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.
This book presents a systematic and focused study of the application of fuzzy sets to two basic areas of decision theory, namely Mathematical Programming and Matrix Game Theory. Apart from presenting most of the basic results available in the literature on these topics, the emphasis is on understanding their natural relationship in a fuzzy environment. The study of duality theory for fuzzy mathematical programming problems plays a key role in understanding this interrelationship. For this, a theoretical framework of duality in fuzzy mathematical programming and conceptualization of the solution of a fuzzy game is created on the lines of their crisp counterparts. Most of the theoretical results and associated algorithms are illustrated through small numerical examples from actual applications.
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)
