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.
|Publisher:||Springer Berlin Heidelberg|
|Series:||Studies in Fuzziness and Soft Computing Series , #169|
|Edition description:||Softcover reprint of hardcover 1st ed. 2005|
|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.