### 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)

**Your feedback is expected and welcome!**

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