Fuzzy Sets and Fuzzy Logic

1 Logical Preliminaries.- 1.1 Basic notions.- 1.2 t-norms and ?-operators.- 1.3 t-norm based connectives.- 2 Basic fuzzy set theory.- 2.1 Set algebra for fuzzy sets.- 2.2 Fuzzy relations.- 2.3 The full image under a relation.- 2.4 Special types of fuzzy relations.- 2.5 Graded properties of fuzzy relations.- 3 Set equations with fuzzy sets.- 3.1 Fuzzy equations and some of their applications.- 3.2 Solvability of fuzzy relational equations.- 3.3 Solvability of fuzzy arithmetical equations.- 3.4 Solvability of systems of fuzzy equations.- 3.5 Solvability degrees and approximate solutions.- 3.6 Towards more difficult equations.- 4 Fuzzy controllers.- 4.1 The construction of fuzzy controllers.- 4.2 The problem of interaction.- 4.3 Manipulation of fuzzy data.- 5 Methodological issues.- 5.1 Comparison of fuzzy sets.- 5.2 Approximate solutions.- 5.3 Fuzzy equations for processing fuzzy data.- 5.4 Evaluation of fuzzy models.- 5.5 Controllability and predictability.

1 Logical Preliminaries. - 1. 1 Basic notions. - 1. 2 t-norms and ? -operators. - 1. 3 t-norm based connectives. - 2 Basic fuzzy set theory. - 2. 1 Set algebra for fuzzy sets. - 2. 2 Fuzzy relations. - 2. 3 The full image under a relation. - 2. 4 Special types of fuzzy relations. - 2. 5 Graded properties of fuzzy relations. - 3 Set equations with fuzzy sets. - 3. 1 Fuzzy equations and some of their applications. - 3. 2 Solvability of fuzzy relational equations. - 3. 3 Solvability of fuzzy arithmetical equations. - 3. 4 Solvability of systems of fuzzy equations. - 3. 5 Solvability degrees and approximate solutions. - 3. 6 Towards more difficult equations. - 4 Fuzzy controllers. - 4. 1 The construction of fuzzy controllers. - 4. 2 The problem of interaction. - 4. 3 Manipulation of fuzzy data. - 5 Methodological issues. - 5. 1 Comparison of fuzzy sets. - 5. 2 Approximate solutions. - 5. 3 Fuzzy equations for processing fuzzy data. - 5. 4 Evaluation of fuzzy models. - 5. 5 Controllability and predictability.