Curricula of the course Fuzzy Logic

Lectures 2013:

Preliminaries: Printable version of lectures: English, Czech

19.2.2013
System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.

27.2.2013
Fuzzy inclusion.
Fuzzy negations.
Representation theorem for fuzzy negations.

6.3.2013
Fuzzy conjunctions (triangular norms),
Triangular Norms and Conorms. Scholarpedia, p.10029.

13.3.2013
Representation theorems.
Fuzzy disjunctions (triangular conorms), representation theorems.
Examples of fuzzy intersections and unions.

20.3.2013
Exercises on fuzzy negations and conjunctions and their generators.
Properties of fuzzy propositional and set operations.

3.4.2013
Fuzzy implications and biimplications.
For the following topics, see Lectures on classical and fuzzy logics.
Classical logic: syntax, semantics, tautologies.

10.4.2013
Classical logic: axioms, deduction, theorems.

17.4.2013
Classical logic: completeness.
Fuzzy logic: axioms and theorems of basic logic.

2.5.2013
Fuzzy logic: semantics of basic logic, deduction in basic logic, completeness.

7.5.2013
Other types of fuzzy logics: Gödel logic, product logic (its alternative axiomatization, formulas which are tautologies of product logic but not of Gödel or basic logic), £ukasiewicz logic and its alternative axiomatization.

15.5.2013
Rational Pavelka logic.