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A First Course in Fuzzy Logic

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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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