XEP33FLO Fuzzy Logic

• The latest news will be here.
• In the summer semester 2025/26, the course will be held in English. Lectures will be in Dejvice, JP3:B-633 (Jugoslávských partyzánů 3, building B - the lower one), entrance closer to the square (not to the canteen), on the 6th floor; you will probably have to wait in front of the door. The course will take place each Monday, 11:00-12:30, starting on February 16. A shift of up to 15 minutes is possible.
• The lectures will be available also online using BigBlueButton (BBB) Open Source software; Tutorial video for students.

The connection can be found in Brute → Conference Rooms or using the following links: XEP33FLO_1 - Scope: 1 - Mon 11:00 - 12:30, Planed on:16.2.2026 10:45, duration: 120 Invitation link for all students/teachers at CTU: https://cw.felk.cvut.cz/brute/bbb/course/cw_S1h85iRC1Z
Invitation link for non-CTU users: https://cw.felk.cvut.cz/bbb/course/cw_S1h85iRC1Z

• The curricula will contain a general introduction to fuzzy sets (about 5 weeks), followed by lectures on specific topics chosen by you from several options. Please, read the previous curricula and prepare your comments.

• BRUTE
• Lecture notes and other supporting material

• Basic notions. System of cuts of a fuzzy set, theorem on representation of fuzzy sets by cuts, conversion between vertical and horizontal representation.
• Fuzzy inclusion. Fuzzy negations. Representation theorem for fuzzy negations.
• Fuzzy complements. Fuzzy conjunctions (triangular norms).
• Representation theorem for strict conjunctions. Representation theorem for nilpotent conjunctions. Fuzzy disjunctions (triangular conorms), representation theorems. Fuzzy algebras and their properties. Examples of fuzzy intersections and unions.
• Fuzzy disjunctions, representation theorems. Examples of fuzzy intersections and unions. Properties of fuzzy propositional and set operations.
• Fuzzy implications and biimplications.

• Alternative definition of a sigma-algebra and probability on it.
• Comparison to the Kolmogorov axiomatization of probability.
• Fuzzifications of sigma-algebras.
• Properties of fuzzy sigma-algebras.
• Motivation and definitions of probabilities of fuzzy events.
• Properties and characterizations of probabilities of fuzzy events.

• Syntax of classical logic: formulas, axioms, deduction, theorems.
• Deduction theorem in classical logic.
• Semantics of classical logic: evaluation, tautologies. Interplay of syntax and semantics of classical logic: soundness, completeness.
• Basic logic: axioms, theorems, semantics.
• Deduction in basic logic.
• Completeness of basic logic.
• 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), Łukasiewicz logic and its alternative axiomatization.
• Rational Pavelka logic.
• Compactness of logics.
• Testing tautologies in Gödel and Łukasiewicz logic.