A First Course in Fuzzy Logic / Edition 3

A First Course in Fuzzy Logic / Edition 3

by Hung T. Nguyen, Elbert A. Walker
     
 

ISBN-10: 1584885262

ISBN-13: 9781584885269

Pub. Date: 10/28/2005

Publisher: Taylor & Francis

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

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Overview

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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    Product Details

    ISBN-13:
    9781584885269
    Publisher:
    Taylor & Francis
    Publication date:
    10/28/2005
    Edition description:
    New Edition
    Pages:
    440
    Product dimensions:
    6.10(w) x 9.30(h) x 1.10(d)

    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 Möbius 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

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