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Characterizations of some fuzzy prefilters (filters) in EQ-algebras
Xiao Long Xin1, Peng Fei He1, Yong Wei Yang1
1Department of Mathematics, Northwest University, Xi'an 710127, China.
Abstract:
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.
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