4 research outputs found
Normal filters in residuated lattices
Residuated lattices play an important role in the study of fuzzy logic. In the present paper, we introduce the notion of a normal filter in a residuated lattice and give some characterizations of them. We state and prove some theorems and examples which determine the relationship between this notion and the other types of filters of a residuated lattice. Finally we investigate the relation between the set of dense elements and normal filters of a residuated lattice
Normal filters in residuated lattices
Residuated lattices play an important role in the study of fuzzy logic. In the present paper, we introduce the notion of a normal filter in a residuated lattice and give some characterizations of them. We state and prove some theorems and examples which determine the relationship between this notion and the other types of filters of a residuated lattice. Finally we investigate the relation between the set of dense elements and normal filters of a residuated lattice.</span
Characterizations of Some Fuzzy Prefilters (Filters) in E
We introduce and study some
types of fuzzy prefilters (filters) in EQ-algebras. First,
we present several characterizations of fuzzy positive
implicative prefilters (filters), fuzzy implicative prefilters
(filters), and fuzzy fantastic prefilters (filters). Next,
using their characterizations, we mainly consider the
relationships among these special fuzzy filters. Particularly,
we find some conditions under which a fuzzy
implicative prefilter (filter) is equivalent to a fuzzy positive
implicative prefilter (filter). As applications, we
obtain some new results about classical filters in EQ-algebras and some related results about fuzzy filters in
residuated lattices