3 research outputs found
Study of Pseudo BL–Algebras in View of Left Boolean Lifting Property
In this paper, we define left Boolean lifting property (right Boolean lifting property) LBLP (RBLP) for pseudo BL–algebra which is the property that all Boolean elements can be lifted modulo every left filter (right filter) and next, we study pseudo BL-algebra with LBLP (RBLP). We show that Quasi local, local and hyper Archimedean pseudo BL–algebra that have LBLP (RBLP) has an interesting behavior in direct products. LBLP (RBLP) provides an important representation theorem for semi local and maximal pseudo BL–algebra
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