lukasiewicz anti fuzzy set and its application in be-algebras

The idea of lukasiewicz t-conorm is used to construct the concept of lukasiewicz anti fuzzy sets based on a given anti fuzzy set, and it is applied to be-algebras. the notion of lukasiewicz anti fuzzy be-ideal is introduced, and its properties are investigated. the conditions under which lukasiewicz anti fuzzy set will be lukasiewicz anti fuzzy be-ideal are explored, and the relationship between anti fuzzy be-ideal and lukasiewicz anti fuzzy be-ideal are discussed. three types of subsets so called ⋖-subset, υ-subset, and anti subset are constructed, and the conditions under which they can be be-ideals are explored.