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Fuzzy Mathematical Programming and Fuzzy Matrix Games

  • Fester Einband
  • 236 Seiten
Game theory has already proved its tremendous potential for con?ict resolution problems in the ?elds of Decision Theory and Econom... Weiterlesen
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Beschreibung

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.

Klappentext

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. TOC:Preliminaries.- Fuzzy Sets.- Fuzzy Numbers and Fuzzy Arithmetic.- Linear and Quadratic Programming under Fuzzy Environment.- Duality for Linear and Quadratic Programming under Fuzzy Environment.- Matrix Games with Fuzzy Goals.- Matrix Games with Fuzzy Pay-Offs.- Fuzzy Bimatrix Games.- Multiobjective Programming under Fuzzy Enviornment and Multiobjective Fuzzy Games.- Modality and Other Approaches for Fuzzy Linear Programming and Fuzzy Matrix Games.

Zusammenfassung
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)

Inhalt

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.

Produktinformationen

Titel: Fuzzy Mathematical Programming and Fuzzy Matrix Games
Untertitel: Ein Anwenderhandbuch für den Mittelstand
Autor:
EAN: 9783540237297
ISBN: 978-3-540-23729-7
Format: Fester Einband
Genre: Technik
Anzahl Seiten: 236
Jahr: 2005
Auflage: 2005.