$\varepsilon$-Lukasiewicz fuzzy UP (BCC)-subalgebras of UP (BCC)-algebras

Abstract

The idea of Lukasiewicz $t$-norm is used to construct the concept of $\varepsilon$-Lukasiewicz fuzzy sets based on a given fuzzy set. The $\varepsilon$-Lukasiewicz fuzzy sets are applied to UP (BCC)-algebras. Moreover, the notion of $\varepsilon$-Lukasiewicz fuzzy UP (BCC)-subalgebras is introduced, and its various properties are investigated. Three subsets, so-called $\in$-set, $q$-set, and $O$-set, are constructed, and the conditions under which they can be UP (BCC)-subalgebras are explored.