Positive implicative BE-filters of BE-algebras based on Lukasiewicz fuzzy sets

Lukasiewicz fuzzy set is applied to positive implicative filter of BE-algebra. The notion of positive implicative Lukasiewiczfuzzy BE-filters is introduced, and its properties are investigated. The relationship between fuzzy positive implicative BE-filter and positive implicative Lukasiewicz fuzzy BE-filter is discussed, and conditions under which Lukasiewicz fuzzy BE-filter can be positive implicative Lukasiewicz fuzzy BE-filter are explored. Characterizations of positive implicative Lukasiewicz fuzzy BE-filter are provided. Conditions for Lukasiewicz fuzzy set to be positive implicative Lukasiewicz fuzzy BE-filter are considered. Conditions are found where E-set, q-set, and O-set of the Lukasiewicz fuzzy set can be positive implicative BE-filter.