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 $\lessdot$-subset, $\Upsilon$-subset, and anti subset are constructed, and the conditions under which they can be BE-ideals are explored.
