**Lectures 2017:**

**Introduction**

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.

Representation theorem for fuzzy negations.

Fuzzy conjunctions (triangular norms),

Triangular Norms and Conorms. Scholarpedia, p.10029.

Representation theorems.

Fuzzy disjunctions (triangular conorms), representation theorems.

Examples of fuzzy intersections and unions.

Exercises on fuzzy negations and conjunctions and their generators.

Properties of fuzzy propositional and set operations.

Fuzzy implications and biimplications.

**Fuzzy clustering**

EM-algorithm as a fuzzy clustering method.

**Quantum logics** (pp. 1-25 and 45-58)

Generalized models of probability based on set-representable quantum logics.

Generalized models of probability based on set-representable quantum logics.

Generalized models of probability based on quantum logics which are not set-representable.
Problems of conditional probability.