Hung T. Nguyen (New Mexico State University, Las Cruces, USA), Carol Walker, Elbert A. Walker (New Mexico State University, Las Cruces, USA)

A First Course in Fuzzy Logic

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Textbooks in Mathematics
• Verlag: Taylor & Francis Ltd
• 4 ed
• Seitenzahl: 458
• Erscheinungstermin: 21. Januar 2023
• Englisch
• Abmessung: 154mm x 234mm x 27mm
• Gewicht: 694g
• ISBN-13: 9781032475943
• ISBN-10: 1032475943
• Artikelnr.: 69033443

Autorenporträt

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.

Inhaltsangabe

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.