**Lectures 2010:**

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

16.2.2010

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.

2.3.2010

Representation theorem for fuzzy negations.

Fuzzy conjunctions (triangular norms), representation theorems.

16.3.2010

Fuzzy disjunctions (triangular conorms), representation theorems.

Triangular Norms and Conorms. Scholarpedia, p.10029.

Fuzzy algebras and their properties.

23.3.2010

Properties of fuzzy propositional and set operations.

Fuzzy implications.

30.3.2010

Fuzzy implications and biimplications.

Fuzzy relations, their composition.

6.4.2010

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)

13.4.2010

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

20.4.2010

Extension principle for binary operations

Algebra of fuzzy numbers and intervals

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

27.4.2010

Principles of fuzzy control.

Which tasks are suitable for fuzzy control.

Mamdani-Assilian and residuum-based controllers.

4.5.2010

Requirements on a fuzzy rule base.

Fuzzy inference and fuzzy relational equations.

11.5.2010

Methods of defuzzification and their properties.

Comparison of fuzzy control to other approaches.

Takagi-Sugeno controllers.

**Quantum logic:**

18.5.10 (the last lecture, change of programme)

Motivation of quantum probability in real-world situations

Models of probability including quantum uncertainty:
classes of subsets, generalized probability spaces, orthomodular lattices as a generalization of Boolean algebras