This book starts with the basic concepts of Fuzzy Logic: the membership function, the intersection and the union of fuzzy sets, fuzzy numbers, and the extension principle underlying the algorithmic operations. Several chapters are devoted to applications of Fuzzy Logic in Operations Research: PERT planning with uncertain activity durations, Multi-Criteria Decision Analysis (MCDA) with vague preferential statements, and Multi-Objective Optimization (MOO) with weighted degrees of satisfaction. New items are: Fuzzy PERT using activity durations with triangular membership functions, Fuzzy SMART with a sensitivity analysis based upon Fuzzy Logic, the Additive and the Multiplicative AHP with a similar feature, ELECTRE using the ideas of the AHP and SMART, and a comparative study of the ideal-point methods for MOO. Finally, earlier studies of colour perception illustrate the attempts to find a physiological basis for the set-theoretical and the algorithmic operations in Fuzzy Logic. The last chapter also discusses some key issues in linguistic categorization and the prospects of Fuzzy Logic as a multi-disciplinary research activity. Audience: Researchers and students working in applied mathematics, operations research, management science, business administration, econometrics, industrial engineering, information systems, artificial intelligence, mathematical psychology, and psycho-physics.
This book starts with the basic concepts of Fuzzy Logic: the membership function, the intersection and the union of fuzzy sets, fuzzy numbers, and the extension principle underlying the algorithmic operations. Several chapters are devoted to applications of Fuzzy Logic in Operations Research: PERT planning with uncertain activity durations, Multi-Criteria Decision Analysis (MCDA) with vague preferential statements, and Multi-Objective Optimization (MOO) with weighted degrees of satisfaction. New items are: Fuzzy PERT using activity durations with triangular membership functions, Fuzzy SMART with a sensitivity analysis based upon Fuzzy Logic, the Additive and the Multiplicative AHP with a similar feature, ELECTRE using the ideas of the AHP and SMART, and a comparative study of the ideal-point methods for MOO. Finally, earlier studies of colour perception illustrate the attempts to find a physiological basis for the set-theoretical and the algorithmic operations in Fuzzy Logic. The last chapter also discusses some key issues in linguistic categorization and the prospects of Fuzzy Logic as a multi-disciplinary research activity. Audience: Researchers and students working in applied mathematics, operations research, management science, business administration, econometrics, industrial engineering, information systems, artificial intelligence, mathematical psychology, and psycho-physics.
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