Lectures 2023:

Fuzzy sets

February 22
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.
Record of the lecture, mp4, pdf

March 1
Fuzzy negations. Representation theorem for fuzzy negations. Fuzzy complements.
Record of the lecture, mp4, pdf

March 8
Fuzzy conjunctions (triangular norms), Triangular Norms and Conorms. Scholarpedia, p.10029. Representation theorem for strict conjunctions.
Record of the lecture, mp4, pdf

March 15
Representation theorem for nilpotent conjunctions.
Fuzzy disjunctions (triangular conorms), representation theorems. Fuzzy algebras and their properties. Examples of fuzzy intersections and unions.
Properties of fuzzy propositional and set operations.
Record of the lecture, mp4

March 22 Fuzzy implications and biimplications.
Fuzzy relations, their composition.
Special fuzzy relations, fuzzy equivalence (similarity).
Record of the lecture, mp4, pdf

March 29
Projections of fuzzy relations.
Cylindric extension (cartesian product) of fuzzy sets.
Extension principle for binary relations (unary operations).
Record of the lecture, mp4, pdf

Fuzzy control: PDF (English) PDF (Czech)

April 5
Principles of classical control.
Descriptions of dynamic systems.
Connections of dynamic systems.
The role of feedback in control.
Principles of classical linear control.
The role of eigenvalues on stability and the problem of their determination.
Record of the lecture, mp4, pdf

April 12
Convex fuzzy sets.
Principles of fuzzy control.
Which tasks are suitable for fuzzy control.
Record of the lecture, mp4

April 19
Mamdani-Assilian and residuum-based controllers.
Requirements on a fuzzy rule base.
Record of the lecture, mp4, pdf

April 26
Fuzzy inference and fuzzy relational equations.
Methods of defuzzification and their properties.
Record of the lecture, mp4, pdf

Probability of fuzzy events

May 3
Fuzzifications of sigma-algebras.
Record of the lecture, mp4, pdf

May 10
Rector's day; no lecture.

May 17
Properties of fuzzy sigma-algebras.
Motivation and definitions of probabilities of fuzzy events.
Record of the lecture, mp4, pdf

May 24
Properties and characterizations of probabilities of fuzzy events.