Junzo Watada - Botho University | Welcome · 2017-09-28 · Junzo Watada Oct. 19, 2012 Botho Colledge Conference 2012 LP Problem Vagueness upper bound lower bound coefficient 24 (

Junzo WatadaThe Concept and Progress of Fuzzy

Regression AnalysisThe Formation of

Fuzzy Variable Model and Its Applications

Junzo WatadaGraduate School of ISP

Waseda University

[email protected]

Botho CollegeInterdisciplinary Research Conference 2012

Botho Education Park, Kgale, Gaborone18 th and 19 th October, 2012

Junzo Watada

Fuzzy Sets

Oct. 19, 2012 Botho Collage Conference 201２ 2

Junzo Watada

Fuzzy Sets Lotfi A. Zadeh

June 27, 2012 at & CAIRO, UTM 3

Oil Palm Fruit Evaluation


Oil Palm Fruit Anatomy

DECISION MAKING

QUALITY INSPECTION

Graded Fruit

Condition

FruitletsColor

Surface

(MPOB, 2003)

Junzo Watada


Junzo Watada

Oct. 19, 2012 100th meetinhBotho Collage Conference 201２ 6

Statistical Regression Analysis

-1950s Fransis Golton

- The solution can be obtained by Normal Equation

0

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Junzo WatadaDr. Hideo Tanaka

At Grand Hotel,

Taipei in 1983


Junzo Watada


Junzo Watada１． Fuzzy Regression Analysis


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Upper Bound

Lower Bound

Possibility

Junzo WatadaFuzzy Regression Model


nicaA iii ,,2,1,

1.0

c ca

n

n

n

xxxcccaaa

Y

,,,,,,,,,

,,

21

21

21

xca

xcaxxcaAx



Ax nn xAxAxAY 2211

where nicaA iii ,,2,1,

n

n

n

xxxcccaaa

Y

,,,,,,,,,

,,

21

21

21

xca

xcaxxcaAx



0

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250

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0 10 20 30 40 50 60 70 80 90 100

Upper Bound

Lower Bound

Possibility

Junzo Watada

Fuzzy Regression Model


LP Problem

),,2,1(0

tosubject

minimize1

mj

xxy

xxy

x

jjj

jjj

m

jj

c

ca

ca

c Vagueness

upperbound

lowerbound

coefficient

13

Junzo Watada

Introduction

• Hybrid uncertainty is a pivotal factor in building models.

• That is, fuzziness, possibility and probability

• Several models are illustrated here to understand fuzzy random variables.

Oct. 19, 2012 Botho Colledge Conference 2012 14

Junzo Watada


Junzo Watada

Evaluation


Measure some dimensions of the target apparatus

Measure some features of the target subject

Measure some dimensions of the target car

Thes

e nu

mer

ical

mea

sure

men

ts d

o no

t exp

ress

th

eir b

eaut

ifuln

ess.

Usu

ally

the

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ness

sh

ould

be

expr

esse

d us

ing

hum

an li

ngui

stic

ex

pres

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the

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ion

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atur

es.


Oct. 19, 2012 CJS2011 at Hejnice, Czech Republic 1717


DECISION MAKING

QUALITY INSPECTION

Graded Fruit

Condition

FruitletsColor

Surface

(MPOB, 2003)

Junzo Watada


Junzo WatadaLinguistic Evaluation

Oct. 19, 2012 19

Junzo Watada

2. Summery of Fuzzy Regression Models


Junzo WatadaFuzzy Linear Function


numberfuzzyare,where, 10110 AAxAAY

n

n

n

xxxcccaaa

Y

,,,,,,,,,

,,

21

21

21

xca

xcaxxcaAx

0

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0 10 20 30 40 50 60 70 80 90

regression

Possibility110 xAAY

0A

1x

y

Junzo WatadaFuzzy Linear Function



n

n

n

xxxxccccaaaa

Y

,,,,,,,,,,,,,,

210

210

210

xca

xcaxxcaAx

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regression

Possibility

110 xAAY

0A

1x

x cxa

x cxa

y

y

y

Junzo WatadaFuzzy Regression Analysis of Crisp Data



n

n

n

xxxcccaaa

Y

,,,,,,,,,

,,

21

21

21

xca

xcaxxcaAx

0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90

Possibility

110 xAAY

1x

y

x cxa

x cxa

y

y

ii y,x

Junzo Watada

Oct. 19, 2012 Botho Colledge Conference 2012

LP Problem

Vagueness

upper bound

lower boundcoefficient

24

),,2,1(0

tosubject

minimize1

mj

y

y

jjj

jjj

m

jj

c

x cxa

x cxa

xc

[001] H. Tanaka, S. Uejima and K. Asai, “Linear Regression Analysis with Fuzzy Model,“ IEEE Transactions on Systems, Man and Cybernetics, 12(6), 903-907, 1982.

[042] H. Tanaka, Junzo Watada, Possibilistic linear systems and their application, Int. J. Fuzzy Sets and Systems, Vol. 27, No. 3, pp. 275--289, 1988.

[044] H. Tanaka, I. Hayashi and Junzo Watada, Possibilistic linear regression for fuzzy data, European J. of Operational Research, Vol. 40, No. 3, pp. 389--396, 1989.

Fuzzy Regression Analysis of Crisp Data

Junzo Watada


2.1. Crisp Data

x y

1 x1 y1

2 x2 y2

n xn yn

Junzo WatadaFuzzy Regression Analysis of Crisp Data



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250

300

0 10 20 30 40 50 60 70 80 90

Possibility

110 xAAY

1x

y

),,2,1( mj

y

y

jjj

jjj

x cxa

x cxa

x cxa

x cxa

y

y

ii y,x

Junzo Watada


LP Problem

Vagueness

upper bound

lower bound

coefficient

27

),,2,1(0

tosubject

minimize1

mj

y

y

jjj

jjj

m

jj

c

x cxa

x cxa

xc

Fuzzy Regression Analysis of Crisp Data

Junzo Watada


2.2. Y values are fuzzy

1 x1

2 x2

n xn

x ),( YYY

),( 111 YYY

),( 222 YYY

),( nnn YYY

Junzo WatadaFuzzy Regression Analysis of Fuzzy Data (Y)



0

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200

250

300

0 10 20 30 40 50 60 70 80 90 100

Possibility

110 xAAY

1x

y

),,2,1( mj

Y

Y

jjj

jjj

x cxa

x cxa

x cxa

x cxa

y

y

ii Y,x

Junzo Watada


LP Problem

Vagueness

upper bound


30

),,2,1(0

tosubject

minimize1

mj

Y

Y

jjj

jjj

m

jj

c

x cxa

x cxa

xc

Fuzzy Regression Analysis of Fuzzy Data (Y)



[067] Y. Toyoura, M. Kambara, M. Uemura, T. Miyake, K. Kawasaki and Junzo Watada, Evaluation of Fuzzy Regression Analysis and Its Application to Oral Age Model, Official Journal of Biomedical Fuzzy Systems Association, Vol. 6, No. 1, pp. 41--49, 2000.

[191] Junzo Watada, Fuzzy Regression Analysis of Software Bug Structure, 3rd Czech-Japan Seminar on Data Analysis and Decision Making under uncertainty, at Osaka university, 2000.10

[231] Junzo Watada, Recent Development of Fuzzy Regression Model, Proceedings, the 6th Czech-Japan Seminar, Valtice, Czech Republic., pp. -, 2003.9

Junzo Watada


3 X and Y are Fuzzy Data

1

2

n

),( YYY

),( 111 YYY

),( 222 YYY

),( nnn YYY

),( XXX

),( 111 XXX

),( 222 XXX

),( nnn XXX

(-5,-4)X(-3,-2)=(8,15)

(-5,-4)X(2,3)=(-15,-8)

(4,5)X(2,3)=(8,15)

Junzo WatadaFuzzy Regression Analysis of Fuzzy-Fuzzy Data



0

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100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

Possibility

110 xAAY

1x

y

X cXa

X cXa

Y

Y

ii Y,X

?

How to solve this fuzzy regression model

?(-5,-4)X(-3,-2)=(8,15)

(-5,-4)X(2,3)=(-15,-8)

(4,5)X(2,3)=(8,15)

Junzo Watada

[J053] Junzo Watada, Hideo Tanaka, Kiyoji Asai, "Fuzz Quantification Model Type I, Japan Society of Behavioral Metrics, Vol. 11, No. 1, pp. 66--73, 1984 in Japanese.

[B023] Junzo Watada, Applied Fuzzy System, Ed. by Toshiro Terano, Kiyoji Asai, Michio Sugeno, Chapter 5 Applications in Business, 5. 5 Multiattribute Decision-Making, AP Professional, pp. 244--252, 1994.5

[J159] Junzo Watada, Shuming Wang and Witold Pedrycz, Building Confidence-Interval-Based Fuzzy Random Regression Models, IEEE Trans. Fuzzy Systems, vol. 17, issue 6, pp. 1273-1283, Dec. 2009.

[J073] Yabuuchi, Y., Watada, J., Fuzzy robust regression analysis based on a hyper elliptic function, Journal of the Operations Research Society of Japan 39 (4), pp. 512-524, 1996

[J170] Azizul Azhar Ramli, Junzo Watada, and Witold Pedrycz, Performance Measurement in Manufacturing Enterprises: New Paradigm on Intelligent Data Analysis (IDA) Implementation, JCSES, Accepted 2010

[J182] Azizul Azhar Ramli, Junzo Watada, Witold Pedrycz: Real-Time Fuzzy Regression Analysis: A Convex Hull Approach. European Journal of Operational Research, vol. 210, issue 3, pp. 606-617 (2011)

[185] Yoshiyuki Yabuuchi and Junzo Watada, Fuzzy Robust Regression Model by Possibility Maximization, JACIII, Accepted, 2011


Junzo Watada


4. Fuzzy-Fuzzy Random Data

1

2

n

),( YYY

),( 111 YYY

),( 222 YYY

),( nnn YYY

),( XXX

),( 111 XXX

),( 222 XXX

),( nnn XXX

Junzo Watada


Junzo WatadaFuzzy Regression Analysis of Fuzzy Random Data



0

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100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

Possibility

110 xAAY

1x

y

X cXa

X cXa

Y

Y

ii Y,X?How to solve this fuzzy regression model

Junzo Watada


[Cxxx] Junzo Watada, Shuming Wang and Witold Pedrycz, Building a fuzzy random regression model with confidence interval, Proc. of the 11th Czech-Japan Seminar on Data Analysis and Decision Making under Uncertainty, Japan, pp. 39-44, 2008.

[J159] Junzo Watada, Shuming Wang and Witold Pedrycz, Building Confidence-Interval-Based Fuzzy Random Regression Models, IEEE Trans. Fuzzy Systems, vol. 17, issue 6, pp. 1273-1283, Dec. 2009.

[B038] Junzo Watada, Shuming Wang, and Witold Pedrycz, "Formulation of Fuzzy Random Regression Model," In: (Eds) by Antonio E.B. Ruano and Annamaria R. Varkonyi-Koczy (editors), New Advances in Intelligent Signal Processing on occasion of the ten years existence of the IEEE WISP (IEEE International Symposium on Intelligent Signal Processing) series, in Studies in Computational Intelligence, Springer

[B035] Junzo Watada, Shuming Wang, Regression model based on fuzzy random variables, Chapter 26, Seising Rodulf (Ed.), Views on Fuzzy Sets and Systems from Different Perspectives - Philosophy and Logic, Criticisms and Applications -, Studies in Fuzziness and Soft Computing, Volume 243, Spring-Verlag, Berlin, pp. 533-546, 2009.

Junzo Watada


5. Linguistic Data

1

2

n

),( YYY

),( 111 YYY

),( 222 YYY

),( nnn YYY

),( XXX

),( 111 XXX

),( 222 XXX

),( nnn XXX ?

How to solve this Linguistic regression model

Junzo WatadaNumerical Example


TotalTraining Corrosion St. Cracking St. Loading and Env. State Assessment

Sample X1 X2 X3 Y

1 extremely good extremely bad 　　　　below normal not safe

2 bad very bad 　　　　below normal not safe

3 very bad very bad 　　　　below normal not safe 4 very bad very good 　　　　below normal questionable5 good extremely good 　　　　below normal safe 6 good bad 　　　　normal not safe7 bad very bad 　　　　normal not safe

8 very bad good 　　　　normal not safe

9 bad very good 　　　　normal questionable10 very bad very good 　　　　normal questionable11 extremely good bad 　　　　severe not safe12 very good bad 　　　　severe not safe

13 good very bad 　　　　severe not safe

14 very bad good 　　　　severe not safe

15 very good good 　　　　severe not safe

16 very good very good 　　　　severe questionable

Attributes

Junzo WatadaFuzzy Regression Analysis of Linguistic Data



0

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250

300

0 10 20 30 40 50 60 70 80 90 100

Possibility

110 xAAY

1x

y

X cXa

X cXa

Y

Y

ii Y,X?

How to solve this linguistic regression model

?

Junzo Watada

[C204] Watada, J., Fu, K.S., Yao, J.T.P., DAMAGE ASSESSMENT USING FUZZY MULTIVARIANT ANALYSIS., Purdue University, School of Civil Engineering, Structural Engineering (Technical Report) CE-STR, 1984

[C209] A. Hinkle, Junzo Watada and Junzo T. P. Yao, Linguistic Assessment of Fatigue Damage, Proceeding, North American Fuzzy Information Processing Society, at New Orleans, 1986.7

[B031] Junzo Watada and Witold Pedrycz, A Fuzzy Regression Approach to Acquisition of Linguistic Rules, Chapter 32, Witold Pedrycz, Andrzej Skowron and Vladik Kreinovich (Eds.), Handbook of Granular Computing, John Wiley & Sons, Chichester, Chapter 32, pp. 719-740, July 2008.


Junzo Watada


5. Linguistic Random Data

1

2

n

),( YYY

),( 111 YYY

),( 222 YYY

),( nnn YYY

),( XXX

),( 111 XXX

),( 222 XXX

),( nnn XXX ?

How to solve this Linguistic Random regression model


Oct. 19, 2012 44

Junzo WatadaFuzzy Regression Analysis of Linguistic Random Data



0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

Possibility

110 xAAY

1x

y

X cXa

X cXa

Y

Y

ii Y,X?

How to solve this linguistic random regression model ?

Junzo Watada3． Fuzzy Regression Analysis


Upper Bound

Lower Bound0

50

100

150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

Possibility

[001] H. Tanaka, S. Uejima and K. Asai, “Linear Regression Analysis with Fuzzy Model,“ IEEE Transactions on Systems, Man and Cybernetics, 12(6), 903-907, 1982.

[042] H. Tanaka, Junzo Watada, Possibilistic linear systems and their application, Int. J. Fuzzy Sets and Systems, Vol. 27, No. 3, pp. 275--289, 1988.

[044] H. Tanaka, I. Hayashi and Junzo Watada, Possibilistic linear regression for fuzzy data, European J. of Operational Research, Vol. 40, No. 3, pp. 389--396, 1989.



Ax nn xAxAxAY 2211

where nicaA iii ,,2,1,

n

n

n

xxxcccaaa

Y

,,,,,,,,,

,,

21

21

21

xca

xcaxxcaAx

[067] Y. Toyoura, M. Kambara, M. Uemura, T. Miyake, K. Kawasaki and Junzo Watada, Evaluation of Fuzzy Regression Analysis and Its Application to Oral Age Model, Official Journal of Biomedical Fuzzy Systems Association, Vol. 6, No. 1, pp. 41--49, 2000.

[191] Junzo Watada, Fuzzy Regression Analysis of Software Bug Structure, 3rd Czech-Japan Seminar on Data Analysis and Decision Making under uncertainty, at Osaka university, 2000.10[

231] Junzo Watada, Recent Development of Fuzzy Regression Model, Proceedings, the 6th Czech-Japan Seminar, Valtice, Czech Republic., pp. -, 2003.9

1.0

c ca

Junzo Watada



LP Problem

Vagueness

upper bound


48

[074] Yoshihiro Toyoura, Junzo Watada, Yoshiyuki Yabuuchi, Hajime Ikegame, Seiichi Sato, Katsuhiko Watanabe, Masahiro Tohyama, Fuzzy Regression Analysis of Software Bug Structure, Central European Journal of Operations Research(CEOR), Vol. 12, No. 1, pp. 13-23, 2004.2.

[253] Yoshiyuki Yabuuchi & Junzo Watada, Possibilistic Forecasting Model and Its Application to Analyze the Economy in Japan, Knowledge-Based Intelligent Information Engineering Systems, Springer, Vol. LNCS 3215No., pp. 151-158, 2004.9

[293] Yoshiyuki Yabuuchi, Junzo Watada, Model Building Based on Central Position for a Fuzzy Regression Model, Proceedings, CzJp2006, Czech Japan Seminar 2006, pp. 114-119, Aug 18 (Fri)- 22 (Tue) 2006., pp. 114-229, 2006.

),,2,1(0

tosubject

minimize1

mj

xxy

xxy

x

jjj

jjj

m

jj

c

ca

ca

c

Junzo WatadaRegression Analysis based on Convex Hull

[193] Y. Toyoura, Junzo Watada, Efficient Fuzzy Regression Model based on Convex Hull, 3rd Czech-Japan Seminar on Data Analysis and Decision Making under uncertainty, at Osaka university, 2000.10

[073] Y. Toyoura, Junzo Watada, Efficient Fuzzy Regression Model based on Convex Hull, Central European Journal of Operations Research(CEOR), 2002.


Robust Regression Analysis [058] Yoshiyuki Yabuuchi, Junzo Watada, “Fuzzy Robust Regression Analysis Based on

Ecrisp Function,” Japan Society Journal of Operations Research, Vol. 39, No. 4, pp. 512--524, 1996.12

[111] Kunio Shibata, Junzo Watada, Yoshiyuki Yabuuchi, “A Fuzzy Robust Regression Analysis Approach to Evaluation of Electronic Apparatus Industry In Japan ,” Japan Society of Management Engineering, 2007

Junzo WatadaSwitching Regression Analysis

[169] Junzo Watada and Hirohito Mizunuma, Fuzzy Switching Regression Model based on Genetic Algorithm, Invited Proceeding, The 7th International Fuzzy Systems Association World Congress(IFSA'97) in Prague, Czech Republic, 1997.6

[071] Junzo Watada, Y. Toyoura, Formulation of Fuzzy Switching Auto-Regression Model, International Journal of Chaos Theory and Applications,, Vol. 7, No. 1,2, pp. 67--76, 2002.7

[086] 薮内賢之, 和多田淳三, ファジィスイッチング回帰モデルの構成 (解説）, 日本知能情報ファジィ学会誌, Vol. 16, No. 1, pp. 53-59, 2004.12


Auto Regression Analysis[076] Junzo Watada, Y. Toyoura, Formulation of Fuzzy Switching Auto-Regression Model,

International Journal of Chaos Theory and Applications, Vol. 7, No. 1, 2, pp. 67-76, 2002.7

[215] Yoshiyuki Yabuuchi, Yoshihiro Toyoura & Junzo Watada, Fuzzy AR Model of Stock Price, Proceedings, 5th Czech-Japan Seminar (CZJP2002), at Koyasan, ., pp. 127-132, 2002.9

Junzo WatadaTime-series Analsysis

[034] 和多田淳三、田中英夫、横山宏、浅居喜代治, ファジィ時系列モデルと予測問題への応用, 日本経営工学会, Vol. 34, No. 3, pp. 180-186, 1983.8

[153] Junzo Watada, H. Tanaka and K. Asai, Analysis of Time-Series Data by Possibilistic Model, Processing, Int.Workshop on Fuzzy System Applications, at Fukuoka, pp. 228--229, 1988.8

[015] J. Watada, Fuzzy Regression Analysis, J. Kacprzyk & M. Fedrizzi eds., Fuzzy time-series analysis and forecasting of sales , Vol.ume, Omnitech Press, Warsaw, Poland, pp. 211--217, 1992.5

[021] Junzo Watada, Fuzzy Information Engineering, ed. by D. Duboir and M. M. Yager, Possibilistic Time-series Analysis and its analysis of Consumption, John Wiley & Sons, Inc., pp. 187--200, 1996.4


Junzo Watada


4. Fuzzy-Fuzzy Random Data

Junzo Watada


Junzo Watada


Junzo Watada


Junzo Watada


Junzo Watada


Junzo Watada


Junzo Watada


Junzo Watada




0

50

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150

200

250

300

0 10 20 30 40 50 60 70 80 90 100

Upper Bound

Lower Bound

Possibility

Junzo Watada


Junzo Watada


Junzo Watada


Junzo Watada


Junzo Watada


Junzo Watada


Junzo Watada





Sample X1 X2 X3 Y










Attributes

5. Linguistic Data

Junzo Watada

[C204] Watada, J., Fu, K.S., Yao, J.T.P., DAMAGE ASSESSMENT USING FUZZY MULTIVARIANT ANALYSIS., Purdue University, School of Civil Engineering, Structural Engineering (Technical Report) CE-STR, 1984

[C209] A. Hinkle, Junzo Watada and Junzo T. P. Yao, Linguistic Assessment of Fatigue Damage, Proceeding, North American Fuzzy Information Processing Society, at New Orleans, 1986.7

[B031] Junzo Watada and Witold Pedrycz, A Fuzzy Regression Approach to Acquisition of Linguistic Rules, Chapter 32, Witold Pedrycz, Andrzej Skowron and Vladik Kreinovich (Eds.), Handbook of Granular Computing, John Wiley & Sons, Chichester, Chapter 32, pp. 719-740, July 2008.



Oct. 19, 2012 71

5. Linguistic Random Data

Junzo Watada

3．Linguistic Regression Model


Variable

Lnumber(visiting customers) = “bad”

Lvolume(production) = “extremely bad”

πnumber(visiting customers) ≡ πstate(number)≡U(bad)

Possibility

Fuzzy number




Sample X1 X2 X3 Y










Attributes

Junzo Watada

Linguistic Variable


（1） Translation

1.0

0.00.0 0.2 0.4 0.6 0.8 1.0

extremelygood

verygood

good bad verybad

extremelybad

Deg

ree

Fuzzy Number

)15.0,15.0,00.1(

)15.0,15.0,80.0(

)15.0,15.0,60.0(

)15.0,15.0,40.0(

)15.0,15.0,20.0(

)15.0,00.0,00.0(

)badextremely (

)badvery (

)bad(

)good(

)goodvery (

)goodextremely (

UUUUUU

Dictionary




Sample X1 X2 X3 Y

1 (0.00,0.00,0.15) (1.00,0.15,0.15) (0.00,0.00,0.40) (1.00,0.40,0.00)2 (0.60,0.15,0.15) (0.80,0.15,0.15) (0.00,0.00,0.40) (1.00,0.40,0.00)3 (0.80,0.15,0.15) (0.80,0.15,0.15) (0.00,0.00,0.40) (1.00,0.40,0.00)4 (0.80,0.15,0.15) (0.20,0.15,0.15) (0.00,0.00,0.40) (0.50,0.20,0.20)5 (0.40,0.15,0.15) (0.00,0.00,0.15) (0.00,0.00,0.40) (0.00,0.00,0.40)6 (0.40,0.15,0.15) (0.60,0.15,0.15) (0.50,0.20,0.20) (1.00,0.40,0.00)7 (0.60,0.15,0.15) (0.80,0.15,0.15) (0.50,0.20,0.20) (1.00,0.40,0.00)8 (0.80,0.15,0.15) (0.40,0.15,0.15) (0.50,0.20,0.20) (1.00,0.40,0.00)9 (0.60,0.15,0.15) (0.20,0.15,0.15) (0.50,0.20,0.20) (0.50,0.20,0.20)10 (0.80,0.15,0.15) (0.20,0.15,0.15) (0.50,0.20,0.20) (0.50,0.20,0.20)11 (0.00,0.00,0.15) (0.60,0.15,0.15) (1.00,0.40,0.00) (1.00,0.40,0.00)12 (0.20,0.15,0.15) (0.60,0.15,0.15) (1.00,0.40,0.00) (1.00,0.40,0.00)13 (0.40,0.15,0.15) (0.80,0.15,0.15) (1.00,0.40,0.00) (1.00,0.40,0.00)14 (0.80,0.15,0.15) (0.40,0.15,0.15) (1.00,0.40,0.00) (1.00,0.40,0.00)15 (0.20,0.15,0.15) (0.40,0.15,0.15) (1.00,0.40,0.00) (1.00,0.40,0.00)16 (0.20,0.15,0.15) (0.20,0.15,0.15) (1.00,0.40,0.00) (0.50,0.20,0.20)

Attributes

Junzo WatadaProcess of Linguistic Regression Model


UUU k,,,21

LLL k,, ,21

Uw

Translation EstimationVocabularyMatching

AttributesFuzzy Number

Total AssessmentFuzzy Number

Total AssessmentLinguistic Words

AttributesLinguistic Words

Dictionary

Lw

),,,(21

UUUV LLLfL kw

[146] A. Hinkle, Junzo Watada and Junzo T. P. Yao, Linguistic Assessment of Fatigue Damage, Proceeding, North American Fuzzy Information Processing Society, at New Orleans, 1986.7

[077] Junzo Watada, T. Watanabe, Formulation of Linguistic Regression Model Based on Natural Words, Journal of Intelligent and Fuzzy Systems., pp. 1-15, 2002.

[211] Junzo Watada, T. Watanabe, Formulation of Linguistic Regression Model Base on Natural Words, Journal of Intelligent and Fuzzy Systems, pp. 1--15, 2002.

[084] Y. Toyoura, J. Watada, M. Khalid, & R. Yusof, Formulation of linguistic regression model based on natural words, Soft Computing Journal, Vol. 8, No. 10, pp. 681-688, 2004.11

Junzo Watada

Process of Linguistic Regression Model


UUU k,,,21

LLL k,, ,21

Uw


AttributesFuzzy Number Total Assessment

Fuzzy Number

Total AssessmentLinguistic WordsAttributes

Linguistic Words

Dictionary

Lw

)L,,L,Lf(L UUUVkw

21

Junzo Watada

Linguistic Regression


（2） K

f LLL U,,U,UV21

Junzo Watada

Process of Linguistic Regression Model


UUU k,,,21

LLL k,, ,21

Uw


AttributesFuzzy Number Total Assessment

Fuzzy Number

Total AssessmentLinguistic WordsAttributes

Linguistic Words

Dictionary

Lw

),,,(21

UUUV LLLfL kw

Junzo WatadaEvaluation of Linguistic Variable


（3） Linguistic MatchingAssign the most appropriate word to the fuzzy number in the dictionary given

)()(max maxLiWVtDW0 tt

i

1.0

0.0

0.0 0.2 0.4 0.6 0.8 1.0

extremelygood

verygood

good bad verybad

extremelybad

度合

ファジィ数

0L

1.0

0.0

0.0 0.2 0.4 0.6 0.8 1.0

extremelygood

verygood

good bad verybad

extremelybad

度合

ファジィ数

1.0

0.0

0.0 0.2 0.4 0.6 0.8 1.0

extremelygood

verygood

good bad verybad

extremelybad

度合

ファジィ数

1.0

0.0

0.0 0.2 0.4 0.6 0.8 1.0

extremelygood

verygood

good bad verybad

extremelybad

度合

ファジィ数

1.0

0.0

0.0 0.2 0.4 0.6 0.8 1.0

extremelygood

verygood

good bad verybad

extremelybad

1.0

0.0

0.0 0.2 0.4 0.6 0.8 1.0

1.0

0.0

0.0 0.2 0.4 0.6 0.8 1.0

1.0

0.0

0.0 0.2 0.4 0.6 0.8 1.0

extremelygood

verygood

good bad verybad

extremelybad

度合

ファジィ数

0L

Junzo WatadaLinguistic Regression Model


K

ii i

Kf

1)(L

)(L)(L)(L)(L

UA

U,,U,UV210

It is most important to determine an fuzzy valuation function pursued in an expert(s).

Where ω is an training sample to build a model

Two evaluations of the model are employed to determinethe optimal fuzzy coefficients Ai.

)()()( )(L)(L 0yyh

iRy

Fitness：

Vagueness of System：

K

iii aa

1

LUS



Modeling the damage assessment of buildings by experts

Linguistic Var. Fuzzy Number extremely good (0.00,0.00,0.15)

very good (0.20,0.15,0.15)

good (0.40,0.15,0.15)

bad (0.60,0.15,0.15) very bad (0.80,0.15,0.15) extremely bad (1.00,0.15,0.15) extremely good (0.00,0.00,0.15) very good (0.20,0.15,0.15)

good (0.40,0.15,0.15)

bad (0.60,0.15,0.15) very bad (0.80,0.15,0.15) extremely bad (1.00,0.15,0.15)

below normal (0.00,0.00,0.40)

X3 normal (0.50,0.20,0.20)

severe (1.00,0.40,0.00)

safe (0.00,0.00,0.40)

Y questionable (0.50,0.20,0.20) not safe (1.00,0.40,0.00)

X2

X1Corrosion State

Cracking State

Loading andEnvironment

State

TotalAssssment

Dictionary




Sample X1 X2 X3 Y










Attributes




Sample X1 X2 X3 Y

1 (0.00,0.00,0.15) (1.00,0.15,0.15) (0.00,0.00,0.40) (1.00,0.40,0.00)2 (0.60,0.15,0.15) (0.80,0.15,0.15) (0.00,0.00,0.40) (1.00,0.40,0.00)3 (0.80,0.15,0.15) (0.80,0.15,0.15) (0.00,0.00,0.40) (1.00,0.40,0.00)4 (0.80,0.15,0.15) (0.20,0.15,0.15) (0.00,0.00,0.40) (0.50,0.20,0.20)5 (0.40,0.15,0.15) (0.00,0.00,0.15) (0.00,0.00,0.40) (0.00,0.00,0.40)6 (0.40,0.15,0.15) (0.60,0.15,0.15) (0.50,0.20,0.20) (1.00,0.40,0.00)7 (0.60,0.15,0.15) (0.80,0.15,0.15) (0.50,0.20,0.20) (1.00,0.40,0.00)8 (0.80,0.15,0.15) (0.40,0.15,0.15) (0.50,0.20,0.20) (1.00,0.40,0.00)9 (0.60,0.15,0.15) (0.20,0.15,0.15) (0.50,0.20,0.20) (0.50,0.20,0.20)10 (0.80,0.15,0.15) (0.20,0.15,0.15) (0.50,0.20,0.20) (0.50,0.20,0.20)11 (0.00,0.00,0.15) (0.60,0.15,0.15) (1.00,0.40,0.00) (1.00,0.40,0.00)12 (0.20,0.15,0.15) (0.60,0.15,0.15) (1.00,0.40,0.00) (1.00,0.40,0.00)13 (0.40,0.15,0.15) (0.80,0.15,0.15) (1.00,0.40,0.00) (1.00,0.40,0.00)14 (0.80,0.15,0.15) (0.40,0.15,0.15) (1.00,0.40,0.00) (1.00,0.40,0.00)15 (0.20,0.15,0.15) (0.40,0.15,0.15) (1.00,0.40,0.00) (1.00,0.40,0.00)16 (0.20,0.15,0.15) (0.20,0.15,0.15) (1.00,0.40,0.00) (0.50,0.20,0.20)

Attributes

Junzo Watada

Numerical Example


)loading(

)cracking(

)corrosion(

LLL

)065.0,065.0,373.0(

)000.0,000.0,813.0(

)000.0,000.0,322.0(

U,U,UV321

f

Fuzzy Evaluation Function



TrainingSample Assessed Fuzzy Num.rAssessed Word Givn Word by Experts

1 (0.81,0.12,0.29) not safe not safe

2 (0.84,0.17,0.56) not safe not safe3 (0.91,0.17,0.40) not safe not safe4 (0.42,0.17,0.41) questionable questionable5 (0.13,0.05,0.41) safe safe6 (0.80,0.31,0.40) not safe not safe7 (1.03,0.31,0.40) not safe not safe8 (0.77,0.31,0.35) not safe not safe9 (0.54,0.22,0.40) questionable questionable10 (0.61,0.31,0.39) questionable questionable11 (0.86,0.40,0.39) not safe not safe12 (0.93,0.45,0.38) not safe not safe13 (1.15,0.45,0.39) not safe not safe14 (0.96,0.45,0.39) not safe not safe15 (0.76,0.45,0.40) not safe not safe16 (0.60,0.45,0.39) questionable questionable

Predicted Valu by the Model



Evaluation using testing samples

New Corrosion St. Cracking St. Loading and Env. State Linguistic Value Linguistic Value

Samples X1 X2 X3 by the Model by Experts

21 good extremely bad below normal not safe not safe 22 very good very good normal questionable questionable 23 bad extremely good below normal safe safe 24 very good extremely good below normal safe safe 25 bad very bad normal not safe not safe

Attribute Total Assessment Y




DECISION MAKING

QUALITY INSPECTION

Graded Fruit

Condition

FruitletsColor

Surface

(MPOB, 2003)

Junzo Watada



Oct. 19, 2012 90

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99

Thank You !Thank You !

Junzo Watada


Junzo Watada



LP Problem

),,2,1(0

tosubject

minimize1

mj

xxy

xxy

x

jjj

jjj

m

jj

c

ca

ca

c Vagueness

upper bound

lower bound

coefficient

101

Documents

Junzo Watada - Botho University | Welcome · 2017-09-28 · Junzo Watada Oct. 19, 2012 Botho Colledge Conference 2012 LP Problem Vagueness upper bound lower bound coefficient 24 (