### Curricula of the course Fuzzy Logic

**Lectures 2004:**

16.3. Introduction to Boolean algebras:
definition, basic examples, incl. Lindenbaum-Tarski algebra
partial order
partitions of unity and their refinements
23.3.
Many-valued logics and algebras (in general):
basic examples and difference from Boolean algebras
standard, product, and Lukasiewicz connectives
algebras of generalized membership functions (clans)
Lukasiewicz clans, MV-algebras
30.3.
MV-algebras as lattices, distributivity
partitions of unity and their refinements
5.4.
Boolean elements
classification of linearly ordered MV-algebras
Chang's Completeness Theorem
19.4.
Why classical measure theory is what it is:
sigma-additivity, Banach-Tarski paradox, sigma-algebra of sets
Measures on Borel sigma-algebra are determined by values on balls
26.4.
Measures on collections of fuzzy sets (tribes)
characterization of measures on Lukasiewicz and other tribes
Basic ideas of fuzzy control
4.5.
Fuzzy implications.
Basics of fuzzy control.
Mamdani-Assilian and residuum-based fuzzy controller.
11.5. přednáška se nekoná kvůli konferenci ECCV.
18.5.
Fuzzy control.
Requirements for the rule base.
Fuzzy relational equations and their solvability.
25.5.
Requirements for a fuzzy rule base and its consequences.
Literature:
D. Driankov, H. Hellendoorn, M. Reinfrank,
An Introduction to Fuzzy Control, Springer, Berlin, Heidelberg, 1993.
(Part 2)
Moser, B., Navara, M.:
Which triangular norms are convenient for fuzzy controllers?
In: Proc. EUSFLAT-ESTYLF Joint Conf. 99,
Universitat de les Illes Balears, Palma (Mallorca), Spain, 1999, 75-78.
or Moser, B., Navara, M.:
Fuzzy controllers with conditionally firing rules.
IEEE Trans. Fuzzy Systems 10 (2002), No. 3, 340-348.
(Sections 1-3)
1.6.
Defuzzification

**Your feedback is expected and welcome!**

navaracmp.felk.cvut.cz