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  Math Research  

About Dana Hlinena 's scientific research in mathematics, fuzzy logic and related interesting areas...

Dana Hlinena 's Research

I started my math research with work on construction of triangular norms. Triangular norms (t-norms) are binary operations used in the framework of probabilistic metric spaces and in multi-valued logic, specifically in fuzzy logic. T-norms are a generalization of the usual two-valued logical conjunction, studied by classical logic, for fuzzy logic. Indeed, the classical Boolean conjuction is both commutative and associative. The monotonicity property ensures that the thrue value of conjuction does not decrease if the thrue values of conjucts increase. The requirement that 1 be an identity element corresponds to the interpretation of 1 as thrue. T-norms are also used to construct the intersection of fuzzy sets or as a basis for aggregation operators. In probabilistic metric spaces, t-norms are used to generalize triangle inequality of ordinary metric spaces. Individual t-norms may of course frequently occur in further disciplines of mathematics, since the class contains many familiar functions.

Namely, my phd thesis was about constructions and properties of implikators and conjunctors in multi-valued logic. My phd advisor was Prof. Radko Mesiar.

Now a days I work on some problems of multicriterial decision making with Pavol Kral and Martin Kalina.

List of my publications.

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Created by © Dana Hlinena
Dept. of Mathematics, FEEC BUT Brno
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