A First Course in Fuzzy Logic, Third EditionThe second edition of the popular A First Course in Fuzzy Logic will continue to provide the ideal introduction to the theory and applications of fuzzy logic. The authors provide a firm mathematical basis for the calculus of fuzzy concepts-necessary to design intelligent systems-and give the student a solid background for further studies and real-world applications. This new edition provides many new exercises designed to enhance the reader's understanding of the concepts. The authors have expanded on the algebra background needed for the more advanced topics, and include significant new material on basic connectives and the algebraic properties of fuzzy logic, rough sets, conditional events, distributions of random sets, and derivatives of fuzzy measures. With its comprehensive updates, A First Course in Fuzzy Logic, Second Edition presents all the background necessary for students to begin using fuzzy logic in its many-and rapidly growing-applications. |
Contents
The Concept of Fuzziness | 1 |
Basic Connectives | 5 |
Universal Approximation | 8 |
Some Algebra of Fuzzy Sets | 19 |
7 | 38 |
Fuzzy Quantities | 47 |
Logical Aspects of Fuzzy Sets | 61 |
6 | 94 |
Fuzzy Relations | 189 |
8 | 233 |
Fuzzy Measures | 269 |
Fuzzy Integrals | 293 |
Fuzzy Modeling and Control | 319 |
Bibliography | 335 |
143 | 336 |
Answers to Selected Exercises | 343 |
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Common terms and phrases
a-cuts antiautomorphism Archimedean t-norm Aut(I automorphism averaging operator belief function binary operation Boolean algebra Chapter comonotonic complete lattice conditional convex Corollary defined Definition defuzzification denote element equation equivalence classes equivalence relation example Exercise formulas Frank system function f fuzzy concepts fuzzy control fuzzy equivalence relation fuzzy interval fuzzy logic fuzzy measure fuzzy numbers fuzzy partition fuzzy quantities fuzzy relation fuzzy sets fuzzy subset ƒ and g homomorphism implies induces integral isomorphism Kleene algebra Let f mapping mathematical membership function Morgan algebra Morgan systems morphisms N(R+ natural negation nilpotent t-norm partially ordered set possibility distribution probability measure probability space Proof properties propositional calculus pseudocomplement random set random variable real numbers respect rough sets rules satisfies set functions Show Stone algebra strict t-norm subgroup Suppose t-conorm Theorem three-valued truth values Verify