Introduction to Fuzzy Logic and Fuzzy Linear Programming

Pandian Vasant (Universiti Teknologi Petronas, Malaysia) and Hrishikesh S. Kale (K.K.Wagh Institute of Engineering Education & Research, India)
DOI: 10.4018/978-1-59904-843-7.ch061

Abstract

Fuzzy logic (FL) is a mathematical technique for dealing with imprecise data and problems that have many solutions rather than one. Although it is implemented in digital computers which ultimately make only yesno decisions, FL works with ranges of values, solving problems in a way that more resembles human logic. FL is a multi-valued (as opposed to binary) logic developed to deal with imprecise or vague data. Classical logic holds that everything can be expressed in binary terms: 0 and 1, black and white, yes or no; in terms of Boolean algebra, everything is in one set or another but not in both. FL allows for partial membership in asset values between 0 and 1, shades of gray, and introduces the concept of the “fuzzy set.” When the approximate reasoning of FL (Zadeh, 1965) is used with an expert system, logical inferences can be drawn from imprecise relationships. FL theory was developed by Lofti A. Zadeh at the University of California in the mid 1960s. However, it was not applied commercially until 1987 when the Matsushita Industrial Electric Co. used it to automatically optimize the wash cycle of a washing machine by sensing the load size, fabric mix, and quantity of detergent and has applications in the control of passenger elevators, household applications, and so forth.

Key Terms in this Chapter

Fuzzy Linear Programming (FLP): FLP deals with the optimization (maximization or minimization) of a function of variables known as fuzzy objective function, subject to a set of fuzzy linear equations and/or inequality known as restrictions or fuzzy constraints.

Fuzzy Band: The fuzzy groups also can be called a fuzzy band.

Membership Function (MF): An MF is a curve that defines how each point in the input space is mapped to a membership value (or degree of membership) between 0 and 1.

MATLAB®: MATLAB® is a very highly sophisticated technical computing tool box for solving FLP problems.

Fuzzy Set: A fuzzy set on a classical set ? is defined as follows: The MF µA(x) quantifies the grade of membership of the elements x to the fundamental set ?.

Degree of Satisfaction: The degree of satisfaction is the level of satisfaction with respect to vagueness in the fuzzy parameter, and it is measured between 0 and 1.

Fuzzy Logic: Fuzzy logic is a mathematical technique for dealing with imprecise data and problems that have many solutions rather than one.

Linear Programming (LP): LP deals with the optimization (maximization or minimization) of a function of variables known as objective function, subject to a set of linear equations and/or inequality known as restrictions or constraints.

Satisfactory/Compromise Solution: Satisfactory/compromise solution is a fuzzy optimization solution that will be provided to the decision makers for the implementation purpose.

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Foreword
Jean-Charles Pomerol
Preface
Acknowledgment
Chapter 1
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Chapter 2
Zita Zoltay Paprika
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John Wang, Chandana Chakraborty, Huanyu Ouyang
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Sven A. Carlsson
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Ricardo Colomo Palacios, Juan Miguel Gómez Berbís, Ángel García Crespo
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Maria Eugénia Captivo, João Clímaco, Sérgio Fernandes
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Amit V. Deokar, Omar F. El-Gayar
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Sergio F. Ochoa, José A. Pino
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Malcolm J. Beynon
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Thomas Madritsch, Michael May, Herwig Ostermann, Roland Staudinger
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Alexandre Gachet, Ralph Sprague
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Patrick Brézillon, Jean-Charles Pomerol
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Pascale Zaraté
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Dashboards for Management  (pages 116-123)
Werner Beuschel
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Chapter 15
John Wang, James Yao, Qiyang Chen
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Patrick Humphreys
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A. Dolgui, O. Guschinskaya, N. Guschinsky, G. Levin
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A. Dolgui, O. Guschinskaya, N. Guschinsky, G. Levin
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Ivan Bruha
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Viviane Barbosa Diniz, Marcos R.S. Borges, José Orlando Gomes, José H. Canós
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Chapter 22
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Hannu Kivijärvi, Markku Tuominen
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Udo Richard Averweg
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Chapter 26
Patrick Humphreys
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Daniel J. Power
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James Yao, John Wang, Qiyang Chen, June Lu
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Dina Neiger, Leonid Churilov
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Zhen Chen, Heng Li, Qian Xu, Szu-Li Sun
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Omar F. El-Gayar, Amit V. Deokar
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Chapter 32
DS/AHP  (pages 278-285)
Malcolm J. Beynon
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Chapter 33
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Chapter 34
Ran M. Bittmann, Roy M. Gelbard
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Norman Pendegraft, Mark Rounds
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Gloria E. Phillips-Wren, Manuel Mora, Guisseppi Forgionne
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Giusseppi Forgionne, Stephen Russell
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Margaret W. Wood, David C. Rine
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David Sammon
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Simon Woodworth, Joe Cunningham
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Chapter 42
G. Kouamou, C. Pettang
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Chapter 43
Fátima C.C. Dargam
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Chapter 44
Fuzzy Decision Trees  (pages 382-390)
Malcolm J. Beynon
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Chapter 45
P. Serra, R. A. Ribeiro, R. Marques Pereira, R. Steel, M. Niezette, A. Donati
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Games of Strategy  (pages 402-409)
Geraldine Ryan, Seamus Coffey
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John Wang, Dajin Wang, Aihua Li
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Chapter 48
Alexey Petrovsky
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Frédéric Adam, Jean-Charles Pomerol, Patrick Brézillon
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Marcelo Índio dos Reis, Marcos R.S. Borges, José Orlando Gomes
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Fergal Carton
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Manual Mora, Ovsei Gelman, Guisseppi Forgionne, Francisco Cervantes
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John McAvoy, Tom Butler
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Peter O’Donnell, Rob Meredith
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Cristina Casado Lumbreras, Ricardo Colomo Palacios, Juan Miguel Gómez Berbís
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Ramon Brena, Carlos Chesñevar
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Dina Neiger, Leonid Churilov
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Gloria E. Phillips-Wren
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Ilya Ashikhmin, Eugenia Furems, Alexey Petrovsky, Michael Sternin
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R.A. Ribeiro, I.L. Nunes
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Pandian Vasant, Hrishikesh S. Kale
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Peer-Olaf Siebers, Uwe Aickelin
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Chapter 63
Knowledge Based DSS  (pages 565-575)
Michel R. Klein
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Chapter 64
James D. Jones
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Camille Rosenthal-Sabroux, Michel Grundstein, Fernando Iafrate
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James D. Jones
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Stephan Scheuerer
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Osvaldo García de la Cerda, Renato Orellana Muermann
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Chapter 71
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Peer-Olaf Siebers, Uwe Aickelin, Helen Celia, Chris Clegg
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Csaba Csáki
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Brad Morantz, Thomas Whalen, G. Peter Zhang
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Chris Schlueter Langdon
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Manual Mora, Francisco Cervantes, Guisseppi Forgionne, Ovsei Gelman
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Tan Yigitcanlar, Jung Hoon Han, Sang Ho Lee
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Tan Yigitcanlar, Omur Saygin
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João Carlos Namorado Clímaco, João Carlos Soares de Mello, Lidia Angulo Meza
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Luis Antunes, Ana Respício, João Balsa, Helder Coelho
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Geraldine Ryan, Edward Shinnick
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N. Chugunov, G. Shepelyov, M. Sternin
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PROMETHEE  (pages 743-750)
Malcolm J. Beynon
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Malcolm J. Beynon
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Todd McElroy
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Chapter 86
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Edward Shinnick, Geraldine Ryan
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Rough Set Theory  (pages 783-789)
Malcolm J. Beynon
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Chapter 89
Dorrie DeLuca, Joseph S. Valacich
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Software Agents  (pages 798-806)
Stanislaw Stanek, Maciej Gawinecki, Malgorzata Pankowska, Shahram Rahimi
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Chapter 91
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Hannu Kivijärvi, Markku Tuominen, Kalle Elfvengren, Kalle Piirainen, Samuli Kortelainen
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C.W. Holsapple
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Mattias Strand, Sven A. Carlsson
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Robert Fitzgerald, John Findlay
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Hanan Yaniv, Susan Crichton
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Hanan Yaniv
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Pat Finnegan, Jeremy Hayes
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Giusseppi Forgionne, Stephen Russell
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Chapter 102
David Sammon
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Chapter 103
David Sammon
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Chapter 104
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Chapter 105
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Chapter 106
Giusseppi Forgionne, Stephen Russell
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Chapter 107