Algebraické aspekty fuzzy logiky

In this thesis we study filters on algebras of fuzzy logics and their possible applications. We are going to generalize the notion of an implicative/ positive implicative/fantastic filter on BL-algebras by introducing a notion of R-S-filter. We state and prove some properties of R-S-filters and then we show the connection between characterization of R-S-filter and alternative axiomatization of a given logic. We are going to describe the way how to characterize given algebra of implicative logic via R-S-filters. We show that the results published in [1] and [3] are simple consequences of our theory. Next topics of this work are uniform spaces and uniform topologies. Filters are there used to set up so-called Leibnitz congruences. A set of this congruences on the algebra is a (sub)base of a uniformity that we are going to study. We are going to show that results published in [2] and [4] can be easily generalized for any implicative logics