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. پرونده مقاله

‎‎Using the concept of fuzzy points‎, ‎the notion of fuzzy filters in pre-ordered residuated systems is introduced‎, ‎and their relevant properties are investigated and analyzed‎. ‎Characterization of fuzzy filters are displayed‎. ‎Fuzzy filters are formed using filters‎. ‎The concepts of positive set‎, ‎$\in_{t}$-set‎, ‎(extended) $q_{t}$-set are defined and the conditions under which they become filters are explored‎. ‎The concept of fuzzy filter with thresholds is introduced and related properties are investigated‎. پرونده مقاله