A First Course in Fuzzy Logic

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