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.
Fuzzy conjunctions (triangular norms), representation theorems.
Fuzzy disjunctions (triangular conorms), representation theorems.
Triangular Norms and Conorms. Scholarpedia, p.10029.
Fuzzy algebras and their properties.
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
Algebra of fuzzy numbers and intervals
Fuzzy control: PDF (English) PDF (Czech)
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.
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