SOME PROPERTIES OF FUZZY FILTERS IN BCI/BCK-ALGEBRAS

Abstract

BCI, BCK, MV-algebras arose as the algebras of non classical logic in the same way as boolean algebra arose as the algebra of classical logic. As a dual to the notion of fuzzy ideals of BCI-algebra, in [4], we have introduced the notion of fuzzy filters and established their basic properties and characterization. In this paper, we consider the notion of ultrafilters and show that such fuzzy filters take only the values {0, 1} and have level filters which are maximal filters. It is shown that fuzzy ultrafilters of MV-algebra are fuzzy primes and that fuzzy ideals and fuzzy filters come in pairs. Finally, we established some algorithms for filters and fuzzy filters.