Fuzzy Mathematical Programming and Fuzzy Matrix Games

✍ Scribed by Dr. C. R. Bector, Dr. Suresh Chandra (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2005
• Tongue: English
• Leaves: 250
• Series: Studies in Fuzziness and Soft Computing 169
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Crisp matrix and bi-matrix games: some basic results....Pages 1-20
Fuzzy sets....Pages 21-38
Fuzzy numbers and fuzzy arithmetic....Pages 39-56
Linear and quadratic programming under fuzzy environment....Pages 57-94
Duality in linear and quadratic programming under fuzzy environment....Pages 95-116
Matrix games with fuzzy goals....Pages 117-132
Matrix games with fuzzy pay-offs....Pages 133-155
More on matrix games with fuzzy pay-offs....Pages 157-174
Fuzzy Bi-Matrix Games....Pages 175-198
Modality and other approaches for fuzzy linear programming....Pages 199-229

✦ Subjects

Appl.Mathematics/Computational Methods of Engineering; Game Theory, Economics, Social and Behav. Sciences; Artificial Intelligence (incl. Robotics); Operations Research/Decision Theory; Computational Mathematics and Numerical Analysis; O