Curricula of the course Fuzzy Logic

Past lectures:

26.2. The problem of choice of many-valued conjunction; according to Bartušek, T., Navara, M.: Conjunctions of many-valued criteria. In: M. Komorníková and R. Mesiar (eds.) Proc. Int. Conf. Uncertainty Modelling'2001, Bratislava, Slovakia, 2001, 67-77.
5.3. Introduction to Boolean algebras: definition, basic examples, incl. Lindenbaum-Tarski algebra partial order functionally complete sets of connectives partitions of unity and their refinements products, subalgebras, homomorphisms, intervals 12.3. Birkhoff's characterization of varieties (WP) Stone representation, ideals, maximal ideals 2.4. Boolean algebras as algebras of characteristic (=membership) functions Many-valued logics and algebras (in general): basic examples and difference from Boolean algebras standard and Lukasiewicz connectives problem of functionally complete sets of connectives algebras of generalized membership functions (clans) Design of fuzzy logical circuits 9.4. MV-algebras: Lukasiewicz clans, MV-algebras 16.4. MV-algebras as lattices, distributivity partitions of unity and their refinements constructions with MV-algebras: products, subalgebras, homomorphisms 23.4. Intervals in MV-algebras, Boolean elements and irreducibility classification of linearly ordered MV-algebras Chang's Completeness Theorem varieties of MV-algebras 30.4. Why classical measure theory is what it is: sigma-additivity, Banach-Tarski paradox, sigma-algebra of sets mixtures and extensions of measures Measures on Borel algebra are determined by values on balls 7.5. Measures on collections of fuzzy sets: tribes, (T-)measures characterization of measures on Lukasiewicz tribes 14.5. Frank triangular norms characterization of measures on tribes w.r.t. strict triangular norms 21.5. lecture cancelled (shifted to 14.5.) 28.5. Measures on sigma-complete MV-algebras, Loomis-Sikorski theorem

(WP = without proof)

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