FUZZY MEDIAL FILTERS OF PSEUDO BE-ALGEBRAS

Abstract

In this paper, the notion of fuzzy medial filters of a pseudo BE-algebra is defined, and some of the properties are investigated. We show that the set of all fuzzy medial filters of a pseudo BE-algebra is a complete lattice. Moreover, we state that in commutative pseudo BE-algebras fuzzy filters and fuzzy medial filters coincide. Finally, the notion of a fuzzy implicative filter is introduced and proved that every fuzzy implicative filter is a fuzzy medial filter, and we show that the converse is not valid in general.