Preliminaries: Printable version of lectures: English, Czech
System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.
Representation theorem for fuzzy negations.
4.3.2015 Lecture cancelled.
Fuzzy conjunctions (triangular norms),
Triangular Norms and Conorms. Scholarpedia, p.10029.
Fuzzy disjunctions (triangular conorms), representation theorems.
Examples of fuzzy intersections and unions.
Exercises on fuzzy negations and conjunctions and their generators.
Properties of fuzzy propositional and set operations.
Fuzzy implications and biimplications.
Fuzzy relations, their composition.
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).
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)
Brķef introduction to classical control, its difficulties.
Principles of fuzzy control.
Which tasks are suitable for fuzzy control.
Mamdani-Assilian and residuum-based controllers.
Requirements on a fuzzy rule base.
Fuzzy inference and fuzzy relational equations.
Methods of defuzzification and their properties.
Comparison of fuzzy control to other approaches.
Motivation of quantum probability in real-world situations.
Models of probability including quantum uncertainty: classes of subsets.
27.5.2015 Lecture postponed
Generalized probability spaces, (non-)additivity of expectations and other strange quantum phenomena demonstrated on this mathematical model.