L-Fuzzy Filters of Almost Distributive Lattices

Abstract

The notion of an Almost Distributive lattice (ADL) is a common abstraction of several lattice theoretic and ring theoretic generalizations of Boolean algebra and Boolean ring. A complete lattice satisfying the infinite meet distributive law is called a frame. In this paper, we introduce the notion of $L$-fuzzy filter of a given ADL $A$ with a maximal element, where $L$ is a given frame and here we apply the general theory of algebraic fuzzy systems to the class of $L-$fuzzy filters of an ADL.