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Fuzzy Mathematical Programming and Fuzzy Matrix Games [electronic resource] /by C. R. Bector, Suresh Chandra.

by Bector, C. R [author.]; Chandra, Suresh [author.]; SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Studies in Fuzziness and Soft Computing: 169Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.Description: XII, 236 p. online resource.ISBN: 9783540323716.Subject(s): Engineering | Artificial intelligence | Mathematics | Computer science -- Mathematics | Operations research | Engineering mathematics | Engineering | 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 | Operations Research, Mathematical ProgrammingDDC classification: 519 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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.
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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.

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.

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