Curricula of the course Fuzzy Logic

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.