Fuzzy Mathematical Programming and Fuzzy Matrix Games / Edition 1

by C. R. Bector, Suresh Chandra

Overview

Game theory has already proved its tremendous potential for conflict resolution problems in the fields of Decision Theory and Economics. In the recent past, there have been attempts to extend the results of crisp game theory to those conflict 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 programming. 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.

Product Details

ISBN-13:	9783642062650
Publisher:	Springer Berlin Heidelberg
Publication date:	12/15/2010
Series:	Studies in Fuzziness and Soft Computing , #169
Edition description:	Softcover reprint of hardcover 1st ed. 2005
Pages:	236
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

Crisp matrix and bi-matrix games: some basic results.- Fuzzy sets.- Fuzzy numbers and fuzzy arithmetic.- Linear and quadratic programming under fuzzy environment.- Duality in linear and quadratic programming under fuzzy environment.- Matrix games with fuzzy goals.- Matrix games with fuzzy pay-offs.- More on matrix games with fuzzy pay-offs.- Fuzzy Bi-Matrix Games.- Modality and other approaches for fuzzy linear programming.

Editorial 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)

From the Publisher