**Lectures 2007:**

**Preliminaries:**

12.3.07

System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.

Fuzzy inclusion.

Fuzzy negations.

19.3.07

Triangular Norms and Conorms. Scholarpedia, p.10029.

Properties of fuzzy propositional and set operations.

26.3.07

Fuzzy implications and biimplications.

Fuzzy relations, their composition, fuzzy equivalence (similarity), hereditary (consistent) properties.

2.4.07

Projection of a fuzzy relation.

Cylindric extension (cartesian product) of fuzzy sets.

Exercises: Fuzzy relations, their composition, fuzzy equivalence (similarity)

**Fuzzy Logic:**

16.4.07

Summary of syntax and semantics of classical logic, deduction, consistence and completeness.

Syntax and semantics of basic (fuzzy) logic, deduction.

23.4.07

Basic logic, deduction, consistence and completeness.

Extensions of basic logic: Gödel, Lukasiewicz, and product logic.

**Similarity:**

30.4.07

Wajsberg algebras (MV-algebras), residuated lattices, BL-algebras.

7.5.07

Divisibility.

Fuzzy similarity and its applications.

14.10.07 Seminar by Magdalena Rencova: Probability on IF-sets: an elementary approach