119895119899

max119894119887119900

119894119895119899

times 5 (14)

where max119894119887119900

119894119895119899 gt 0 and




119894119895119899is larger

119894119895119899=

min119894119888119900

119894119895119899

119900

119894119895119899

times 5 (15)

where min119894119888119900

119894119895119899 gt 0 and




119894119895119899is larger


119872 =[[[

[

111

121


112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]

]

(16)


=

[[[[

[

111

121


112

122


sdot sdot sdot

11119873

12119873

sdot sdot sdot 119868119869119873

]]]]

]

otimes

[[[[

[

119882111

119882112

119882119868119868119869

]]]]

]

=

[[[[

[

1

2

119873

]]]]

]

(17)


119875 (119899) =

1

6(119888119899+ 4119886119899+ 119887119899) (18)

4 A Case Study


1 the







25)



33)


Table4Survey

dataforfuzzy

comparativ

eweightsfore

achcriterio

n

Criteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Cr

iteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 1geographical

XC 2

cost

C 1geographical

XC 3

econo

my

C 1geographical

XC 4

governm

ent

C 1geographical

XC 5

investm

ent

C 1geographical

XC 6

infrastr

ucture

andeffi

ciency

C 2cost

XC 3

econo

my

C 2cost

XC 4

governm

ent

C 2cost

XC 5

investm

ent

C 2cost

XC 6

infrastr

ucture

andeffi

ciency

C 3econo

my

XC 4

governm

ent

C 3econo

my

XC 5

investm

ent

C 3econo

my

XC 6

infrastr

ucture

andeffi

ciency

C 4governm

ent

XC 5

investm

ent

C 4governm

ent

XC 6

infrastr

ucture

andeffi

ciency

C 5investm

ent

XC 6

infrastr

ucture

andeffi

ciency


Table5Survey

dataforfuzzy

comparativ

eweightsfore

achsubcriterion

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 11impexparea

XC 1

2feeder

port

C 11impexparea

XC 1

3mainroute

C 11impexparea

XC 1

4fre

quency

C 11impexparea

XC 1

5delivery

C 12feeder

port

XC 1

3mainroute

C 12feeder

port

XC 1

4fre

quency

C 12feeder

port

XC 1

5delivery

C 13mainroute

XC 1

4fre

quency

C 13mainroute

XC 1

5delivery

C 14fre

quency

XC 1

5delivery

C 21transportcost

XC 2

2op

erationcost

C 21transportcost

XC 2

3land

cost

C 21transportcost

XC 2

4labo

rcost

C 21transportcost

XC 2

5po

rtcharge

C 22op

erationcost

XC 2

3land

cost

C 22op

erationcost

XC 2

4labo

rcost

C 22op

erationcost

XC 2

5po

rtcharge

C 23land

cost

XC 2

4labo

rcost

C 23land

cost

XC 2

5po

rtcharge

C 24labo

rcost

XC 2

5po

rtcharge

C 31volof

impo

rtX

C 32volof

expo

rtC 3

1volof

impo

rtX

C 33volof

tranship

C 31volof

impo

rtX

C 34econ

omy

C 31volof

impo

rtX

C 35tradev

ariable

C 32volof

expo

rtX

C 33volof

tranship

C 32volof

expo

rtX

C 34econ

omy

C 32volof

expo

rtX

C 35tradev

ariable

C 33volof

tranship

XC 3

4econ

omy

C 33volof

tranship

XC 3

5tradev

ariable

C 34econ

omy

XC 3

5tradev

ariable

C 41private

XC 4

2custo

ms

C 41private

XC 4

3government

C 41private

XC 4

4coop

eration

C 41private

XC 4

5po

litical

C 42custo

ms

XC 4

3government

C 42custo

ms

XC 4

4coop

eration

C 42custo

ms

XC 4

5po

litical

C 43government

XC 4

4coop

eration

C 43government

XC 4

5po

litical

C 44coop

eration

XC 4

5po

litical

C 51taxbreak

XC 5

2law

C 51taxbreak

XC 5

3socialsta

bility

C 51taxbreak

XC 5

4expansion

C 51taxbreak

XC 5

5labo

rquality

C 52law

XC 5

3socialsta

bility

C 52law

XC 5

4expansion

C 52law

XC 5

5labo

rquality

C 53socialsta

bility

XC 5

4expansion

C 53socialsta

bility

XC 5

5labo

rquality

C 54expansion

XC 5

5labo

rquality


Table5Con

tinued

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 6

1po

rtfacilities

XC 6

2loaddisc

harge

C 61po

rtfacilities

XC 6

3mod

allin

kC 6

1po

rtfacilities

XC 6

4cargohand

leC 6

1po

rtfacilities

XC 6

5inform

ation

C 62loaddisc

harge

XC 6

3mod

allin

kC 6

2loaddisc

harge

XC 6

4cargohand

leC 6

2loaddisc

harge

XC 6

5inform

ation

C 63mod

allin

kX

C 64cargohand

leC 6

3mod

allin

kX

C 65inform

ation

C 64cargohand

leX

C 65inform

ation




A2 (5401 5401 5401) (50 50 50)

A3 (7288 7288 7288) (37 37 37)


A2 (167 177 187) (18 19 21)

A3 (186 206 226) (21 23 25)


A2 (100 110 120) (27 30 33)

A3 (65 70 75) (43 46 50)


A2 (1887381 1906255 1925318) (07 07 07)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (2116017 2158338 2201505) (08 08 08)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (5406461 5647846 5710712) (26 27 28)

A3 (300000 400000 5000000) (01 02 02)


A2 (7453 7453 7453) (44 44 44)

A3 (8387 8387 8387) (49 49 49)


A2 (66 67 68) (39 39 40)

A3 (81 82 83) (48 48 49)


A2 (31 32 33) (44 46 47)

A3 (29 30 31) (41 43 44)



62)









119860119908 =

[[[[[[[[[[[[[[[[[[[[

[

11

43 3 2

1

2

4 1 4 5 4 4

1

3

1

41 2 1

1

3

1

3

1

5

1

21 1 1

1

2

1

41 1 1

1

3

21

43 1 3 1

]]]]]]]]]]]]]]]]]]]]

]

[[[[[[[

[

01527

04394

00824

00757

00785

01714

]]]]]]]

]

=

[[[[[[[

[

09793

27574

05301

05055

04799

11449

]]]]]]]

]

120582max =1

6(09793

01527+27574

04394+05301

00824+05055

00757

+04799

00785+11449

01714) = 64331

CI =120582max minus 119899

119899 minus 1=64331 minus 6

6 minus 1= 008

CR = CIRI

=008

124= 007

(19)








1 the port 119860

2 and the port





5 Conclusions


Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table4Survey

dataforfuzzy

comparativ

eweightsfore

achcriterio

n

Criteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Cr

iteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 1geographical

XC 2

cost

C 1geographical

XC 3

econo

my

C 1geographical

XC 4

governm

ent

C 1geographical

XC 5

investm

ent

C 1geographical

XC 6

infrastr

ucture

andeffi

ciency

C 2cost

XC 3

econo

my

C 2cost

XC 4

governm

ent

C 2cost

XC 5

investm

ent

C 2cost

XC 6

infrastr

ucture

andeffi

ciency

C 3econo

my

XC 4

governm

ent

C 3econo

my

XC 5

investm

ent

C 3econo

my

XC 6

infrastr

ucture

andeffi

ciency

C 4governm

ent

XC 5

investm

ent

C 4governm

ent

XC 6

infrastr

ucture

andeffi

ciency

C 5investm

ent

XC 6

infrastr

ucture

andeffi

ciency


Table5Survey

dataforfuzzy

comparativ

eweightsfore

achsubcriterion

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 11impexparea

XC 1

2feeder

port

C 11impexparea

XC 1

3mainroute

C 11impexparea

XC 1

4fre

quency

C 11impexparea

XC 1

5delivery

C 12feeder

port

XC 1

3mainroute

C 12feeder

port

XC 1

4fre

quency

C 12feeder

port

XC 1

5delivery

C 13mainroute

XC 1

4fre

quency

C 13mainroute

XC 1

5delivery

C 14fre

quency

XC 1

5delivery

C 21transportcost

XC 2

2op

erationcost

C 21transportcost

XC 2

3land

cost

C 21transportcost

XC 2

4labo

rcost

C 21transportcost

XC 2

5po

rtcharge

C 22op

erationcost

XC 2

3land

cost

C 22op

erationcost

XC 2

4labo

rcost

C 22op

erationcost

XC 2

5po

rtcharge

C 23land

cost

XC 2

4labo

rcost

C 23land

cost

XC 2

5po

rtcharge

C 24labo

rcost

XC 2

5po

rtcharge

C 31volof

impo

rtX

C 32volof

expo

rtC 3

1volof

impo

rtX

C 33volof

tranship

C 31volof

impo

rtX

C 34econ

omy

C 31volof

impo

rtX

C 35tradev

ariable

C 32volof

expo

rtX

C 33volof

tranship

C 32volof

expo

rtX

C 34econ

omy

C 32volof

expo

rtX

C 35tradev

ariable

C 33volof

tranship

XC 3

4econ

omy

C 33volof

tranship

XC 3

5tradev

ariable

C 34econ

omy

XC 3

5tradev

ariable

C 41private

XC 4

2custo

ms

C 41private

XC 4

3government

C 41private

XC 4

4coop

eration

C 41private

XC 4

5po

litical

C 42custo

ms

XC 4

3government

C 42custo

ms

XC 4

4coop

eration

C 42custo

ms

XC 4

5po

litical

C 43government

XC 4

4coop

eration

C 43government

XC 4

5po

litical

C 44coop

eration

XC 4

5po

litical

C 51taxbreak

XC 5

2law

C 51taxbreak

XC 5

3socialsta

bility

C 51taxbreak

XC 5

4expansion

C 51taxbreak

XC 5

5labo

rquality

C 52law

XC 5

3socialsta

bility

C 52law

XC 5

4expansion

C 52law

XC 5

5labo

rquality

C 53socialsta

bility

XC 5

4expansion

C 53socialsta

bility

XC 5

5labo

rquality

C 54expansion

XC 5

5labo

rquality


Table5Con

tinued

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 6

1po

rtfacilities

XC 6

2loaddisc

harge

C 61po

rtfacilities

XC 6

3mod

allin

kC 6

1po

rtfacilities

XC 6

4cargohand

leC 6

1po

rtfacilities

XC 6

5inform

ation

C 62loaddisc

harge

XC 6

3mod

allin

kC 6

2loaddisc

harge

XC 6

4cargohand

leC 6

2loaddisc

harge

XC 6

5inform

ation

C 63mod

allin

kX

C 64cargohand

leC 6

3mod

allin

kX

C 65inform

ation

C 64cargohand

leX

C 65inform

ation




A2 (5401 5401 5401) (50 50 50)

A3 (7288 7288 7288) (37 37 37)


A2 (167 177 187) (18 19 21)

A3 (186 206 226) (21 23 25)


A2 (100 110 120) (27 30 33)

A3 (65 70 75) (43 46 50)


A2 (1887381 1906255 1925318) (07 07 07)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (2116017 2158338 2201505) (08 08 08)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (5406461 5647846 5710712) (26 27 28)

A3 (300000 400000 5000000) (01 02 02)


A2 (7453 7453 7453) (44 44 44)

A3 (8387 8387 8387) (49 49 49)


A2 (66 67 68) (39 39 40)

A3 (81 82 83) (48 48 49)


A2 (31 32 33) (44 46 47)

A3 (29 30 31) (41 43 44)



62)









119860119908 =

[[[[[[[[[[[[[[[[[[[[

[

11

43 3 2

1

2

4 1 4 5 4 4

1

3

1

41 2 1

1

3

1

3

1

5

1

21 1 1

1

2

1

41 1 1

1

3

21

43 1 3 1

]]]]]]]]]]]]]]]]]]]]

]

[[[[[[[

[

01527

04394

00824

00757

00785

01714

]]]]]]]

]

=

[[[[[[[

[

09793

27574

05301

05055

04799

11449

]]]]]]]

]

120582max =1

6(09793

01527+27574

04394+05301

00824+05055

00757

+04799

00785+11449

01714) = 64331

CI =120582max minus 119899

119899 minus 1=64331 minus 6

6 minus 1= 008

CR = CIRI

=008

124= 007

(19)








1 the port 119860

2 and the port





5 Conclusions


Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table5Survey

dataforfuzzy

comparativ

eweightsfore

achsubcriterion

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 11impexparea

XC 1

2feeder

port

C 11impexparea

XC 1

3mainroute

C 11impexparea

XC 1

4fre

quency

C 11impexparea

XC 1

5delivery

C 12feeder

port

XC 1

3mainroute

C 12feeder

port

XC 1

4fre

quency

C 12feeder

port

XC 1

5delivery

C 13mainroute

XC 1

4fre

quency

C 13mainroute

XC 1

5delivery

C 14fre

quency

XC 1

5delivery

C 21transportcost

XC 2

2op

erationcost

C 21transportcost

XC 2

3land

cost

C 21transportcost

XC 2

4labo

rcost

C 21transportcost

XC 2

5po

rtcharge

C 22op

erationcost

XC 2

3land

cost

C 22op

erationcost

XC 2

4labo

rcost

C 22op

erationcost

XC 2

5po

rtcharge

C 23land

cost

XC 2

4labo

rcost

C 23land

cost

XC 2

5po

rtcharge

C 24labo

rcost

XC 2

5po

rtcharge

C 31volof

impo

rtX

C 32volof

expo

rtC 3

1volof

impo

rtX

C 33volof

tranship

C 31volof

impo

rtX

C 34econ

omy

C 31volof

impo

rtX

C 35tradev

ariable

C 32volof

expo

rtX

C 33volof

tranship

C 32volof

expo

rtX

C 34econ

omy

C 32volof

expo

rtX

C 35tradev

ariable

C 33volof

tranship

XC 3

4econ

omy

C 33volof

tranship

XC 3

5tradev

ariable

C 34econ

omy

XC 3

5tradev

ariable

C 41private

XC 4

2custo

ms

C 41private

XC 4

3government

C 41private

XC 4

4coop

eration

C 41private

XC 4

5po

litical

C 42custo

ms

XC 4

3government

C 42custo

ms

XC 4

4coop

eration

C 42custo

ms

XC 4

5po

litical

C 43government

XC 4

4coop

eration

C 43government

XC 4

5po

litical

C 44coop

eration

XC 4

5po

litical

C 51taxbreak

XC 5

2law

C 51taxbreak

XC 5

3socialsta

bility

C 51taxbreak

XC 5

4expansion

C 51taxbreak

XC 5

5labo

rquality

C 52law

XC 5

3socialsta

bility

C 52law

XC 5

4expansion

C 52law

XC 5

5labo

rquality

C 53socialsta

bility

XC 5

4expansion

C 53socialsta

bility

XC 5

5labo

rquality

C 54expansion

XC 5

5labo

rquality


Table5Con

tinued

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 6

1po

rtfacilities

XC 6

2loaddisc

harge

C 61po

rtfacilities

XC 6

3mod

allin

kC 6

1po

rtfacilities

XC 6

4cargohand

leC 6

1po

rtfacilities

XC 6

5inform

ation

C 62loaddisc

harge

XC 6

3mod

allin

kC 6

2loaddisc

harge

XC 6

4cargohand

leC 6

2loaddisc

harge

XC 6

5inform

ation

C 63mod

allin

kX

C 64cargohand

leC 6

3mod

allin

kX

C 65inform

ation

C 64cargohand

leX

C 65inform

ation




A2 (5401 5401 5401) (50 50 50)

A3 (7288 7288 7288) (37 37 37)


A2 (167 177 187) (18 19 21)

A3 (186 206 226) (21 23 25)


A2 (100 110 120) (27 30 33)

A3 (65 70 75) (43 46 50)


A2 (1887381 1906255 1925318) (07 07 07)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (2116017 2158338 2201505) (08 08 08)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (5406461 5647846 5710712) (26 27 28)

A3 (300000 400000 5000000) (01 02 02)


A2 (7453 7453 7453) (44 44 44)

A3 (8387 8387 8387) (49 49 49)


A2 (66 67 68) (39 39 40)

A3 (81 82 83) (48 48 49)


A2 (31 32 33) (44 46 47)

A3 (29 30 31) (41 43 44)



62)









119860119908 =

[[[[[[[[[[[[[[[[[[[[

[

11

43 3 2

1

2

4 1 4 5 4 4

1

3

1

41 2 1

1

3

1

3

1

5

1

21 1 1

1

2

1

41 1 1

1

3

21

43 1 3 1

]]]]]]]]]]]]]]]]]]]]

]

[[[[[[[

[

01527

04394

00824

00757

00785

01714

]]]]]]]

]

=

[[[[[[[

[

09793

27574

05301

05055

04799

11449

]]]]]]]

]

120582max =1

6(09793

01527+27574

04394+05301

00824+05055

00757

+04799

00785+11449

01714) = 64331

CI =120582max minus 119899

119899 minus 1=64331 minus 6

6 minus 1= 008

CR = CIRI

=008

124= 007

(19)








1 the port 119860

2 and the port





5 Conclusions


Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Table5Con

tinued

Subcriteria

(999)

(789)(678)

(567)(456)(345)(234)(123)(111)

(13121)

(141312

)(151413

)(161514

)(171615

)(181716)(191817

)(19191

9)Subcriteria

AI

IVDI

IVSI

IVWI

IVEI

IVWUI

IVSU

IIV

DUI

IVAU

IC 6

1po

rtfacilities

XC 6

2loaddisc

harge

C 61po

rtfacilities

XC 6

3mod

allin

kC 6

1po

rtfacilities

XC 6

4cargohand

leC 6

1po

rtfacilities

XC 6

5inform

ation

C 62loaddisc

harge

XC 6

3mod

allin

kC 6

2loaddisc

harge

XC 6

4cargohand

leC 6

2loaddisc

harge

XC 6

5inform

ation

C 63mod

allin

kX

C 64cargohand

leC 6

3mod

allin

kX

C 65inform

ation

C 64cargohand

leX

C 65inform

ation




A2 (5401 5401 5401) (50 50 50)

A3 (7288 7288 7288) (37 37 37)


A2 (167 177 187) (18 19 21)

A3 (186 206 226) (21 23 25)


A2 (100 110 120) (27 30 33)

A3 (65 70 75) (43 46 50)


A2 (1887381 1906255 1925318) (07 07 07)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (2116017 2158338 2201505) (08 08 08)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (5406461 5647846 5710712) (26 27 28)

A3 (300000 400000 5000000) (01 02 02)


A2 (7453 7453 7453) (44 44 44)

A3 (8387 8387 8387) (49 49 49)


A2 (66 67 68) (39 39 40)

A3 (81 82 83) (48 48 49)


A2 (31 32 33) (44 46 47)

A3 (29 30 31) (41 43 44)



62)









119860119908 =

[[[[[[[[[[[[[[[[[[[[

[

11

43 3 2

1

2

4 1 4 5 4 4

1

3

1

41 2 1

1

3

1

3

1

5

1

21 1 1

1

2

1

41 1 1

1

3

21

43 1 3 1

]]]]]]]]]]]]]]]]]]]]

]

[[[[[[[

[

01527

04394

00824

00757

00785

01714

]]]]]]]

]

=

[[[[[[[

[

09793

27574

05301

05055

04799

11449

]]]]]]]

]

120582max =1

6(09793

01527+27574

04394+05301

00824+05055

00757

+04799

00785+11449

01714) = 64331

CI =120582max minus 119899

119899 minus 1=64331 minus 6

6 minus 1= 008

CR = CIRI

=008

124= 007

(19)








1 the port 119860

2 and the port





5 Conclusions


Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












A2 (5401 5401 5401) (50 50 50)

A3 (7288 7288 7288) (37 37 37)


A2 (167 177 187) (18 19 21)

A3 (186 206 226) (21 23 25)


A2 (100 110 120) (27 30 33)

A3 (65 70 75) (43 46 50)


A2 (1887381 1906255 1925318) (07 07 07)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (2116017 2158338 2201505) (08 08 08)

A3 (9042000 10860000 13075000) (35 42 50)


A2 (5406461 5647846 5710712) (26 27 28)

A3 (300000 400000 5000000) (01 02 02)


A2 (7453 7453 7453) (44 44 44)

A3 (8387 8387 8387) (49 49 49)


A2 (66 67 68) (39 39 40)

A3 (81 82 83) (48 48 49)


A2 (31 32 33) (44 46 47)

A3 (29 30 31) (41 43 44)



62)









119860119908 =

[[[[[[[[[[[[[[[[[[[[

[

11

43 3 2

1

2

4 1 4 5 4 4

1

3

1

41 2 1

1

3

1

3

1

5

1

21 1 1

1

2

1

41 1 1

1

3

21

43 1 3 1

]]]]]]]]]]]]]]]]]]]]

]

[[[[[[[

[

01527

04394

00824

00757

00785

01714

]]]]]]]

]

=

[[[[[[[

[

09793

27574

05301

05055

04799

11449

]]]]]]]

]

120582max =1

6(09793

01527+27574

04394+05301

00824+05055

00757

+04799

00785+11449

01714) = 64331

CI =120582max minus 119899

119899 minus 1=64331 minus 6

6 minus 1= 008

CR = CIRI

=008

124= 007

(19)








1 the port 119860

2 and the port





5 Conclusions


Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119860119908 =

[[[[[[[[[[[[[[[[[[[[

[

11

43 3 2

1

2

4 1 4 5 4 4

1

3

1

41 2 1

1

3

1

3

1

5

1

21 1 1

1

2

1

41 1 1

1

3

21

43 1 3 1

]]]]]]]]]]]]]]]]]]]]

]

[[[[[[[

[

01527

04394

00824

00757

00785

01714

]]]]]]]

]

=

[[[[[[[

[

09793

27574

05301

05055

04799

11449

]]]]]]]

]

120582max =1

6(09793

01527+27574

04394+05301

00824+05055

00757

+04799

00785+11449

01714) = 64331

CI =120582max minus 119899

119899 minus 1=64331 minus 6

6 minus 1= 008

CR = CIRI

=008

124= 007

(19)








1 the port 119860

2 and the port





5 Conclusions


Acknowledgment


References









































Volume 2014




Journal of











Journal of


Function Spaces






Algebra






































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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