Lukasiewicz Anti Fuzzy Set and Its Application in BE-algebras - Young Bae Jun (Transactions on Fuzzy Sets and Systems, 2022)
‎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, ‎$Υ$-subset‎, ‎and anti subset are constructed‎, ‎and the conditions under which they can be BE-ideals are explored‎.