title: Characterizations of some fuzzy prefilters (filters) in EQ-algebras.
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.
authors.affiliation: Department of Mathematics, Northwest University, Xi'an 710127, China.
authors.forename: Xiao Long
authors.initials: XL
authors.lastname: Xin
authors.affiliation: Department of Mathematics, Northwest University, Xi'an 710127, China.
authors.forename: Peng Fei
authors.identifier: 0000-0002-0788-9872
authors.initials: PF
authors.lastname: He
authors.affiliation: Department of Mathematics, Northwest University, Xi'an 710127, China.
authors.forename: Yong Wei
authors.initials: YW
authors.lastname: Yang
mesh_terms: D017143:Fuzzy Logic; D008433:Mathematics; D008962:Models, Theoretical