A First Course in Fuzzy Logic
4th Edition
Published on 7. December 2018
458 pages
978-0-429-01261-7 (ISBN)
Description
A First Course in Fuzzy Logic, Fourth Edition is an expanded version of the successful third edition. It provides a comprehensive introduction to the theory and applications of fuzzy logic.
This popular text offers 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 Fourth Edition:
Features new results on fuzzy sets of type-2
Provides more information on copulas for modeling dependence structures
Includes quantum probability for uncertainty modeling in social sciences, especially in economics
With its comprehensive updates, this new edition presents all the background necessary for students, instructors and professionals to begin using fuzzy logic in its many-applications in computer science, mathematics, statistics, and engineering.
About the Authors:
Hung T. Nguyen is a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. He is also an Adjunct Professor of Economics at Chiang Mai University, Thailand.
Carol L. Walker is also a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University.
Elbert A. Walker is a Professor Emeritus, Department of Mathematical Sciences, New Mexico State University.
This popular text offers 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 Fourth Edition:
Features new results on fuzzy sets of type-2
Provides more information on copulas for modeling dependence structures
Includes quantum probability for uncertainty modeling in social sciences, especially in economics
With its comprehensive updates, this new edition presents all the background necessary for students, instructors and professionals to begin using fuzzy logic in its many-applications in computer science, mathematics, statistics, and engineering.
About the Authors:
Hung T. Nguyen is a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. He is also an Adjunct Professor of Economics at Chiang Mai University, Thailand.
Carol L. Walker is also a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University.
Elbert A. Walker is a Professor Emeritus, Department of Mathematical Sciences, New Mexico State University.
More details
Series
Edition
4th edition
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Illustrations
3 Tables, black and white; 36 Illustrations, black and white
File size
12,84 MB
ISBN-13
978-0-429-01261-7 (9780429012617)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Hung T. Nguyen | Carol Walker | Elbert A. Walker
A First Course in Fuzzy Logic
Book
01/2023
4th Edition
Chapman & Hall/CRC
€73.90
Shipment within 10-20 days
Hung T. Nguyen | Carol Walker | Elbert A. Walker
A First Course in Fuzzy Logic
Book
11/2018
4th Edition
CRC Press
€193.13
Shipment within 10-20 days
Persons
Hung T. Nguyen is a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. He is also an Adjunct Professor of Economics at Chiang Mai University, Thailand.
Carol L. Walker is also a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University.
Elbert A. Walker is a Professor Emeritus, Department of Mathematical Sciences, New Mexico State University.
Carol L. Walker is also a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University.
Elbert A. Walker is a Professor Emeritus, Department of Mathematical Sciences, New Mexico State University.
Content
The Concept of Fuzziness
Examples. Mathematical modeling. Some operations on fuzzy sets. Fuzziness as uncertainty.
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.
Basic Connectives
t-norms. Generators of t-norms. Isomorphisms of t-norms. Negations. Nilpotent t-norms and negations. T-conforms. De Morgan systems. Groups and t-norms. Interval-valued fuzzy sets. Type-2 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. Approximate reasoning. Approximate reasoning in expert systems. A simple form of generalized modus ponens. The compositional rule of inference.
Universal Approximation
Fuzzy rule bases. Design methodologies. Some mathematical background. Approximation capability.
Possibility Theory
Probability and uncertainty. Random sets. Possibility measures.
Partial Knowledge
Motivations. Belief functions and incidence algebras. Monotonicity. Beliefs, densities, and allocations. Belief functions on infinite sets. Mobius transforms of set-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.
The Choquet Integral
The Lebesgue integral. The Sugeno integral. The Choquet integral.
Fuzzy Modeling and Control
Motivation for fuzzy control. The methodology of fuzzy control. Optimal fuzzy control. An analysis of fuzzy control techniques.
Examples. Mathematical modeling. Some operations on fuzzy sets. Fuzziness as uncertainty.
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.
Basic Connectives
t-norms. Generators of t-norms. Isomorphisms of t-norms. Negations. Nilpotent t-norms and negations. T-conforms. De Morgan systems. Groups and t-norms. Interval-valued fuzzy sets. Type-2 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. Approximate reasoning. Approximate reasoning in expert systems. A simple form of generalized modus ponens. The compositional rule of inference.
Universal Approximation
Fuzzy rule bases. Design methodologies. Some mathematical background. Approximation capability.
Possibility Theory
Probability and uncertainty. Random sets. Possibility measures.
Partial Knowledge
Motivations. Belief functions and incidence algebras. Monotonicity. Beliefs, densities, and allocations. Belief functions on infinite sets. Mobius transforms of set-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.
The Choquet Integral
The Lebesgue integral. The Sugeno integral. The Choquet integral.
Fuzzy Modeling and Control
Motivation for fuzzy control. The methodology of fuzzy control. Optimal fuzzy control. An analysis of fuzzy control techniques.
