====== XEP33FLO Fuzzy Logic ======
=== News ===
  * The latest news will be here.
  * In the winter semester 2025/26, the course will be held in English or Czech, depending on the students enrolled. The schedule will be decided in September by a Doodle poll so that it would fit as many students as possible.
  * 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.
  * The text on fuzzy propositional operations was updated on March 21, 2025. Comments are welcome.
  * The lectures can be streamed and recorded on request. However, they are mostly covered by recordings from previous years.
=== Links ===
  *[[https://cw.felk.cvut.cz/brute/|BRUTE]]
=== Curricula ===
== Fuzzy sets ==
  * 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.
== Probability of fuzzy events ==
  * 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.
== Fuzzy logic ==
  * 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.