A first course in fuzzy logic

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