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A First Course in Fuzzy Logic

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A First Course in Fuzzy Logic, Third Edition continues to provide the ideal introduction to the theory and applications of fuzzy logic. This best-selling text provides a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world applications. New in the Third Edition: A section on type-2 fuzzy sets - a topic that has received much attention in the past few years Additional material on copulas and t-norms More discussions on generalized modus ponens and the compositional rule of inference Complete revision to the chapter on possibility theory Significant expansion of the chapter on fuzzy integrals Many new exercises With its comprehensive updates, this new edition presents all the background necessary for students and professionals to begin using fuzzy logic in its many-and rapidly growing- applications in computer science, mathematics, statistics, and engineering.
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Table of Contents

THE CONCEPT OF FUZZINESS Examples Mathematical modeling Some operations on fuzzy sets Fuzziness as uncertainty Exercises SOME ALGEBRA OF FUZZY SETS Boolean algebras and lattices Equivalence relations and partitions Composing mappings Isomorphisms and homomorphisms Alpha-cuts Images of alpha-level sets Exercises FUZZY QUANTITIES Fuzzy quantities Fuzzy numbers Fuzzy intervals Exercises LOGICAL ASPECTS OF FUZZY SETS Classical two-valued logic A three-valued logic Fuzzy logic Fuzzy and Lukasiewicz logics Interval-valued fuzzy logic Canonical forms Notes on probabilistic logic Exercises BASIC CONNECTIVES t-norms Generators of t-norms Isomorphisms of t-norms Negations Nilpotent t-norms and negations t-conorms DeMorgan systems Groups and t-norms Interval-valued fuzzy sets Type- fuzzy sets Exercises ADDITIONAL TOPICS ON CONNECTIVES Fuzzy implications Averaging operators Powers of t-norms Sensitivity of connectives Copulas and t-norms Exercises FUZZY RELATIONS Definitions and examples Binary fuzzy relations Operations on fuzzy relations Fuzzy partitions Fuzzy relations as Chu spaces Approximate reasoning Approximate reasoning in expert systems A simple form of generalized modus ponens The compositional rule of inference Exercises UNIVERSAL APPROXIMATION Fuzzy rule bases Design methodologies Some mathematical background Approximation capability Exercises POSSIBILITY THEORY Probability and uncertainty Random sets Possibility measures Exercises PARTIAL KNOWLEDGE Motivation Belief functions and incidence algebras Monotonicity Beliefs, densities, and allocations Belief functions on infinite sets Note on Moebius transforms of set-functions Reasoning with belief functions Decision making using belief functions Rough sets Conditional events Exercises FUZZY MEASURES Motivation and definitions Fuzzy measures and lower probabilities Fuzzy measures in other areas Conditional fuzzy measures Exercises THE CHOQUET INTEGRAL The Lebesgue integral The Sugeno integral The Choquet integral Exercises FUZZY MODELING AND CONTROL Motivation for fuzzy control The methodology of fuzzy control Optimal fuzzy control An analysis of fuzzy control techniques Exercises Bibliography Answers to Selected Exercises Index on>

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