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Research ArticleApplying Hybrid Decision-Making Method Based on FuzzyAHP-WOWA Operator for Emergency Alternative Evaluation ofUnattended Train Operation Metro System

Bobo Zhao1 Tao Tang2 and Bin Ning2

1National Engineering Research Center of Rail Transportation Operation and Control System Beijing Jiaotong UniversityNo 3 Shang Yuan Cun Haidian District Beijing 100044 China2State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University No 3 Shang Yuan Cun Haidian DistrictBeijing 100044 China

Correspondence should be addressed to Bobo Zhao bbzhaobjtueducn

Received 27 October 2015 Accepted 17 December 2015

Academic Editor Konstantinos Karamanos

Copyright copy 2016 Bobo Zhao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Optimal alternative selection to address the emergency situation is critical for dispatcher group in Unattended Train Operation(UTO) to guide emergency process It is difficult to provide the precise decision value under one criterion and to evaluate theemergency alternatives among multiple dispatchers This paper presents a hybrid emergency decision-making method integratingfuzzy analytic hierarchy process (FAHP) described by linguistic terms with enhanced weighted ordered weighted averaging(WOWA) operatorThe enhancedWOWA operator aggregates the preference matrices of multidispatcher through the constructedemergency response task model of dispatcher group in OCC This calculation approach takes into consideration the relations ofemergency tasks to derive the importance weights of dispatchers and integrates them into the ordered weighted averaging (OWA)operator weights based on a fuzzymembership relation A case study of applying themethod in an emergency of a train fire is givento demonstrate the feasibility and usefulness of the methods associated with the group multicriteria decision-making (GMCDM)theory in emergency management of UTO metro system

1 Introduction

Unattended Train Operation (UTO) refers to the automatedmetro system in which trains run fully automatically withoutany operating staff onboard [1] For the advantages suchas cost-effectiveness high traffic frequency and flexibilitythe UTO metro has a worldwide application spread as aglobal adoption trend Researches on UTO metro have beenmostly concentrated on how to operate the trains safely andtimely and the studies on decision support for the emergencysituation of UTO system have spread scarcely

Nevertheless there have been many researches on deci-sion support for decision makers in emergency responsesystem in other domains The integrated and comprehensivereal-time on-line decision support system (RODOS) was

designed to provide off-site emergency management in theevent of a radiation accident in nuclear emergencies [2ndash4] The method of multicriteria decision analysis (MCDA)was integrated into RODOS to evaluate alternatives or coun-termeasure strategies within emergency and remediationmanagement [5 6] Other decision support systems alsowere presented tomanage emergency response operations forlarge scale industrial accidents such as hazardous materialsemergencies [7 8]

Besides several studies have investigated on the emer-gency response system bymodelling the emergency responsetask network Abrahamsson et al [9] provided a betterframework in which an emergency response system couldfunctionalize during a specific operation and helped toidentify the potential events andor circumstances which

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2016 Article ID 4105079 12 pageshttpdxdoiorg10115520164105079

2 Mathematical Problems in Engineering

could significantly affect the performance of the emergencyresponse system Using task network mapping and analysisWang et al [10] presented a method of improving the per-formance of emergency response system by taking the timefactor into consideration Modelling the emergency responsetask network is an effective way for decision support inemergencies However these studies overlooked that peopleare the ultimate decision makers who are responsible fordealing with the emergency accidents and minimizing thecasualties and property loss

Moreover some researchers studied on the effect ofhuman factors under emergency situation in UTO metrosystem For example Wang and Fang [11] presented a struc-tured procedure to analyze the error behaviors of trafficdispatcher in emergencies based on the human informationprocessing theory and the modified task analysis frameworkKarvonen et al [12] analyzed the requirements of metrodrivers to reveal what should be provided to compensatefor the absence of driver in UTO metro system Howeverthese papers only studied the effect of human factors onsingle type position such as traffic dispatcher or driver ratherthan group decision for metro emergencies The challengesof UTO metro operation are without driver onboard howthe abnormal situation could be found out and be restored tothe normal operations and this indicates that the OperatingControl Center (OCC) should ensure the detection andmanagement of emergency situations [13] and take properemergency responses and clearance to avoid further damage

In case of any emergency in UTO metro the emergencyresponse process is to immediately organize the relatedagencies raise and dispatch various resources and developand carry out the emergency response plans with the goalof minimizing casualty and losses caused by disasters [14]The crucial point is how the dispatchers differentiate thedistinct and real information and make the proper decisionSuch decision making is an expertise balancing processwithin a number of criteria and opinions from differentdispatchers who have different knowledge about emergencyalternatives and make different contributions to differentemergency alternatives [15] Sometimes the opinions fromdifferent dispatchersrsquo conflict with each other and thereforeemergency alternative evaluation in UTO metro system isa typical group multicriteria decision-making (GMCDM)problem GMCDM is an evaluation approach to aggregatethe information of alternatives to obtain the best solution foremergency decision makers [16]

Saaty [17] proposed a method named analytic hierar-chy process (AHP) which provided a pairwise comparisonmatrix for decision makers to express their preferencesregarding multiple criteria and alternatives This method iswidely used for solving multicriteria decision-making prob-lems including planning selecting a best alternative resourceallocation and resolving conflicts [18]Nevertheless theAHPmethod is often criticized for its inability to incorporate theinherent uncertainty and imprecision associated with map-ping the decision makerrsquos perceptions to exact numbers [19]To solve this problem the fuzzy analytic hierarchy process(FAHP) used fuzzy preference relations to incorporate theambiguities and uncertainties that usually exist in human

judgment generally [20 21]The FAHP adopting the conceptsof fuzzy set theory and hierarchical structure analysis hasbeen widely employed to solve the alternative selection andjustification problem in different research areas [22ndash25]

The ordered weighted averaging (OWA) operator pro-posed by Yager [26] provided the selection of variouspreferences of decision makers from the optimistic viewto the pessimistic one [27] However it did not considerimportance weights through OWA operator Actually theweighted mean cannot be described by the arithmetic meanof OWA aggregations [28] To solve this problem Torra[29] proposed the weighted OWA (WOWA) aggregationwhich incorporated the important weighting into the OWAoperator Since WOWA operator was proposed it has beenwidely applied in the fields of multicriteria decision-making(MCDM) system and metadata aggregation problems [3031]

Great efforts have beenmade to solve GMCDMproblemsin UTO emergencies In this paper we adopted the methodof FAHP to solve the decision support under multicriteriaand employed enhanced WOWA operator to aggregate eachdecision from different decision makers in which the weightassigned to operator was one key factor for the performanceof the alternatives selection

The remainder of the paper is organized as follows Firstan overview of UTO system in China is given SecondFAHPmethod andWOWA operator are introducedThird ahybrid method combining FAHP and the enhancedWOWAoperator weights is specified This method integrates theweights applied to represent the significance level associatedwith the importance of dispatchers in a scenario of emergencyresponse task system for UTO metro system Then it ordersweights into the enhancedWOWAoperator and connects theoperator with the concept of fuzzy logic in a hierarchy patternunder the different knowledge situation of dispatcher groupFourth a case study is presented to demonstrate how theproposed method is applied to obtain the sequence order ofemergency alternatives in case of train fire occurring betweenstations Finally some conclusions are drawn

2 UTO System

We adopted the Line YanFang in Beijing as an investigationtarget which is under construction and will become thefirst UTO line regulated in automated operation in BeijingFurthermore we investigated Line 10 in Shanghai in whichthe organization has been designed for operational serviceof UTO system Based on the learning experience of Line 10in Shanghai we attended the designation and constructionprocess of the Line YanFang and discussed the new challengesin UTO metro which should be understood fully in futureoperation

The characteristics of UTO system under emergencyenvironment are that the dispatchers in OCC cannot reachavailable personnel to obtain the contingent factors of emer-gency situation remotely in a short time The factors includethe location the scope of emergency and the passengeremotion under emergency Without personnel in train anymajor functional failures or emergencies from the operated

Mathematical Problems in Engineering 3

Table 1 Detailed responsibilities of dispatchers in OCC

Different types of dispatchers Responsibility

Traffic dispatcher Managing and supervising the operation such as daily timetable train service and train operationEnvironment dispatcher Managing and supervising electromechanical devices water supply and drainage systemPower dispatcher Managing and supervising third rail power supply devicesPassenger dispatcher Supervising the passengers onboard and providing passengers with service under emergencyVehicle dispatcher Supervising the status of equipment onboard and handling the exceptional situation onboard remotelyMaintenance dispatcher Receiving the failure and assigning the maintenance task

train are not easy to be handled quickly and the passengershave to be supplied remote service or guidance of station staffwith some delay As a result the OCC becomes the initial andprimary responding organization to emergency situationThe major responsibilities of dispatchers in OCC are tocapture the characteristics of emergency situation and toapply appropriate recovery process which involves removingthe passengers in stranding train locating the equipmentfailure in system monitoring and responding the alarm fromthe different sensors and so forth It could be sequence orderof EMT (ExecutiveManagement Team) application and needsophisticated automatic techniques without driver onboard

The organization of metro faces a big challenge to restorethe emergency situation and to supply safe and flexibleoperational services for passengers For this reason thesimultaneous efforts of organization training for adaptingto a new pattern of emergency have been done with thedevelopment of UTO metro system The dispatchers shouldbe assigned the corresponding reasonable responsibility withrespect to different elements in the UTOmetroThe elementsinclude the passengers train signaling system station andinfrastructure In order to reveal the interdependence amongthese elements and the management pattern of OCC organi-zation we investigated Line 10 in Shanghai to learn the orga-nization pattern and management content of UTO metroand then we designed OCCrsquos organization with six types ofdispatcher role in the YangFang line of Beijing represented bytraffic dispatcher environment dispatcher power dispatcherpassenger dispatcher vehicle dispatcher and maintenancedispatcher respectively The detailed responsibilities of dis-patchers from the role-function are summarized in Table 1

From Table 1 the new obligation of dispatcher is to com-pensate for the absent responsibility of driver In conventionalmetro the driver has to participate observe interpret andreact to emergency events in the surrounding situation [12]From this point of view taking care of the passengers andhandling the exceptional events onboard are the hiddentasks for the driver to execute and compared with theconventional actor group the organization in OCC shouldsupply new job positions to compensate for the indispensableparts of operation service Therefore the added dispatchersare named as passenger dispatcher and vehicle dispatcherrespectively which replace the driver to provide emergencyservice for the passenger and handle exceptional situationonboard

3 Methods

31 FAHP Based on the pair-by-pair comparison values fora set of alternatives FAHP is applied to elicit a correspondingpriority vector that represents preferences [32] and is capableof capturing a humanrsquos appraisal of ambiguity when complexmulticriteria decision-making problems are considered [33]Fuzziness and vagueness are the characteristics of emergencydecision-making problems [34 35] and FAHP can be able totolerate vagueness or ambiguity in the emergency decision-making process

The basics about the fuzzy preference relations employedin FAHP are the following let119883 = 119909

1 1199092 119909

119899 (119899 ge 2) be

the set of alternatives A fuzzy preference relation 119877 on a setof objects 119883 is a fuzzy set on the product set 119883 times 119883 and it ischaracterized by amembership function120583

119877 119883times119883 rarr [0 1]

The preference relations can be expressed by 119899 times 119899 matrix119877 = (119903

119894119895)119899times119899

and 119903119894119895is interpreted as the preference degree or

intensity of the alternative 119909119894over 119909

119895The 119903

119894119895has the following

characteristics(1) 119903119894119895

= 05 it indicates indifference between 119909119894and 119909

119895

(119909119894sim 119909119895)

(2) 0 le 119903119894119895lt 05 it indicates that 119909

119895is strictly preferred to

119909119894(119909119895≻ 119909119894)

(3) 05 lt 119903119894119895

le 1 it indicates that 119909119894is strictly preferred

to 119909119895(119909119894≻ 119909119895) In particular 119903

119894119895= 1 denotes that 119909

119894is

definitely preferred to 119909119895

In general the matrix 119877 = (119903119894119895)119899times119899

is called a reciprocalfuzzy preference relation (FPR) such that 119903

119894119894= 05 and 119903

119894119895+

119903119895119894

= 1 for all 119894 119895 = 1 2 119899

Definition 1 (see [20]) A reciprocal fuzzy preference relation119877 = (119903

119894119895)119899times119899

is additive consistency if for all 119894 119895 119896 = 1 2 119899

with 119894 lt 119896 lt 119895 the condition 119903119894119896+ 119903119896119895

= 119903119894119896+ 05

The additive consistency of fuzzy preference relation isa strong condition to assess whether the decision-makingjudgment is consistent In this study the matrix 119877 is alwaysassumed to be reciprocal fuzzy preference relation and to havethe property of additive consistency

32 WOWA Operator The WOWA operator takes twoaspects of weighting vectors into consideration the impor-tance weights 119901 and OWA operator weights 119908


Emergency alternatives evaluation

Safety of passengers (C1) Emergency response time (C2) Performance of emergency recovery (C3)

EA1 EA2 EAnmiddot middot middot

Figure 1 The UTO emergency alternative evaluation construction using the FAHP method

Definition 2 Let 120572 = 1205721 1205722 120572

119899 be a set of alternatives

Vectors 119901 = 1199011 1199012 119901

119899119879 and 119908 = 119908

1 1199082 119908

119898119879

are two sets of weighting vectors with sum119899

119894=0119901119894

= 1 119901119894

isin

[0 1] sum119898

119894=0119908119894= 1 119908

119894isin [0 1]

Definition 3 Let the vector 120572120590(1)

120572120590(2)

120572120590(119899)

be a per-mutation of vector 120572 = 120572

1 1205722 120572

119899 such that 120572

120590(1)ge

120572120590(2)

ge sdot sdot sdot ge 120572120590(119899)

A WOWA operator of dimension 119899 is a mapping func-tion 119877

119899rarr 119877 with the two weighting vectors of 119901 =

1199011 1199012 119901

119899119879 and 119908 = 119908

1 1199082 119908

119898119879 The WOWA

operator is defined as follows

WOWA (1205721 1205722 120572

119899) =

119899

sum

119894=0

V119894120572120590(119894)

with V119894= 120596lowast(sum

119895le119894

119901120590(119895)

) minus 120596lowast(sum

119895lt119894

119901120590(119895)

)

(1)

where 120596lowast is an increasing function interpolating points

(119894119898sum119895le119894

119908119895) together with the point (00) Function 120596

lowast

is required to be a straight line when the points can beinterpolated in this way [29 36]

4 Hybrid Method for Selection of EmergencyAlternatives for UTO Metro System

41 Defining the Preference with Linguistic Term From theinvestigation of Line 10 in Shanghai it can be concludedthat the criteria used in UTO metro system are the safetyof passengers (C1) the emergency response time (C2) andthe performance of emergency recovery (C3) Applying theFAHP method to evaluate emergency alternatives accordingto emergency criteria is shown in Figure 1 However thedispatchers cannot make accurate decision precisely withuncertain environment and usually have vague descriptionto describe their preferences or judgments To obtain the

Table 2 Linguistic terms for the comparison of emergency alterna-tive evaluation and corresponding fuzzy preference values

Linguistic terms Fuzzy preference valuesVery good (VG) 09Good (G) 07Medium (M) 05Bad (B) 03Very bad (VB) 01

precise value linguistic terms are taken by dispatchers togive their preferences in a familiar style Table 2 gives the setof linguistic terms and their respective responding valuesThe preference value of pair to pair comparison to somealternatives can be derived according to the linguistic termsFor example a traffic dispatcher would use the word ldquoGoodrdquorather than give the precise value difficultly when he makesdecision with comparing two dispatching commands Thenthe precise preference value 09 can be obtained from linguis-tic term in fuzzy preference value table

As shown in Figure 1 it is supposed that there are 119898

dispatchers as decisionmakers (1198631 1198632 119863

119898) in a decision

team in case of UTOmetro emergency for evaluating 119899 alter-natives (EA

1EA2 EA

119899) according to the three criteria

(C1C2C3) Fortunately each dispatcher has the familiarand rational knowledge with the relative weights of theproposed three criteria because of the excellent safe cultureof metro organization and normal training process for metrostaff in China So we suppose the weights of the three criteriaare 05 03 02 in a unified pattern based on interviewswith dispatchers working inOCC Each dispatcher119863

119896has his

(or her) relative evaluation 119908119894119895between alternative EA

119894and

alternative EA119895with respect to each criterionTherefore there

will be a decision matrix 119866[119906(119908119894119895)119899times119899

]119898times3

where 119906(119908119894119895)119899times119899

is the pair to pair evaluation matrix among all emergencyalternatives 119899 The exact value of 119908

119894119895can be obtained from

the linguistic terms in Table 2


t1n t1

1

t12t1

3

middot middot middot

middot middot middot middot middot middot



Dm

t2n

t21

t22

t23

t3n

t31

t32

t33

Emergency response goal (ge) Emergency event (e)

D1 D2

D3

Figure 2 The emergency response task model of dispatchers in OCC

42 The Calculating Approach for Enhanced WOWAOperator Weights

421 Determining the Importance Weights of DispatcherIn order to minimize the loss of emergency on operationservices the dispatchers try to carry out necessary andeffective tasks to deal with the emergency and restore thedisturbed metro system For example in case of a switchfailure in front of the track the traffic dispatcher shouldexecute three tasks (1) locking the failure zone to avoidthe entrance of train (2) setting the temporary train routeto maintain continuous revenue service and (3) adjustingthe operation timetable to adapt to the failure event Themore the dispatcher participates in the emergency responseprocess the more important hisher duty is From this pointof view the importance weights of dispatchers are dependenton their specific job responsibilities which are indicated bythe emergency tasks number

Moreover each dispatcher works in hisher own domainand derives the necessary tasks at the operational level undercurrent emergency to meet the arising requirements after theevent The operational steps are formed with the cooperationof different dispatchers These dispatchers undertake taskswith different contents and numbers which are relative tothe type of emergency event For example in case of personfalling onto the platform track the traffic dispatcher confirmsto brake the train the power dispatcher cuts off the electricityof the third rail and the passenger dispatcher provides theeasing service to passengers in the train to prevent thesecond damage It also implies that the dispatchers in OCCas decision maker have a close and entire dependence on thecurrent emergency goal and the goal of emergency responsedetermines the contents of the tasks and the following oper-ations Therefore the dependence of dispatcher related to

the emergency goals under uncertain environment is anotherimportant aspect to define the importance of dispatchers

The remote characteristic of management and super-vision for the UTO metro system determinates that theperformance of emergency response process under emer-gency highly depends on dispatchers and their tasks involvedin the emergency event The dispatchers in OCC shouldcooperate with each other according to the priorities oftheir task relations Considering these factors an OCCemergency response task model was proposed to coverthree aspects emergency goals emergency related dispatcherand dispatcher related tasks under each emergency eventIt is noted that the key points of this study include theimportance of decision makers and how their preferencedecisions of emergency alternatives are aggregated Hencewe constructed the OCC emergency response task model toanalyze the dependence relationship between different tasksand to obtain importance weights of dispatchers There arefive steps for construction of the emergency response taskmodel of UTO metro system as shown in Figure 2

Step 1 Confirm the type and scope of emergency event 119890represented by node of rectangle

Step 2 Set the goal 119892119890of emergency response represented by

node of rectangle

Step 3 Identify the dispatchers related to the emergency rep-resented by node of ellipse which may include119898 dispatchers1198631 1198632 119863

119898

Step 4 Select the tasks following the dispatchers representedby node of circle which may include 119899 tasks 119905119896

1 119905119896

2 119905

119896

119899 of

dispatcher 119896 with 1 le 119896 le 119898


Step 5 For each task add a directed edge to denote thesequence and priority between the tasks selected in Step 4The last task will be executed at the end of task network andreach the emergency response goal 119892

119890

After the type and scope of emergency are identifiedfrom the remote alarming and failure information in Step1 Step 2 defines emergency goals explicitly according to theurgency level and scope of emergency Then the imperativephase of emergency response process categorizes dispatchersinvolved in the emergency decision-making operation andtheir necessary tasks in Steps 3 to 5

As aforementioned the calculating formula of impor-tance weight (IW) of dispatcher is proposed before findingout the appropriate priority of emergency decisions Theformulation refers to the typical proximity prestige definedby Wasserman and Faust [37] and takes into considerationthe concept of decision maker involved in the task network

The IW of dispatcher 119896 is defined by

IW119896= sum

119894isin119879119896

119873119896

1sum119898

119896=1119873119896

sum119895isin119873119896

1

(119889 (119905119895 119905119896

119894) 119873119896

1)

(2)

As shown in (2) 119872 = 1 2 119898 | 119898 isin 119873 isassumed as the set of different types of dispatchers in OCCThe set of 119879

119896= 119905119896

1 119905119896

2 119905

119896

119899 is composed of dispatcher

119896 related tasks with respect to the emergency goals and theresponsibility of each dispatcher 119873

119896represents the number

of tasks involved in dispatcher1198631198961198731198961denotes the number of

tasks outside dispatcher119863119896but it can reach to dispatcher119863

119896

119889(119905119895 119905119896

119894) represents the distance of task 119905

119895outside dispatcher

119863119896reachable to task 119905

119896

119894 The IW of dispatcher 119896 is the sum of

the ratio of reachable tasks and average distance of all tasksreachable to dispatcher119863

119896

From the emergency task network we consider the IW119896

as the ratio of the average reachable distance of all tasksrelated with the dispatcher 119896 According to (2) dispatcher119896 becomes more important when (1) dispatcher 119896 shouldexecute more tasks to reach 119892

119890 (2) more tasks executedby other dispatchers should be cooperated with dispatch 119896(3) the distance between the tasks 119905

119896

119894and 119905119895is shorter The

normalization process is necessary to obtain the sum of IW1015840119896

equal to 1 as shown in the following

IW1015840119896=

IW119896

sum119898

119896=1IW119896

(3)

422 Determining the OWA Operator Weights of DispatcherThe OWA operator uses different decision criteria such asMaximax (optimistic) and Maximin (pessimistic) to expressthe optimism degree of the decision maker [38] The OWAoperator weights are measured by two important parame-ters dispersion (or entropy) and orness which indicate theentropy of the probability distribution and the measure ofthe optimism of the decision maker respectively [26] Fullerand Majlender [39] introduced a method of minimizing thevariance of OWA operator weights under a given level of

orness Wang and Parkan [40] employed a linear program-ming (LP) to minimize the maximum disparity between twoadjacent weights under a given level of orness Wang et al[41] presented OWA operator weights named least squaresdeviation (LSD) minimizing the sum square of deviationbetween 119908

119894and 119908

119894+1 In this paper fuzzy membership

function was employed to obtain the 119899 dimensional OWAoperator weights [42]

The OWA weights vector 119908lowast119902is calculated by [42]

119908lowast

119902= 119876(

119902

119899) minus 119876(

(119902 minus 1)

119899)

with 119908lowast

119902ge 0

119899

sum

119902=1

119908lowast

119902= 1

(4)

where 119876 is a fuzzy membership function denoted by

119876 (119903) =

0 119903 lt 120572

119903 minus 120572

120573 minus 120572 120572 le 119903 le 120573

1 119903 gt 120573

(5)

with parameter (120572 120573) = (03 08) indicating the fuzzyprinciple of majority

423 Determining the Enhanced WOWA Operator WeightsThe importance weights could be used to evaluate the promi-nence of dispatcher as decision maker based on the proposedemergency response task model However the model isinsufficient to represent the logic of the emergency decisionselection with one single factor of the importance weight ofdispatcher because different decision makers have differentpreferences based on their knowledge and experienceThere-fore it is necessary to aggregate the preferences of groupdecision regarding the optimism degree and prominence ofdecision makers

Adapting to the characteristics of the UTOmetro systeman approach of the enhanced WOWA operator is proposedto assign the importance of the dispatchers to the orderedweights solving emergency alternatives selection from mul-tidispatcher of UTO metro In this systematic approachrelationship between dispatchers and dispatcher related tasksunder the emergency goal is modelled to derive the impor-tance weights and a fuzzymembership function is integratedto decide the OWA operator weights There are four steps forthis approach Suppose there are 119898 dispatchers 1 2 119898

in OCC

Step 1 Construct the emergency response task model pro-posed in Section 421

Step 2 Let119908119896= 1199081 1199082 119908

119898119879 be the importanceweights

of dispatchersThe weights vector is calculated by (2) and (3)

Step 3 Let 119908lowast119902

= 119908lowast

1 119908lowast

2 119908lowast

119898119879 be the OWA weights of

preference relationship The weights vector is calculated by(4) and (5)




S1 S2 S3 S4 S5

Figure 3 The AHP emergency alternative evaluation model in case of a train fire

Step 4 The aggregation weights vector V = V1 V2 V

119898119879

is calculated by (1) based on the importance weights ofdispatchers and OWA weights

43 Integrating the Enhanced WOWA Operator with FAHPMethod The approach integrating the proposed enhancedWOWA operator with FAHP method to obtain the ultimatepriority is described as follows

Step 1 119863 = 1198631 1198632 119863

119898 is assumed as a set of

dispatchers and 119875 = 119875(1)(119904)

119875(2)(119904)

119875(119898)(119904)

is assumedas the set of preference judgment vectors under criterion 119904where 119875

(119896)(119904)= 119906(119908

119894119895

119896(119904))119899times119899

The aggregation matrix 119901lowast119904

119894119895

of preference judgment under criterion 119904 is formulated withenhanced WOWA operator by

119901lowast119904

119894119895=

119898

sum

119897=0

V119897119901119897 (6)

where 119901119897is 119897th largest value of 119908

119894119895

119896(119904) with 1 le 119896 le 119898

Step 2 The aggregation matrix of multidispatcher withrespect to criterion 119904 is 119901

lowast119904= (119901lowast119904

119894119895)119899times119899

1 le 119904 le 3 Thedispatchers in UTO metro have the same perception of theweights of the criteria so themulticriteria aggregationmatrix119901120591

119894119895can be calculated by

119901120591

119894119895=

3

sum

119904=0

120582119904119901lowast119904

119894119895 (7)

where 120582 = (1205821 1205822 1205823) = (05 03 02) is the weights of

criteria and (7) uses the weighted average method to derivethe ultimate matrix

Step 3 Thedegree indicator 119903119894demonstrates that alternative 119894

is superior to other alternatives and from the fuzzy principleof majority it is calculated by

119903119894= 120579 (119901

120591

119894119895 119895 = 1 2 119899) =

119899

sum

119902=1

V119902119888119902

119894 119894 isin 119898 (8)

where V119902is obtained from (1) with parameter (120572 120573) =

(03 08) and 119888119902

119894is 119902th largest element of set 119901

120591

119894119895| 119895 =

1 2 119899

Step 4 The degree indicator 1199031015840119894is normalized by

1199031015840

119894=

119903119894

sum119899

119894=1119903119894

(9)

The priority of emergency alternatives is given from thevector 1199031015840 = 119903

1015840

1 1199031015840

2 119903

1015840

119899

5 Case Study

The proposed FAHP-WOWA method can be applied ondecision support in an emergency event It integrates all theopinions of dispatchers and the relationships between thepreferences and the importance of dispatchers in emergencyresponse task situation are taken into consideration andcombined properly Here a train fire emergency during theoperation process of the train between the stations is taken asa case

In case of fire detection the aforementioned three criteriain the metro emergency are employed to construct the AHPmodel shown in Figure 3 in which there are five emergencyalternatives represented by S1 to S5 respectively which areexplained in Table 3

It is assumed that 119863 = Traffic dispatcher Environmentdispatcher Passenger Dispatcher Vehicle Dispatcher Powerdispatcher is the set of decision makers in OCC

51 Calculating Enhanced WOWA Operator Weights Afterthe analysis of FAHP applied on aforementioned train firecase the enhanced WOWA operator weights are calculatedas follows

Step 1 The emergency response task model is constructedas shown in Figure 4 The detailed tasks according to theresponsibilities of the dispatchers are summarized in Table 4


Table 3 Emergency alternatives of train fire

Number Alternatives

S1 Allowing the train to continue its ride to the next safe place (eg next station) where the train can be stoppedand immobilized

S2 Holding the train between stations and the train door is manually opened by passengers under the guidance ofthe broadcast from OCC

S3 The passengers will be evacuated by the work staff between the stationsS4 The passengers will be evacuated under the guidance of the broadcast from OCC between the stationsS5 The passengers will be evacuated by the station staff on the platform

Powerdispatcher

Traffic dispatcher Environment

dispatcher

A fire aboardA fire aboard

Passenger dispatcher

Vehicledispatcher

response goal (ge)

t1 t2

t3

t4t5 t6

t7

t8

t9

t10

t11 t12

t13

t17

t18 t19

t20

t21

t14

t16 t15

Figure 4 Emergency response task model in case of train fire

Step 2 Based on the emergency response task model in caseof train fire the importance weights vector of dispatchers119908119896defined in set 119863 is calculated by (2) and (3) 119908

119896=

053 007 011 016 013119879

Step 3 Thepreferencematrixes of different dispatchers underthe criterion of safety of passengers are presented fromTables5ndash9 based on the interview of dispatchers in OCC

The OWA operator weights vector of dispatcher 119908lowast

119902is

obtained by (4) and (5) 119908lowast119902= 0 02 04 04 0

119879

Step 4 Based on the vectors 119908119896

and 119908lowast

119902 the aggre-

gation weights vector can be calculated by (1) V =

06 027 0130 0119879

52 Aggregating the Preferences of Dispatchers with WOWAOperator and FAHP The final priority of emergency alter-natives is obtained through the aggregation process of fuzzypreferences derived from the linguistic terms based on FAHPmethod and enhancedWOWAoperator weightsThe processis described as follows

Step 1 From the approach discussed in Section 43 the pref-erence aggregation matrixes of different dispatchers under

multicriteria are calculated by (6) and they are shown fromTables 10ndash12

Step 2 Theaggregationmatrix ofmultidispatcher is obtainedby (7) and it is shown in Table 13

Step 3 Degree indicators vector 119903 which demonstrates thatone alternative is superior to other alternatives is calculatedby (8)

119903 = 08989 07988 04394 05631 06929119879 (10)

Step 4 After normalization with (9) the priority weightsvector 1199031015840 is

1199031015840= 02649 02354 01295 01659 02042

119879 (11)

which means the sequence of the priority of emergencyalternatives is

S1 ≻ S2 ≻ S5 ≻ S4 ≻ S3 (12)

From the investigation on Line 10 in Shanghai it isnoted that the dispatchers always have the guideline in anyemergency situations dispatching the emergency train intostation if the train can move For this reason the emergencyalternative S1 allowing the train to continue running to next


Table 4 Detailed tasks in case of train fire

Task sequence Task content1199051

Monitoring fire alarm indicator1199052

Communicating with traffic dispatcher1199053

Holding train at next station1199054

Opening platform doors1199055

Holding train between stations1199056

Making other trains emergency stop remotely1199057

Communicating with passenger dispatcher1199058

Communicating with environment dispatcher1199059

Communicating with station work staff11990510

Establishing zone of protection11990511

Communicating with fire departments11990512

Releasing fire on board emergency plan11990513

Monitoring coach11990514

Communicating with passengers11990515

Releasing passenger evacuation information11990516

Monitoring passenger evacuation process11990517

Communicating with vehicle dispatcher11990518

Cutting off third rail power11990519


Communicating with power dispatcher11990521

Opening train doors

Table 5 Preference matrix of traffic dispatcher

Emergencyalternatives S1 S2 S3 S4 S5

S1 M VG VG VG GS2 VB M VG G BS3 VB VB M G VBS4 VB B B M BS5 B G VG G M

Table 6 Preference matrix of environment dispatcher



safe place is the first selection The alternative of holdingthe train between stations (S2) is the second selectionAfter making the emergency decision of the fired train thealternatives of evacuating passengers should have a properpriority decision and S5 evacuating by the station staff onthe platform is the third selection for the aforementionedguideline The alternative S4 of evacuating passengers bythe broadcast from OCC between the stations is the fourthselection for its inflexibility and uncontrollability Then thealternative S3 of evacuating the passengers by the work staff

Table 7 Preference matrix of passenger dispatcher


S1 M B B B GS2 G M G VG VGS3 G B M G VGS4 G VB B M VGS5 B VB VB VB M

Table 8 Preference matrix of vehicle dispatcher


S1 M VG VG VG VGS2 VB M G VG GS3 VB B M G BS4 VB VB B M VBS5 VB B G VG M

Table 9 Preference matrix of power dispatcher


S1 M VG VG VG GS2 VB M G VG BS3 VB B M G BS4 VB VB B M VBS5 B G G VG M

Table 10 Aggregation matrix under criterion of the safety ofpassengers (C1)

Emergencyalternatives

C1 the safety of passengersS1 S2 S3 S4 S5

S1 05000 09000 09000 09000 05572S2 06340 05000 08740 09000 07680S3 04600 03000 05000 05400 02200S4 04600 01811 06480 05000 06600S5 03000 05140 06220 06220 05000

Table 11 Aggregation matrix under criterion of the emergencyresponse time (C2)


C2 the emergency response timeS1 S2 S3 S4 S5

S1 05000 08740 09000 09000 05572S2 08220 05000 08200 07000 05400S3 06220 01000 05000 03000 02740S4 06220 01832 07000 05000 08220S5 03000 06480 08200 08740 05000

between the stations is the last selectionThe weakness of thisalternative is that the rescue time will be lost if station staff


Table 12 Aggregation matrix under criterion of the performance ofemergency recovery (C3)


C3 the performance of emergency recoveryS1 S2 S3 S4 S5

S1 05000 09000 09000 09000 04372S2 05800 05000 09000 07000 06600S3 04600 01000 05000 03000 05800S4 04600 01832 07000 05000 06600S5 03000 06220 07960 06220 05000

Table 13 Aggregation matrix under multicriteria


S1 05000 08922 09000 09000 05332S2 06796 05000 08630 08000 06780S3 05086 02000 05000 04200 03082S4 05086 01821 06740 05000 07086S5 03000 05758 07162 06976 05000

goes into the guideway between stations Also the fire in thetrain may cause a second damage to passengers

In summary the result of the aggregation method of dis-patcherrsquos preferences applied on the case of a train fire duringthe operation process between the stations is consistencywiththe real emergency guidance in the situation of UTO system

6 Conclusion

The thinking and preference of dispatcher group in OCChave a key impact on the performance of emergency responsefor their emergency responding behaviors To find out theoptimized emergency solution a hybrid decision-makingmethod is proposed to solve group decision-making supportproblem of emergency alternatives in UTO metro system ofChina

The linguistic terms adopted in FAHP avoid the vague-ness of dispatchers and have a responding relation withfuzzy preference to get precise value For ranking purposeit is important to choose an appropriate WOWA oper-ator weight applied on UTO metro system to aggregatethe preferences of dispatcher group The interrelationshipbetween the dispatchers and their respective preferences iscalculated through assigning the dispatcher importance toOWA operator weights When evaluating the importanceof dispatcher in OCC the proposed formulation processconsiders task interdependencies featured by the structureof the corresponding emergency task model Through inte-grating the FAHP method with the enhanced WOWA thepriority of emergency alternatives is obtained to support thecomplex emergency response procedure in newUTO systemThis proposed method has been demonstrated and partiallyvalidated through a case study of train fire In this way thedispatcher group facing UTO emergency event would focuson performance of emergency response procedure rather


Emergency alternatives S1 S2 S3 S4 S5S1 M VG VG G GS2 VB M VG G VGS3 VB VB M B VGS4 B B G M VGS5 B VB VB VB M


Emergency alternatives S1 S2 S3 S4 S5S1 M VG VG VG GS2 VB M VG G BS3 VB VB M B VBS4 VB B G M BS5 B G VG G M


Emergency alternatives S1 S2 S3 S4 S5S1 M G G G GS2 B M G G BS3 B VB M B VGS4 B B G M VGS5 B G VB VB M


Emergency alternatives S1 S2 S3 S4 S5S1 M G VG VG VGS2 B M G VG GS3 VB B M G BS4 VB VB B M VBS5 VB B G VG M


Emergency alternatives S1 S2 S3 S4 S5S1 M VG VG VG GS2 VB M G VG BS3 VB B M G BS4 VB VB B M VBS5 B G G VG M

than be confused by excessive decision information undermultiple criteria and multiple decision makers

Further studywill focus on aggregationmethodof incom-plete information of dispatcherrsquos preference and validate thealgorithm on the agent based pedestrian simulationmodel inseveral emergency scenarios

Appendix

The preference matrixes of different dispatchers under thecriterion of emergency response time are present in Tables14ndash18







Emergency alternatives S1 S2 S3 S4 S5S1 M VB B B GS2 VG M VG G VGS3 G VB M B VGS4 G B G M VGS5 B VB VB VB M




Emergency alternatives M VG VG VG GS1 VB M VG G BS2 VB VB M B VBS3 VB B G M BS4 B G VG G MS5 M VG VG VG G

Thepreferencematrixes of different dispatchers under thecriterion of performance of emergency recovery are presentin Tables 19ndash23

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work was partly supported by Beijing Laboratory ofUrban Rail Transit Beijing Key Laboratory of Urban RailTransit Automation and Control Beijing Municipal Scienceand Technology Project (Project no D141100000814002) theFundamental Research Funds for the Central Universities(2015JBJ003) and the NSFC under U1434209

References

[1] UITP Press Kit Metro Automation Facts Figures and TrendsmdashA Global Bid for Automation UITP Observatory of Auto-mated Metros Confirms Sustained Growth Rates for the Com-ing Years UITP 2011 httpwwwuitporgsitesdefaultfilesMetro20automation20-20facts20and20figurespdff

[2] W Raskob and J Ehrhardt The RODOS System DecisionSupport for Nuclear Off-Site Emergency Management in EuropeForschungszentrum Karlsruhe 2000

[3] K N Papamichail and S French ldquoDecision support in nuclearemergenciesrdquo Journal of Hazardous Materials vol 71 no 1ndash3pp 321ndash342 2000

[4] J Ehrhardt J Pasler-Sauer O Schule G Benz M Rafatand J Richter ldquoDevelopment of RODOSlowast a comprehensivedecision support system for nuclear emergencies in Europemdashan overviewrdquo Radiation Protection Dosimetry vol 50 no 2ndash4pp 195ndash203 1993

[5] J Geldermann V Bertsch M Treitz S French K NPapamichail and R P Hamalainen ldquoMulti-criteria decisionsupport and evaluation of strategies for nuclear remediationmanagementrdquo Omega vol 37 no 1 pp 238ndash251 2009

[6] V Bertsch M Treitz J Geldermann and O Rentz ldquoSensitivityanalyses in multi-attribute decision support for off-site nuclearemergency and recovery managementrdquo International Journal ofEnergy Sector Management vol 1 no 4 pp 342ndash365 2007

[7] K G Zografos G M Vasilakis and I M Giannouli ldquoMethod-ological framework for developing decision support systems(DSS) for hazardousmaterials emergency response operationsrdquoJournal of Hazardous Materials vol 71 no 1 pp 503ndash521 2000

[8] K G Zografos and K N Androutsopoulos ldquoA decision sup-port system for integrated hazardous materials routing andemergency response decisionsrdquo Transportation Research Part CEmerging Technologies vol 16 no 6 pp 684ndash703 2008

[9] M Abrahamsson H Hassel and H Tehler ldquoTowards a system-oriented framework for analysing and evaluating emergencyresponserdquo Journal of Contingencies and Crisis Management vol18 no 1 pp 14ndash25 2010

[10] D Wang C Qi and HWang ldquoImproving emergency responsecollaboration and resource allocation by task network mappingand analysisrdquo Safety Science vol 70 pp 9ndash18 2014

[11] J Wang and W Fang ldquoA structured method for the traffic dis-patcher error behavior analysis inmetro accident investigationrdquoSafety Science vol 70 pp 339ndash347 2014

[12] H Karvonen I Aaltonen M Wahlstrom L Salo P Saviojaand L Norros ldquoHidden roles of the train driver a challenge formetro automationrdquo Interacting with Computers vol 23 no 4pp 289ndash298 2011

[13] IEC ldquoRailway applicationsmdashurban guided transport man-agement and commandcontrol systemsmdashpart 2 functionalrequirements specificationrdquo Draft EN 62290-2 2011 httpwebstoreiecchWebstorewebstorensfArtnum PK49864


[14] M K Lindell C Prater and R W Perry Wiley PathwaysIntroduction to Emergency Management John Wiley amp Sons2006

[15] Y Ju and A Wang ldquoEmergency alternative evaluation undergroup decision makers amethod of incorporating DSAHPwith extended TOPSISrdquo Expert Systems with Applications vol39 no 1 pp 1315ndash1323 2012

[16] D Meng and Z Pei ldquoOn weighted unbalanced linguisticaggregation operators in group decision makingrdquo InformationSciences vol 223 pp 31ndash41 2013

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

[18] N Subramanian and R Ramanathan ldquoA review of applicationsof Analytic Hierarchy Process in operations managementrdquoInternational Journal of Production Economics vol 138 no 2pp 215ndash241 2012

[19] H Deng ldquoMulticriteria analysis with fuzzy pairwise compar-isonrdquo International Journal of Approximate Reasoning vol 21no 3 pp 215ndash231 1999

[20] T Tanino ldquoFuzzy preference orderings in group decisionmakingrdquo Fuzzy Sets and Systems vol 12 no 2 pp 117ndash131 1984

[21] J Rezaei and R Ortt ldquoMulti-criteria supplier segmentationusing a fuzzy preference relations basedAHPrdquoEuropean Journalof Operational Research vol 225 no 1 pp 75ndash84 2013

[22] C V Altrock and B Krause ldquoMulti-criteria decision making inGerman automotive industry using fuzzy logicrdquo Fuzzy Sets andSystems vol 63 no 3 pp 375ndash380 1994

[23] P-L Chang and Y-C Chen ldquoA fuzzy multi-criteria decisionmaking method for technology transfer strategy selection inbiotechnologyrdquo Fuzzy Sets and Systems vol 63 no 2 pp 131ndash139 1994

[24] G-H Tzeng T-A Shiau and J-Y Teng ldquoMultiobjectivedecision-making approach to energy supply mix decisions inTaiwanrdquo Energy Sources vol 16 no 3 pp 301ndash316 1994

[25] M T Tang andGH Tzeng ldquoA hierarchy fuzzyMCDMmethodfor studying electronic marketing strategies in the informationservice industryrdquo Journal of International Information Manage-ment vol 8 no 1 pp 1ndash22 1998

[26] R R Yager ldquoOn ordered weighted averaging aggregationoperators in multicriteria decisionmakingrdquo IEEE Transactionson Systems Man and Cybernetics vol 18 no 1 pp 183ndash1901988

[27] M Grabisch S A Orlovski and R R Yager ldquoFuzzy aggregationof numerical preferencesrdquo in Fuzzy Sets in Decision AnalysisOperations Research and Statistics pp 31ndash68 Springer US 1988

[28] G R Amin ldquoNotes on properties of the OWAweights determi-nation modelrdquo Computers amp Industrial Engineering vol 52 no4 pp 533ndash538 2007

[29] V Torra ldquoThe weighted OWA operatorrdquo International Journalof Intelligent Systems vol 12 no 2 pp 153ndash166 1997

[30] AValls andV Torra ldquoUsing classification as an aggregation toolin MCDMrdquo Fuzzy Sets and Systems vol 115 no 1 pp 159ndash1682000

[31] D Nettleton and J Muniz ldquoProcessing and representation ofmeta-data for sleep apnea diagnosis with an artificial intelli-gence approachrdquo International Journal of Medical Informaticsvol 63 no 1-2 pp 77ndash89 2001

[32] C-S Yu ldquoA GP-AHP method for solving group decision-making fuzzy AHP problemsrdquo Computers amp OperationsResearch vol 29 no 14 pp 1969ndash2001 2002

[33] Y Ju A Wang and X Liu ldquoEvaluating emergency responsecapacity by fuzzy AHP and 2-tuple fuzzy linguistic approachrdquoExpert Systems with Applications vol 39 no 8 pp 6972ndash69812012

[34] R A Ribeiro ldquoFuzzy multiple attribute decision making areview and new preference elicitation techniquesrdquo Fuzzy Setsand Systems vol 78 no 2 pp 155ndash181 1996

[35] R R Levary and K Wan ldquoA simulation approach for handlinguncertainty in the analytic hierarchy processrdquo European Journalof Operational Research vol 106 no 1 pp 116ndash122 1998

[36] W Ogryczak and T Sliwinski ldquoOn efficient WOWA optimiza-tion for decision support under riskrdquo International Journal ofApproximate Reasoning vol 50 no 6 pp 915ndash928 2009

[37] S Wasserman and K Faust Social Network Analysis Methodsand Applications Cambridge University Press 1994

[38] R R Yager ldquoOn the cardinality index and attitudinal characterof fuzzymeasuresrdquo International Journal of General Systems vol31 no 3 pp 303ndash329 2002

[39] R Fuller and P Majlender ldquoAn analytic approach for obtainingmaximal entropy OWA operator weightsrdquo Fuzzy Sets andSystems vol 124 no 1 pp 53ndash57 2001

[40] Y-M Wang and C Parkan ldquoA minimax disparity approach forobtaining OWA operator weightsrdquo Information Sciences vol175 no 1-2 pp 20ndash29 2005

[41] Y-M Wang Y Luo and X Liu ldquoTwo new models fordetermining OWA operator weightsrdquo Computers amp IndustrialEngineering vol 52 no 2 pp 203ndash209 2007

[42] Y P Jiang and Z P Fan Decision Theory and Method Basedon Judgement Matrix Science Press 2008 httpwwwsciencepcoms singlephpid=16934

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


could significantly affect the performance of the emergencyresponse system Using task network mapping and analysisWang et al [10] presented a method of improving the per-formance of emergency response system by taking the timefactor into consideration Modelling the emergency responsetask network is an effective way for decision support inemergencies However these studies overlooked that peopleare the ultimate decision makers who are responsible fordealing with the emergency accidents and minimizing thecasualties and property loss

Moreover some researchers studied on the effect ofhuman factors under emergency situation in UTO metrosystem For example Wang and Fang [11] presented a struc-tured procedure to analyze the error behaviors of trafficdispatcher in emergencies based on the human informationprocessing theory and the modified task analysis frameworkKarvonen et al [12] analyzed the requirements of metrodrivers to reveal what should be provided to compensatefor the absence of driver in UTO metro system Howeverthese papers only studied the effect of human factors onsingle type position such as traffic dispatcher or driver ratherthan group decision for metro emergencies The challengesof UTO metro operation are without driver onboard howthe abnormal situation could be found out and be restored tothe normal operations and this indicates that the OperatingControl Center (OCC) should ensure the detection andmanagement of emergency situations [13] and take properemergency responses and clearance to avoid further damage

In case of any emergency in UTO metro the emergencyresponse process is to immediately organize the relatedagencies raise and dispatch various resources and developand carry out the emergency response plans with the goalof minimizing casualty and losses caused by disasters [14]The crucial point is how the dispatchers differentiate thedistinct and real information and make the proper decisionSuch decision making is an expertise balancing processwithin a number of criteria and opinions from differentdispatchers who have different knowledge about emergencyalternatives and make different contributions to differentemergency alternatives [15] Sometimes the opinions fromdifferent dispatchersrsquo conflict with each other and thereforeemergency alternative evaluation in UTO metro system isa typical group multicriteria decision-making (GMCDM)problem GMCDM is an evaluation approach to aggregatethe information of alternatives to obtain the best solution foremergency decision makers [16]

Saaty [17] proposed a method named analytic hierar-chy process (AHP) which provided a pairwise comparisonmatrix for decision makers to express their preferencesregarding multiple criteria and alternatives This method iswidely used for solving multicriteria decision-making prob-lems including planning selecting a best alternative resourceallocation and resolving conflicts [18]Nevertheless theAHPmethod is often criticized for its inability to incorporate theinherent uncertainty and imprecision associated with map-ping the decision makerrsquos perceptions to exact numbers [19]To solve this problem the fuzzy analytic hierarchy process(FAHP) used fuzzy preference relations to incorporate theambiguities and uncertainties that usually exist in human

judgment generally [20 21]The FAHP adopting the conceptsof fuzzy set theory and hierarchical structure analysis hasbeen widely employed to solve the alternative selection andjustification problem in different research areas [22ndash25]

The ordered weighted averaging (OWA) operator pro-posed by Yager [26] provided the selection of variouspreferences of decision makers from the optimistic viewto the pessimistic one [27] However it did not considerimportance weights through OWA operator Actually theweighted mean cannot be described by the arithmetic meanof OWA aggregations [28] To solve this problem Torra[29] proposed the weighted OWA (WOWA) aggregationwhich incorporated the important weighting into the OWAoperator Since WOWA operator was proposed it has beenwidely applied in the fields of multicriteria decision-making(MCDM) system and metadata aggregation problems [3031]

Great efforts have beenmade to solve GMCDMproblemsin UTO emergencies In this paper we adopted the methodof FAHP to solve the decision support under multicriteriaand employed enhanced WOWA operator to aggregate eachdecision from different decision makers in which the weightassigned to operator was one key factor for the performanceof the alternatives selection

The remainder of the paper is organized as follows Firstan overview of UTO system in China is given SecondFAHPmethod andWOWA operator are introducedThird ahybrid method combining FAHP and the enhancedWOWAoperator weights is specified This method integrates theweights applied to represent the significance level associatedwith the importance of dispatchers in a scenario of emergencyresponse task system for UTO metro system Then it ordersweights into the enhancedWOWAoperator and connects theoperator with the concept of fuzzy logic in a hierarchy patternunder the different knowledge situation of dispatcher groupFourth a case study is presented to demonstrate how theproposed method is applied to obtain the sequence order ofemergency alternatives in case of train fire occurring betweenstations Finally some conclusions are drawn

2 UTO System

We adopted the Line YanFang in Beijing as an investigationtarget which is under construction and will become thefirst UTO line regulated in automated operation in BeijingFurthermore we investigated Line 10 in Shanghai in whichthe organization has been designed for operational serviceof UTO system Based on the learning experience of Line 10in Shanghai we attended the designation and constructionprocess of the Line YanFang and discussed the new challengesin UTO metro which should be understood fully in futureoperation

The characteristics of UTO system under emergencyenvironment are that the dispatchers in OCC cannot reachavailable personnel to obtain the contingent factors of emer-gency situation remotely in a short time The factors includethe location the scope of emergency and the passengeremotion under emergency Without personnel in train anymajor functional failures or emergencies from the operated








3 Methods



1 1199092 119909

119899 (119899 ge 2) be


119877 119883times119883 rarr [0 1]


119894119895)119899times119899



119895The 119903




119895

(119909119894sim 119909119895)



119909119894(119909119895≻ 119909119894)

(3) 05 lt 119903119894119895


to 119909119895(119909119894≻ 119909119895) In particular 119903

119894119895= 1 denotes that 119909

119894is




119894119894= 05 and 119903

119894119895+

119903119895119894

= 1 for all 119894 119895 = 1 2 119899


119894119895)119899times119899



= 119903119894119896+ 05








Definition 2 Let 120572 = 1205721 1205722 120572


Vectors 119901 = 1199011 1199012 119901

119899119879 and 119908 = 119908

1 1199082 119908

119898119879


119894=0119901119894

= 1 119901119894

isin

[0 1] sum119898

119894=0119908119894= 1 119908

119894isin [0 1]


120572120590(2)

120572120590(119899)


1 1205722 120572

119899 such that 120572

120590(1)ge

120572120590(2)




1199011 1199012 119901

119899119879 and 119908 = 119908

1 1199082 119908

119898119879 The WOWA


WOWA (1205721 1205722 120572

119899) =

119899

sum

119894=0

V119894120572120590(119894)


119895le119894

119901120590(119895)


119895lt119894

119901120590(119895)

)

(1)


(119894119898sum119895le119894


lowast











1EA2 EA



119896has his


119894and



]119898times3

where 119906(119908119894119895)119899times119899





t1n t1

1

t12t1

3





Dm

t2n

t21

t22

t23

t3n

t31

t32

t33


D1 D2

D3









node of rectangle


119898


1 119905119896

2 119905

119896

119899 of




119890




IW119896= sum

119894isin119879119896

119873119896

1sum119898

119896=1119873119896

sum119895isin119873119896

1

(119889 (119905119895 119905119896

119894) 119873119896

1)

(2)


119896= 119905119896

1 119905119896

2 119905

119896






119896

119889(119905119895 119905119896




119896



119896




119896




IW1015840119896=

IW119896

sum119898

119896=1IW119896

(3)



119894and 119908




119908lowast

119902= 119876(

119902

119899) minus 119876(

(119902 minus 1)

119899)

with 119908lowast

119902ge 0

119899

sum

119902=1

119908lowast

119902= 1

(4)


119876 (119903) =

0 119903 lt 120572

119903 minus 120572

120573 minus 120572 120572 le 119903 le 120573

1 119903 gt 120573

(5)




in OCC


Step 2 Let119908119896= 1199081 1199082 119908




= 119908lowast

1 119908lowast

2 119908lowast






S1 S2 S3 S4 S5



119898119879



Step 1 119863 = 1198631 1198632 119863


dispatchers and 119875 = 119875(1)(119904)

119875(2)(119904)

119875(119898)(119904)


(119896)(119904)= 119906(119908

119894119895

119896(119904))119899times119899


119894119895


119901lowast119904

119894119895=

119898

sum

119897=0

V119897119901119897 (6)


119894119895

119896(119904) with 1 le 119896 le 119898


lowast119904= (119901lowast119904

119894119895)119899times119899



119901120591

119894119895=

3

sum

119904=0

120582119904119901lowast119904

119894119895 (7)





119903119894= 120579 (119901

120591

119894119895 119895 = 1 2 119899) =

119899

sum

119902=1

V119902119888119902

119894 119894 isin 119898 (8)


(03 08) and 119888119902


120591

119894119895| 119895 =

1 2 119899


1199031015840

119894=

119903119894

sum119899

119894=1119903119894

(9)


1015840

1 1199031015840

2 119903

1015840

119899

5 Case Study








Number Alternatives




Powerdispatcher


dispatcher



Vehicledispatcher

response goal (ge)

t1 t2

t3

t4t5 t6

t7

t8

t9

t10

t11 t12

t13

t17

t18 t19

t20

t21

t14

t16 t15



119896=

053 007 011 016 013119879



119902is


119879


and 119908lowast

119902 the aggre-


06 027 0130 0119879






119903 = 08989 07988 04394 05631 06929119879 (10)


1199031015840= 02649 02354 01295 01659 02042

119879 (11)


S1 ≻ S2 ≻ S5 ≻ S4 ≻ S3 (12)

























Opening train doors




















S1 05000 09000 09000 09000 05572S2 06340 05000 08740 09000 07680S3 04600 03000 05000 05400 02200S4 04600 01811 06480 05000 06600S5 03000 05140 06220 06220 05000




S1 05000 08740 09000 09000 05572S2 08220 05000 08200 07000 05400S3 06220 01000 05000 03000 02740S4 06220 01832 07000 05000 08220S5 03000 06480 08200 08740 05000






S1 05000 09000 09000 09000 04372S2 05800 05000 09000 07000 06600S3 04600 01000 05000 03000 05800S4 04600 01832 07000 05000 06600S5 03000 06220 07960 06220 05000



S1 05000 08922 09000 09000 05332S2 06796 05000 08630 08000 06780S3 05086 02000 05000 04200 03082S4 05086 01821 06740 05000 07086S5 03000 05758 07162 06976 05000



6 Conclusion















Appendix
















Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















3 Methods



1 1199092 119909

119899 (119899 ge 2) be


119877 119883times119883 rarr [0 1]


119894119895)119899times119899



119895The 119903




119895

(119909119894sim 119909119895)



119909119894(119909119895≻ 119909119894)

(3) 05 lt 119903119894119895


to 119909119895(119909119894≻ 119909119895) In particular 119903

119894119895= 1 denotes that 119909

119894is




119894119894= 05 and 119903

119894119895+

119903119895119894

= 1 for all 119894 119895 = 1 2 119899


119894119895)119899times119899



= 119903119894119896+ 05








Definition 2 Let 120572 = 1205721 1205722 120572


Vectors 119901 = 1199011 1199012 119901

119899119879 and 119908 = 119908

1 1199082 119908

119898119879


119894=0119901119894

= 1 119901119894

isin

[0 1] sum119898

119894=0119908119894= 1 119908

119894isin [0 1]


120572120590(2)

120572120590(119899)


1 1205722 120572

119899 such that 120572

120590(1)ge

120572120590(2)




1199011 1199012 119901

119899119879 and 119908 = 119908

1 1199082 119908

119898119879 The WOWA


WOWA (1205721 1205722 120572

119899) =

119899

sum

119894=0

V119894120572120590(119894)


119895le119894

119901120590(119895)


119895lt119894

119901120590(119895)

)

(1)


(119894119898sum119895le119894


lowast











1EA2 EA



119896has his


119894and



]119898times3

where 119906(119908119894119895)119899times119899





t1n t1

1

t12t1

3





Dm

t2n

t21

t22

t23

t3n

t31

t32

t33


D1 D2

D3









node of rectangle


119898


1 119905119896

2 119905

119896

119899 of




119890




IW119896= sum

119894isin119879119896

119873119896

1sum119898

119896=1119873119896

sum119895isin119873119896

1

(119889 (119905119895 119905119896

119894) 119873119896

1)

(2)


119896= 119905119896

1 119905119896

2 119905

119896






119896

119889(119905119895 119905119896




119896



119896




119896




IW1015840119896=

IW119896

sum119898

119896=1IW119896

(3)



119894and 119908




119908lowast

119902= 119876(

119902

119899) minus 119876(

(119902 minus 1)

119899)

with 119908lowast

119902ge 0

119899

sum

119902=1

119908lowast

119902= 1

(4)


119876 (119903) =

0 119903 lt 120572

119903 minus 120572

120573 minus 120572 120572 le 119903 le 120573

1 119903 gt 120573

(5)




in OCC


Step 2 Let119908119896= 1199081 1199082 119908




= 119908lowast

1 119908lowast

2 119908lowast






S1 S2 S3 S4 S5



119898119879



Step 1 119863 = 1198631 1198632 119863


dispatchers and 119875 = 119875(1)(119904)

119875(2)(119904)

119875(119898)(119904)


(119896)(119904)= 119906(119908

119894119895

119896(119904))119899times119899


119894119895


119901lowast119904

119894119895=

119898

sum

119897=0

V119897119901119897 (6)


119894119895

119896(119904) with 1 le 119896 le 119898


lowast119904= (119901lowast119904

119894119895)119899times119899



119901120591

119894119895=

3

sum

119904=0

120582119904119901lowast119904

119894119895 (7)





119903119894= 120579 (119901

120591

119894119895 119895 = 1 2 119899) =

119899

sum

119902=1

V119902119888119902

119894 119894 isin 119898 (8)


(03 08) and 119888119902


120591

119894119895| 119895 =

1 2 119899


1199031015840

119894=

119903119894

sum119899

119894=1119903119894

(9)


1015840

1 1199031015840

2 119903

1015840

119899

5 Case Study








Number Alternatives




Powerdispatcher


dispatcher



Vehicledispatcher

response goal (ge)

t1 t2

t3

t4t5 t6

t7

t8

t9

t10

t11 t12

t13

t17

t18 t19

t20

t21

t14

t16 t15



119896=

053 007 011 016 013119879



119902is


119879


and 119908lowast

119902 the aggre-


06 027 0130 0119879






119903 = 08989 07988 04394 05631 06929119879 (10)


1199031015840= 02649 02354 01295 01659 02042

119879 (11)


S1 ≻ S2 ≻ S5 ≻ S4 ≻ S3 (12)

























Opening train doors




















S1 05000 09000 09000 09000 05572S2 06340 05000 08740 09000 07680S3 04600 03000 05000 05400 02200S4 04600 01811 06480 05000 06600S5 03000 05140 06220 06220 05000




S1 05000 08740 09000 09000 05572S2 08220 05000 08200 07000 05400S3 06220 01000 05000 03000 02740S4 06220 01832 07000 05000 08220S5 03000 06480 08200 08740 05000






S1 05000 09000 09000 09000 04372S2 05800 05000 09000 07000 06600S3 04600 01000 05000 03000 05800S4 04600 01832 07000 05000 06600S5 03000 06220 07960 06220 05000



S1 05000 08922 09000 09000 05332S2 06796 05000 08630 08000 06780S3 05086 02000 05000 04200 03082S4 05086 01821 06740 05000 07086S5 03000 05758 07162 06976 05000



6 Conclusion















Appendix
















Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra














Definition 2 Let 120572 = 1205721 1205722 120572


Vectors 119901 = 1199011 1199012 119901

119899119879 and 119908 = 119908

1 1199082 119908

119898119879


119894=0119901119894

= 1 119901119894

isin

[0 1] sum119898

119894=0119908119894= 1 119908

119894isin [0 1]


120572120590(2)

120572120590(119899)


1 1205722 120572

119899 such that 120572

120590(1)ge

120572120590(2)




1199011 1199012 119901

119899119879 and 119908 = 119908

1 1199082 119908

119898119879 The WOWA


WOWA (1205721 1205722 120572

119899) =

119899

sum

119894=0

V119894120572120590(119894)


119895le119894

119901120590(119895)


119895lt119894

119901120590(119895)

)

(1)


(119894119898sum119895le119894


lowast











1EA2 EA



119896has his


119894and



]119898times3

where 119906(119908119894119895)119899times119899





t1n t1

1

t12t1

3





Dm

t2n

t21

t22

t23

t3n

t31

t32

t33


D1 D2

D3









node of rectangle


119898


1 119905119896

2 119905

119896

119899 of




119890




IW119896= sum

119894isin119879119896

119873119896

1sum119898

119896=1119873119896

sum119895isin119873119896

1

(119889 (119905119895 119905119896

119894) 119873119896

1)

(2)


119896= 119905119896

1 119905119896

2 119905

119896






119896

119889(119905119895 119905119896




119896



119896




119896




IW1015840119896=

IW119896

sum119898

119896=1IW119896

(3)



119894and 119908




119908lowast

119902= 119876(

119902

119899) minus 119876(

(119902 minus 1)

119899)

with 119908lowast

119902ge 0

119899

sum

119902=1

119908lowast

119902= 1

(4)


119876 (119903) =

0 119903 lt 120572

119903 minus 120572

120573 minus 120572 120572 le 119903 le 120573

1 119903 gt 120573

(5)




in OCC


Step 2 Let119908119896= 1199081 1199082 119908




= 119908lowast

1 119908lowast

2 119908lowast






S1 S2 S3 S4 S5



119898119879



Step 1 119863 = 1198631 1198632 119863


dispatchers and 119875 = 119875(1)(119904)

119875(2)(119904)

119875(119898)(119904)


(119896)(119904)= 119906(119908

119894119895

119896(119904))119899times119899


119894119895


119901lowast119904

119894119895=

119898

sum

119897=0

V119897119901119897 (6)


119894119895

119896(119904) with 1 le 119896 le 119898


lowast119904= (119901lowast119904

119894119895)119899times119899



119901120591

119894119895=

3

sum

119904=0

120582119904119901lowast119904

119894119895 (7)





119903119894= 120579 (119901

120591

119894119895 119895 = 1 2 119899) =

119899

sum

119902=1

V119902119888119902

119894 119894 isin 119898 (8)


(03 08) and 119888119902


120591

119894119895| 119895 =

1 2 119899


1199031015840

119894=

119903119894

sum119899

119894=1119903119894

(9)


1015840

1 1199031015840

2 119903

1015840

119899

5 Case Study








Number Alternatives




Powerdispatcher


dispatcher



Vehicledispatcher

response goal (ge)

t1 t2

t3

t4t5 t6

t7

t8

t9

t10

t11 t12

t13

t17

t18 t19

t20

t21

t14

t16 t15



119896=

053 007 011 016 013119879



119902is


119879


and 119908lowast

119902 the aggre-


06 027 0130 0119879






119903 = 08989 07988 04394 05631 06929119879 (10)


1199031015840= 02649 02354 01295 01659 02042

119879 (11)


S1 ≻ S2 ≻ S5 ≻ S4 ≻ S3 (12)

























Opening train doors




















S1 05000 09000 09000 09000 05572S2 06340 05000 08740 09000 07680S3 04600 03000 05000 05400 02200S4 04600 01811 06480 05000 06600S5 03000 05140 06220 06220 05000




S1 05000 08740 09000 09000 05572S2 08220 05000 08200 07000 05400S3 06220 01000 05000 03000 02740S4 06220 01832 07000 05000 08220S5 03000 06480 08200 08740 05000






S1 05000 09000 09000 09000 04372S2 05800 05000 09000 07000 06600S3 04600 01000 05000 03000 05800S4 04600 01832 07000 05000 06600S5 03000 06220 07960 06220 05000



S1 05000 08922 09000 09000 05332S2 06796 05000 08630 08000 06780S3 05086 02000 05000 04200 03082S4 05086 01821 06740 05000 07086S5 03000 05758 07162 06976 05000



6 Conclusion















Appendix
















Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










t1n t1

1

t12t1

3





Dm

t2n

t21

t22

t23

t3n

t31

t32

t33


D1 D2

D3









node of rectangle


119898


1 119905119896

2 119905

119896

119899 of




119890




IW119896= sum

119894isin119879119896

119873119896

1sum119898

119896=1119873119896

sum119895isin119873119896

1

(119889 (119905119895 119905119896

119894) 119873119896

1)

(2)


119896= 119905119896

1 119905119896

2 119905

119896






119896

119889(119905119895 119905119896




119896



119896




119896




IW1015840119896=

IW119896

sum119898

119896=1IW119896

(3)



119894and 119908




119908lowast

119902= 119876(

119902

119899) minus 119876(

(119902 minus 1)

119899)

with 119908lowast

119902ge 0

119899

sum

119902=1

119908lowast

119902= 1

(4)


119876 (119903) =

0 119903 lt 120572

119903 minus 120572

120573 minus 120572 120572 le 119903 le 120573

1 119903 gt 120573

(5)




in OCC


Step 2 Let119908119896= 1199081 1199082 119908




= 119908lowast

1 119908lowast

2 119908lowast






S1 S2 S3 S4 S5



119898119879



Step 1 119863 = 1198631 1198632 119863


dispatchers and 119875 = 119875(1)(119904)

119875(2)(119904)

119875(119898)(119904)


(119896)(119904)= 119906(119908

119894119895

119896(119904))119899times119899


119894119895


119901lowast119904

119894119895=

119898

sum

119897=0

V119897119901119897 (6)


119894119895

119896(119904) with 1 le 119896 le 119898


lowast119904= (119901lowast119904

119894119895)119899times119899



119901120591

119894119895=

3

sum

119904=0

120582119904119901lowast119904

119894119895 (7)





119903119894= 120579 (119901

120591

119894119895 119895 = 1 2 119899) =

119899

sum

119902=1

V119902119888119902

119894 119894 isin 119898 (8)


(03 08) and 119888119902


120591

119894119895| 119895 =

1 2 119899


1199031015840

119894=

119903119894

sum119899

119894=1119903119894

(9)


1015840

1 1199031015840

2 119903

1015840

119899

5 Case Study








Number Alternatives




Powerdispatcher


dispatcher



Vehicledispatcher

response goal (ge)

t1 t2

t3

t4t5 t6

t7

t8

t9

t10

t11 t12

t13

t17

t18 t19

t20

t21

t14

t16 t15



119896=

053 007 011 016 013119879



119902is


119879


and 119908lowast

119902 the aggre-


06 027 0130 0119879






119903 = 08989 07988 04394 05631 06929119879 (10)


1199031015840= 02649 02354 01295 01659 02042

119879 (11)


S1 ≻ S2 ≻ S5 ≻ S4 ≻ S3 (12)

























Opening train doors




















S1 05000 09000 09000 09000 05572S2 06340 05000 08740 09000 07680S3 04600 03000 05000 05400 02200S4 04600 01811 06480 05000 06600S5 03000 05140 06220 06220 05000




S1 05000 08740 09000 09000 05572S2 08220 05000 08200 07000 05400S3 06220 01000 05000 03000 02740S4 06220 01832 07000 05000 08220S5 03000 06480 08200 08740 05000






S1 05000 09000 09000 09000 04372S2 05800 05000 09000 07000 06600S3 04600 01000 05000 03000 05800S4 04600 01832 07000 05000 06600S5 03000 06220 07960 06220 05000



S1 05000 08922 09000 09000 05332S2 06796 05000 08630 08000 06780S3 05086 02000 05000 04200 03082S4 05086 01821 06740 05000 07086S5 03000 05758 07162 06976 05000



6 Conclusion















Appendix
















Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











119890




IW119896= sum

119894isin119879119896

119873119896

1sum119898

119896=1119873119896

sum119895isin119873119896

1

(119889 (119905119895 119905119896

119894) 119873119896

1)

(2)


119896= 119905119896

1 119905119896

2 119905

119896






119896

119889(119905119895 119905119896




119896



119896




119896




IW1015840119896=

IW119896

sum119898

119896=1IW119896

(3)



119894and 119908




119908lowast

119902= 119876(

119902

119899) minus 119876(

(119902 minus 1)

119899)

with 119908lowast

119902ge 0

119899

sum

119902=1

119908lowast

119902= 1

(4)


119876 (119903) =

0 119903 lt 120572

119903 minus 120572

120573 minus 120572 120572 le 119903 le 120573

1 119903 gt 120573

(5)




in OCC


Step 2 Let119908119896= 1199081 1199082 119908




= 119908lowast

1 119908lowast

2 119908lowast






S1 S2 S3 S4 S5



119898119879



Step 1 119863 = 1198631 1198632 119863


dispatchers and 119875 = 119875(1)(119904)

119875(2)(119904)

119875(119898)(119904)


(119896)(119904)= 119906(119908

119894119895

119896(119904))119899times119899


119894119895


119901lowast119904

119894119895=

119898

sum

119897=0

V119897119901119897 (6)


119894119895

119896(119904) with 1 le 119896 le 119898


lowast119904= (119901lowast119904

119894119895)119899times119899



119901120591

119894119895=

3

sum

119904=0

120582119904119901lowast119904

119894119895 (7)





119903119894= 120579 (119901

120591

119894119895 119895 = 1 2 119899) =

119899

sum

119902=1

V119902119888119902

119894 119894 isin 119898 (8)


(03 08) and 119888119902


120591

119894119895| 119895 =

1 2 119899


1199031015840

119894=

119903119894

sum119899

119894=1119903119894

(9)


1015840

1 1199031015840

2 119903

1015840

119899

5 Case Study








Number Alternatives




Powerdispatcher


dispatcher



Vehicledispatcher

response goal (ge)

t1 t2

t3

t4t5 t6

t7

t8

t9

t10

t11 t12

t13

t17

t18 t19

t20

t21

t14

t16 t15



119896=

053 007 011 016 013119879



119902is


119879


and 119908lowast

119902 the aggre-


06 027 0130 0119879






119903 = 08989 07988 04394 05631 06929119879 (10)


1199031015840= 02649 02354 01295 01659 02042

119879 (11)


S1 ≻ S2 ≻ S5 ≻ S4 ≻ S3 (12)

























Opening train doors




















S1 05000 09000 09000 09000 05572S2 06340 05000 08740 09000 07680S3 04600 03000 05000 05400 02200S4 04600 01811 06480 05000 06600S5 03000 05140 06220 06220 05000




S1 05000 08740 09000 09000 05572S2 08220 05000 08200 07000 05400S3 06220 01000 05000 03000 02740S4 06220 01832 07000 05000 08220S5 03000 06480 08200 08740 05000






S1 05000 09000 09000 09000 04372S2 05800 05000 09000 07000 06600S3 04600 01000 05000 03000 05800S4 04600 01832 07000 05000 06600S5 03000 06220 07960 06220 05000



S1 05000 08922 09000 09000 05332S2 06796 05000 08630 08000 06780S3 05086 02000 05000 04200 03082S4 05086 01821 06740 05000 07086S5 03000 05758 07162 06976 05000



6 Conclusion















Appendix
















Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












S1 S2 S3 S4 S5



119898119879



Step 1 119863 = 1198631 1198632 119863


dispatchers and 119875 = 119875(1)(119904)

119875(2)(119904)

119875(119898)(119904)


(119896)(119904)= 119906(119908

119894119895

119896(119904))119899times119899


119894119895


119901lowast119904

119894119895=

119898

sum

119897=0

V119897119901119897 (6)


119894119895

119896(119904) with 1 le 119896 le 119898


lowast119904= (119901lowast119904

119894119895)119899times119899



119901120591

119894119895=

3

sum

119904=0

120582119904119901lowast119904

119894119895 (7)





119903119894= 120579 (119901

120591

119894119895 119895 = 1 2 119899) =

119899

sum

119902=1

V119902119888119902

119894 119894 isin 119898 (8)


(03 08) and 119888119902


120591

119894119895| 119895 =

1 2 119899


1199031015840

119894=

119903119894

sum119899

119894=1119903119894

(9)


1015840

1 1199031015840

2 119903

1015840

119899

5 Case Study








Number Alternatives




Powerdispatcher


dispatcher



Vehicledispatcher

response goal (ge)

t1 t2

t3

t4t5 t6

t7

t8

t9

t10

t11 t12

t13

t17

t18 t19

t20

t21

t14

t16 t15



119896=

053 007 011 016 013119879



119902is


119879


and 119908lowast

119902 the aggre-


06 027 0130 0119879






119903 = 08989 07988 04394 05631 06929119879 (10)


1199031015840= 02649 02354 01295 01659 02042

119879 (11)


S1 ≻ S2 ≻ S5 ≻ S4 ≻ S3 (12)

























Opening train doors




















S1 05000 09000 09000 09000 05572S2 06340 05000 08740 09000 07680S3 04600 03000 05000 05400 02200S4 04600 01811 06480 05000 06600S5 03000 05140 06220 06220 05000




S1 05000 08740 09000 09000 05572S2 08220 05000 08200 07000 05400S3 06220 01000 05000 03000 02740S4 06220 01832 07000 05000 08220S5 03000 06480 08200 08740 05000






S1 05000 09000 09000 09000 04372S2 05800 05000 09000 07000 06600S3 04600 01000 05000 03000 05800S4 04600 01832 07000 05000 06600S5 03000 06220 07960 06220 05000



S1 05000 08922 09000 09000 05332S2 06796 05000 08630 08000 06780S3 05086 02000 05000 04200 03082S4 05086 01821 06740 05000 07086S5 03000 05758 07162 06976 05000



6 Conclusion















Appendix
















Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Number Alternatives




Powerdispatcher


dispatcher



Vehicledispatcher

response goal (ge)

t1 t2

t3

t4t5 t6

t7

t8

t9

t10

t11 t12

t13

t17

t18 t19

t20

t21

t14

t16 t15



119896=

053 007 011 016 013119879



119902is


119879


and 119908lowast

119902 the aggre-


06 027 0130 0119879






119903 = 08989 07988 04394 05631 06929119879 (10)


1199031015840= 02649 02354 01295 01659 02042

119879 (11)


S1 ≻ S2 ≻ S5 ≻ S4 ≻ S3 (12)

























Opening train doors




















S1 05000 09000 09000 09000 05572S2 06340 05000 08740 09000 07680S3 04600 03000 05000 05400 02200S4 04600 01811 06480 05000 06600S5 03000 05140 06220 06220 05000




S1 05000 08740 09000 09000 05572S2 08220 05000 08200 07000 05400S3 06220 01000 05000 03000 02740S4 06220 01832 07000 05000 08220S5 03000 06480 08200 08740 05000






S1 05000 09000 09000 09000 04372S2 05800 05000 09000 07000 06600S3 04600 01000 05000 03000 05800S4 04600 01832 07000 05000 06600S5 03000 06220 07960 06220 05000



S1 05000 08922 09000 09000 05332S2 06796 05000 08630 08000 06780S3 05086 02000 05000 04200 03082S4 05086 01821 06740 05000 07086S5 03000 05758 07162 06976 05000



6 Conclusion















Appendix
















Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
































Opening train doors




















S1 05000 09000 09000 09000 05572S2 06340 05000 08740 09000 07680S3 04600 03000 05000 05400 02200S4 04600 01811 06480 05000 06600S5 03000 05140 06220 06220 05000




S1 05000 08740 09000 09000 05572S2 08220 05000 08200 07000 05400S3 06220 01000 05000 03000 02740S4 06220 01832 07000 05000 08220S5 03000 06480 08200 08740 05000






S1 05000 09000 09000 09000 04372S2 05800 05000 09000 07000 06600S3 04600 01000 05000 03000 05800S4 04600 01832 07000 05000 06600S5 03000 06220 07960 06220 05000



S1 05000 08922 09000 09000 05332S2 06796 05000 08630 08000 06780S3 05086 02000 05000 04200 03082S4 05086 01821 06740 05000 07086S5 03000 05758 07162 06976 05000



6 Conclusion















Appendix
















Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













S1 05000 09000 09000 09000 04372S2 05800 05000 09000 07000 06600S3 04600 01000 05000 03000 05800S4 04600 01832 07000 05000 06600S5 03000 06220 07960 06220 05000



S1 05000 08922 09000 09000 05332S2 06796 05000 08630 08000 06780S3 05086 02000 05000 04200 03082S4 05086 01821 06740 05000 07086S5 03000 05758 07162 06976 05000



6 Conclusion















Appendix
















Acknowledgments


References



















































Volume 2014




Journal of











Journal of


Function Spaces






Algebra























Acknowledgments


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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