Description
Book Synopsis
1 Elementary Set Theory.- Section 1 Sets and subsets.- Section 2 Functions and relations.- Section 3 Partially ordered sets.- Section 4 The lattice of subsets of a set.- Section 5 Characteristic functions.- Section 6 Notes.- 2 Fuzzy Sets.- Section 1 Definitions and examples.- Section 2 Lattice theoretical operations on fuzzy sets.- Section 3 Pseudocomplementation.- Section 4 Fuzzy sets, functions and fuzzy relations.- Section 5 ?-levels.- Section 6 Notes.- 3 t-Norms, t-Conorms and Negations.- Section 1 Pointwise extensions.- Section 2 t-Norms and t-Conorms.- Section 3 Negations.- Section 4 Notes.- 4 Special Types of Fuzzy Sets.- Section 1 Normal fuzzy sets.- Section 2 Convex fuzzy sets.- Section 3 Piecewise linear fuzzy sets.- Section 4 Compact fuzzy sets.- Section 5 Notes.- 5 Fuzzy Real Numbers.- Section 1 The probabilistic view.- Section 2 The non-probabilistic view.- Section 3 Interpolation.- Section 4 Notes.- 6 Fuzzy Logic.- Section 1 Connectives in classical logic.- Section 2 Fundamental classical theorems.- Section 3 Basic principles of fuzzy logic.- Section 4 Lattice generated fuzzy connectives.- Section 5 t-Norm generated fuzzy connectives.- Section 6 Probabilistically generated fuzzy connectives.- Section 7 Notes.- 7 Bibliography.- Section 1 Books.- Section 2 Articles.
Table of Contents
List of Figures. Preface. 1: Elementary Set Theory. 1. Sets and subsets. 2. Functions and relations. 3. Partially ordered sets. 4. The lattice of subsets of a set. 5. Characteristic functions. 6. Notes. 2: Fuzzy Sets. 1. Definitions and examples. 2. Lattice theoretical operations on fuzzy sets. 3. Pseudocomplementation. 4. Fuzzy sets, functions and fuzzy relations. 5. alpha-levels. 6. Notes. 3: t-Norms, t-Conorms and Negations. 1. Pointwise extensions. 2. t-Norms and t-Conorms. 3. Negations. 4. Notes. 4: Special Types of Fuzzy Sets. 1. Normal fuzzy sets. 2. Convex fuzzy sets. 3. Piecewise linear fuzzy sets. 4. Compact fuzzy sets. 5. Notes. 5: Fuzzy Real Numbers. 1. The probabilistic view. 2. The non-probabilistic view. 3. Interpolation. 4. Notes. 6: Fuzzy Logic. 1. Connectives in classical logic. 2. Fundamental classical theorems. 3. Basic principles of fuzzy logic. 4. Lattice generated fuzzy connectives. 5. t-Norm generated fuzzy connectives. 6. Probabilistically generated fuzzy connectives. 7. Notes. 7: Bibliography. 1. Books. 2. Articles. Index.
