$ε$-Lukasiewicz fuzzy UP (BCC)-ideals: A new frontier in UP (BCC)-algebras (European Journal of Pure and Applied Mathematics, 2024)
This paper presents the development of $ε$-Lukasiewicz fuzzy sets using the Lukasiewicz $t$-norm derived from a given fuzzy set. These $ε$-Lukasiewicz fuzzy sets are subsequently applied to UP (BCC)-algebras. In addition, the paper introduces the concept of $ε$-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.
Keywords: UP (BCC)-algebra; $\in$-set; $q$-set; $O$-set; $ε$-Lukasiewicz fuzzy sets; $ε$-Lukasiewicz fuzzy UP (BCC)-ideal