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Fuzzy Mathematical Programming and Fuzzy Matrix Games

  • Book
  • © 2005

Overview

Authors:
  1. C. R. Bector

    1. Department of Business Administration, Faculty of Management, Asper School of Business, University of Manitoba, Winnipeg, Canada

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  2. Suresh Chandra

    1. Department of Mathematics, Indian Institute of Technology (I.I.T.), Hauz Khas, New Delhi, India

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    You can also search for this author in PubMed   Google Scholar

  • Systematic and focused Study on Fuzzy Mathematical Programming and Matrix
  • Includes supplementary material: sn.pub/extras

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 169)

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Table of contents (10 chapters)

  1. Front Matter

    Pages I-XII
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  2. Crisp matrix and bi-matrix games: some basic results

    Pages 1-20

  3. Fuzzy sets

    Pages 21-38

  4. Fuzzy numbers and fuzzy arithmetic

    Pages 39-56

  5. Linear and quadratic programming under fuzzy environment

    Pages 57-94

  6. Duality in linear and quadratic programming under fuzzy environment

    Pages 95-116

  7. Matrix games with fuzzy goals

    Pages 117-132

  8. Matrix games with fuzzy pay-offs

    Pages 133-155

  9. More on matrix games with fuzzy pay-offs

    Pages 157-174

  10. Fuzzy Bi-Matrix Games

    Pages 175-198

  11. Modality and other approaches for fuzzy linear programming

    Pages 199-229

  12. Back Matter

    Pages 230-236
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Keywords

About this book

Game theory has already proved its tremendous potential for con?ict resolution problems in the ?elds of Decision Theory and Economics. In the recent past, there have been attempts to extend the results of crisp game theory to those con?ict resolution problems which are fuzzy in nature e.g. Nishizaki and Sakawa [61] and references cited there in. These developments have lead to the emergence of a new area in the literature called fuzzy games. Another area in the fuzzy decision theory, which has been growing very fast is the area of fuzzy mathematical programming and its applications to various branches of sciences, Engineering and Management. In the crisp scenario, there exists a beautiful relationship between two person zero sum matrix game theory and duality in linear p- gramming. It is therefore natural to ask if something similar holds in the fuzzy scenario as well. This discussion essentially constitutes the core of our presentation. The objective of this book is to present a systematic and focussed study of the application of fuzzy sets to two very basic areas of decision theory, namely Mathematical Programming and Matrix Game Theory.

Reviews

From the reviews:

"The book presents a systematic theory … oriented primarily to senior undergraduate students, as well as to graduate students and researchers in the area of fuzzy optimization and related topics. Special attention is devoted to various approaches to fuzzy linear and quadratic programming … . Theoretical results and algorithms are illustrated through small numerical examples." (Karel Zimmermann, Zentralblatt MATH, Vol. 1078, 2006)

"Fuzzy Mathematical Programming and Fuzzy Matrix Games studies the extension of mathematical programming and matrix game theory to a fuzzy environment. … provides deep theoretical analyses that include theorems and proofs. … We recommend the book to researchers and postgraduates who have … an interest in mathematical programming, matrix games, and fuzzy sets." (Julius Zilinskas, Interfaces, Vol. 37 (4), 2007)

Authors and Affiliations

  • Department of Business Administration, Faculty of Management, Asper School of Business, University of Manitoba, Winnipeg, Canada

    C. R. Bector

  • Department of Mathematics, Indian Institute of Technology (I.I.T.), Hauz Khas, New Delhi, India

    Suresh Chandra

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