Lectures 2026, summer semester:

Fuzzy sets

February 16
Basic notions. System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.
Record of this lecture, mp4
Record of a former lecture, mp4, pdf

February 23
Lecture cancelled (postponed).

March 2
Fuzzy inclusion.
Fuzzy negations. Representation theorem for fuzzy negations.
Record of this lecture, mp4
Record of a former lecture, mp4, pdf
Record of an older lecture, mp4, pdf

March 9
Fuzzy complements.
Fuzzy conjunctions (triangular norms), Triangular Norms and Conorms. Scholarpedia, p.10029.
Record of this lecture, mp4
Record of a former lecture, mp4, pdf
Record of an older lecture, mp4, pdf

March 16
Representation theorem for strict conjunctions.
Representation theorem for nilpotent conjunctions.
Examples of fuzzy intersections.
Fuzzy disjunctions (triangular conorms).
Record of this lecture, mp4
Record of a former lecture, mp4, pdf
Record of an older lecture, mp4

March 23
Representation theorems for fuzzy disjunctions.
Examples of fuzzy unions.
Properties of fuzzy propositional and set operations.
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March 30
Fuzzy implications and biimplications.
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April 13
Fuzzy relations, their composition.
Special fuzzy relations, fuzzy equivalence (similarity).
Projections of fuzzy relations.
Cylindric extension (cartesian product) of fuzzy sets.
Record of this lecture, mp4.
Record of an older lecture, mp4, pdf

Fuzzy control

Principles of classical control will not be presented. You are directed to the records from previous years.
Descriptions of dynamical systems.
Connections of dynamical 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 a former lecture, mp4
Record of an older lecture, mp4, pdf

April 20
Motivation and principles of fuzzy control.
Record of this lecture, mp4.

April 27
Mamdani-Assilian and residuum-based controllers.
Record of this lecture, mp4.
Record of a former lecture, mp4
Record of an older lecture, mp4, pdf

May 4
Which tasks are suitable for fuzzy control.
Requirements on a fuzzy rule base.
Fuzzy inference and fuzzy relational equations.
Record of this lecture, mp4.
Record of an older lecture, mp4, pdf

May 11
Requirements on a fuzzy rule base 2.
Design of a rule base.
Methods of defuzzification and their properties.
Comparison of fuzzy control to other approaches.
Takagi-Sugeno controllers.
Which tasks are suitable for fuzzy control. Problems and perspectives. Record of this lecture, mp4.
Record of a former lecture, mp4, pdf
Record of an older lecture, mp4, pdf

Miscellaneous

May 18
Fuzzy clustering and its relation to the EM-algorithm