### Curricula of the course Fuzzy Logic

**Lectures 2020:**

**Introduction** (with comments)

Basic notions. 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.

Fuzzy algebras and their properties.

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.

Fuzzy implications and biimplications.

Fuzzy relations.

Fuzzy numbers and intervals, fuzzy arithmetics.

Cluster analysis (with comments)

k-means,

fuzzy c-means,

EM-algorithm.

Hierarchical cluster analysis

transitive closure of a fuzzy relation,

construction of a dendrogram from a fuzzy equivalence relation,

example of application: clustering of European countries according to the Covid-19 expression.