Fuzzy filter spectrum of a BCK algebra

Abstract

The notion of fuzzy s-prime filters of a bounded BCK-algebra is introduced. We discuss the relation between fuzzy s-prime filters and fuzzy prime filters. By the fuzzy s-prime filters of a bounded commutative BCK-algebra X, we establish a fuzzy topological structure on X. We prove that the set of all fuzzy s-prime filters of a bounded commutative BCK-algebra forms a topological space. Moreover, we show that the set of all fuzzy s-prime filters of a bounded implicative BCK-algebra is a Hausdorff space. Copyright 2011 Xiao Long Xin et al.