The notion of fuzzy set.
System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.
Fuzzy propositional operations: fuzzy negations, fuzzy conjunctions (t-norms), fuzzy disjunctions (t-conorms), fuzzy implications and biimplications.
Properties of fuzzy propositional and set operations.
Fuzzy relations, their composition, fuzzy equivalence (similarity), hereditary (consistent) properties.
Projection of a fuzzy relation.
Cylindric extension (cartesian product) of fuzzy sets.
Basic principles of fuzzy control, Takagi-Sugeno and Mamdani-Assilian fuzzy controller, fuzzy relational equations.
Requirements on the rule base.
Methods of defuzzification and their properties.
Comparison of fuzzy control to other approaches.
Wajsberg algebras (MV-algebras), residuated lattices, BL-algebras.
fuzzy similarity and its applications.