$\varepsilon$-Lukasiewicz fuzzy UP (BCC)-ideals: A new frontier in UP (BCC)-algebras

This paper presents the development of $\varepsilon$-Lukasiewicz fuzzy sets using the Lukasiewicz $t$-norm derived from a given fuzzy set. These $\varepsilon$-Lukasiewicz fuzzy sets are subsequently applied to UP (BCC)-algebras. In addition, the paper introduces the concept of $\varepsilon$-Lukasiewicz fuzzy UP (BCC)-ideals and examines their various properties. Three specific subsets, termed the $\in$-set, $q$-set, and $O$-set, are constructed, with an exploration of the conditions under which these subsets qualify as UP (BCC)-ideals.