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

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 

MV-algebras as lattices, distributivity
partitions of unity and their refinements

Boolean elements
classification of linearly ordered MV-algebras
Chang's Completeness Theorem

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

Measures on collections of fuzzy sets (tribes)
characterization of measures on Lukasiewicz and other tribes

Basic ideas of fuzzy control

Fuzzy implications.
Basics of fuzzy control.
Mamdani-Assilian and residuum-based fuzzy controller.

11.5. přednáška se nekoná kvůli konferenci ECCV.

Fuzzy control.
Requirements for the rule base.
Fuzzy relational equations and their solvability.

Requirements for a fuzzy rule base and its consequences.

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)


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