**Lectures 2015:**

**Preliminaries:**
Printable version of lectures:
English,
Czech

18.2.2015

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

25.2.2015

Fuzzy inclusion.

Fuzzy negations.

Representation theorem for fuzzy negations.

4.3.2015 Lecture cancelled.

11.3.2015

Fuzzy conjunctions (triangular norms),

Triangular Norms and Conorms. Scholarpedia, p.10029.

Representation theorems.

18.3.2015

Fuzzy disjunctions (triangular conorms), representation theorems.

25.3.2015

Examples of fuzzy intersections and unions.

Exercises on fuzzy negations and conjunctions and their generators.

Properties of fuzzy propositional and set operations.

1.4.2015

Fuzzy implications and biimplications.

Fuzzy relations, their composition.

8.4.2015

Fuzzy equivalence (similarity), hereditary (consistent) properties.

Projection of a fuzzy relation.

Cylindric extension (cartesian product) of fuzzy sets.

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

15.4.2015

Projections of fuzzy relations.

Cylindrical extension (cartesian product) of fuzzy sets.

Extension principle for binary relations (unary operations).

Convex fuzzy sets, fuzzy numbers and intervals.

Extension principle for binary operations.

**Fuzzy control:**
PDF (English)
PDF (Czech)

22.4.2015

Brķef introduction to classical control, its difficulties.

29.4.2015

Principles of fuzzy control.

Which tasks are suitable for fuzzy control.

Mamdani-Assilian and residuum-based controllers.

6.5.2015

Requirements on a fuzzy rule base.

Fuzzy inference and fuzzy relational equations.

13.5.2015

Methods of defuzzification and their properties.

Comparison of fuzzy control to other approaches.

Takagi-Sugeno controllers.

**Quantum logic:**

20.5.2015

Motivation of quantum probability in real-world situations.

Models of probability including quantum uncertainty:
classes of subsets.

27.5.2015 Lecture postponed

3.6.2015

Generalized probability spaces, (non-)additivity of expectations and other strange quantum phenomena demonstrated on this mathematical model.