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A First Course in Fuzzy Logic: Textbooks in Mathematics

Autor Hung T. Nguyen, Carol Walker, Elbert A. Walker
en Limba Engleză Paperback – 21 ian 2023
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.


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Specificații

ISBN-13: 9781032475943
ISBN-10: 1032475943
Pagini: 458
Ilustrații: 36
Dimensiuni: 156 x 234 x 27 mm
Greutate: 0.63 kg
Ediția:4
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Textbooks in Mathematics

Locul publicării:Boca Raton, United States

Public țintă

Undergraduate

Cuprins

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.

Notă biografică

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.

Descriere

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.