Chapter 1.Theoretical Overview
1.1 Fuzzy Sets
1.1.1 Fuzzy Sets and Terminology
1.2 Set Theoretic Operation
1.2.1 Basic Definitions
1.2.2 t-norms and s-norms for fuzzy sets
1.2.3 Some parametrized operators
1.2.4 Avaraging operators
1.2.5 Criteria for Selecting Appropiate Aggregation
1.3 Fuzzy Measures and Measures of Fuzzyness
1.3.1 General discussion
1.3.2 The Fuzzy System for Fuzzy Measures
1.3.3 Measures of fuzzyness
1.3.3.1 The "entropy" of fuzzy sets
1.3.3.2 The Complement Distance of Two Fuzzy Sets
1.4 Possibility, Probability and Fuzzy Set Theory
1.4.1 Possibility theory
1.4.1.1 Fuzzy Sets and Possibility Discributions
1.4.1.2 Possibility and Necessity Measures
1.4.2 Probability of Fuzzy Events
1.4.2.1 Probability of Fuzzy Events as a Scalar
1.4.2.2 Probability of Fuzzy Events as a Fuzzy Set
1.5 Fuzzy Logic and Approximate Reasoning
1.5.1 Linguistic Variables
1.5.2 Fuzzy Logic
1.5.2.1 Classical Logics Revisited
1.5.2.2 Truth Tables and Linguistic Approximation
1.5.3 Approximate reasoning
1.5.5 Selected Methods of Determination Memembership Functions
1.5.5.1 Some comment
1.5.5.2 "Pairwise comparison" method
1.5.5.3 "Probabilistic characteristics" method
1.5.6 Concluding remarks
2.1 Basic consruction of the Fuzzy Logic Controller
2.1.1 A model of oranisational
2.1.2 Steps of constructing fuzzy controller
2.1.3 Some defuzzification Methods
2.1.3.1 Max procedure
2.1.3.2 Center-of gravity procedure
2.1.4 Examples of Applications of Fuzzy Controllers
1.3 Fuzzy Relations
Crisp and Fuzzy Relations
Binary Relations
The Composition of Binary Relations, the Fuzzy Max-Min Composition
The Relational Join of Binary Relations