Fuzzy Ideals and Fuzzy Filters of Pseudocomplemented Semilattices

Abstract

In this paper, we introduce the concept of kernel fuzzy ideals and ⁎-fuzzy filters of a pseudocomplemented semilattice and investigate some of their properties. We observe that every fuzzy ideal cannot be a kernel of a ⁎-fuzzy congruence and we give necessary and sufficient conditions for a fuzzy ideal to be a kernel of a ⁎-fuzzy congruence. On the other hand, we show that every fuzzy filter is the cokernel of a ⁎-fuzzy congruence. Finally, we prove that the class of ⁎-fuzzy filters forms a complete lattice that is isomorphic to the lattice of kernel fuzzy ideals.