Lectures 2012:
Preliminaries: Printable version of lectures: English, Czech
14.2.2012
System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.
21.2.2012
Fuzzy inclusion.
Fuzzy negations.
Representation theorem for fuzzy negations.
6.3.2012
Fuzzy conjunctions (triangular norms), representation theorems.
Triangular Norms and Conorms. Scholarpedia, p.10029.
13.3.2012
Fuzzy disjunctions (triangular conorms), representation theorems.
Examples of fuzzy intersections and unions.
20.3.2012
Exercises on fuzzy negations and conjunctions and their generators.
Properties of fuzzy propositional and set operations.
27.3.2012
Fuzzy implications and biimplications.
Classical logic: syntax, semantics, tautologies.
3.4.2012
Classical logic: axioms, deduction, theorems, completeness.
10.4.2012
Fuzzy logic: axioms and theorems of basic logic.
17.4.2012
Fuzzy logic: semantics of basic logic.
24.4.2012
Fuzzy logic: deduction in basic logic, completeness.
Other types of fuzzy logics: Gödel logic, product logic.
10.5.2012
Other types of fuzzy logics: product logic (continued: its alternative axiomatization, formulas which are tautologies of product logic but not of Gödel or basic logic), £ukasiewicz logic and its alternative axiomatization.
15.5.2012
Rational Pavelka logic.