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Consistency of fuzzy logic theories of inference systems
 Havlíček, Petr ; Ivánek, Jiří (advisor) ; Jirků, Petr (referee)
This thesis focus on consistency of a specific class of fuzzy logic theories that represent certain inference system. This class of theories is defined as theories containing especially so called special axioms representing rules of modeled inference system and evaluated set of formulas representing case data. Functional approach is used to develop three popular fuzzy calculi: the Gödel logic, Łukasiewicz logic and product logic. As a language it is used the language of first order propositional fuzzy logic with valuation. To check consistency we use the concept of inconsistency degree and in Łukasiewicz logic also the principle of polar index. The concept of consistency degree is also described, but not used. Simple algorithm is developed to check consistency of theory upon the basis of inconsistency degree principle. A method of use of polar index is also described and illustrated. For each fuzzy theory a term of corresponding classical theory is defined. Then consistency of fuzzy theories and their corresponding classical theories are compared. The results of comparison are presented on the example of the ad-hoc created diagnostic inference system MEDSYS II. In the end the relation between consistency of fuzzy theory of inference system and it's corresponding theory is introduced for all three used calculi and both contradiction concepts.
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