A first course in fuzzy logic

Author(s)

• Nguyen, Hung T.
• Walker, E. (Elbert)

Bibliographic Information

A first course in fuzzy logic

Hung T. Nguyen, Elbert A. Walker

Chapman & Hall/CRC, c2000

2nd ed

Note

Includes bibliographical references (p. 335-349) and index

Description and Table of Contents

Description

The 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.

Table of Contents

THE CONCEPT OF FUZZINESS Examples Mathematical Modeling Some Operations on Fuzzy Sets Fuzziness as Uncertainity 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 FUZZY QUANTITIES Fuzzy Quantities Fuzzy Numbers Fuzzy Intervals 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 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 ADDITIONAL TOPICS ON CONNECTIVES Fuzzy Implications Averaging Operators Powers of t-Norms Sensitivity of Connectives Copulas and t-Norms FUZZY RELATIONS Definitions and Examples Binary Fuzzy Relations Operations on Fuzzy Relations Fuzzy Partitions Fuzzy Relations as Chu Spaces UNIVERSAL APPROXIMATION Fuzzy Rule Bases Design Methodologies Some Mathematical Background Approximation Capability POSSIBILITY THEORY Additive and Non-Additive Set Functions Possibility Possibility Theory Based on Fuzzy Sets Approximate Reasoning Approximate Reasoning in Expert Systems A Simple Form of Generalized Modus Ponens The Compositional Rule of Inference PARTIAL KNOWLEDGE Incomplete Probabilistic Information Belief Functions Reasoning with Belief Functions Decision Making Using Belief Functions Rough Sets Conditional Events FUZZY MEASURES Motivation and Definitions Fuzzy Measures and Lower Probabilities Fuzzy Measures in Other Areas Conditional Fuzzy Measures FUZZY INTEGRALS Review of the Lebesgue Integral The Sugeno Integral The Choquet Integral The Choquet Integral as a Fuzzy Integral Radon-Nikodym Derivatives FUZZY MODELING AND CONTROL Motivation for Fuzzy Control The Methodology of Fuzzy Control Optimal Fuzzy Control An Analysis of Fuzzy Control Techniques Plus each chapter includes Exercises BIBLIOGRAPHY ANSWERS TO SELECTED EXERCISES INDEX

by "Nielsen BookData"

Details

• NCID: BA4375896X
• ISBN:
  • 0849316596
• LCCN: 99023550
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Boca Raton, Fla.
• Pages/Volumes: 373 p.
• Size: 24 cm
• Classification:
  • LCC : QA76.87
  • DC21 : 511.3
• Subject Headings:
  • LCSH : Neural networks (Computer science)
  • LCSH : Fuzzy logic