A First Course in Fuzzy Logic

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 Moebius 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 on>