$ε$-Lukasiewicz fuzzy UP (BCC)-subalgebras of UP (BCC)-algebras (European Journal of Pure and Applied Mathematics, 2024)
The idea of Lukasiewicz $t$-norm is used to construct the concept of $ε$-Lukasiewicz fuzzy sets based on a given fuzzy set. The $ε$-Lukasiewicz fuzzy sets are applied to UP (BCC)-algebras. Moreover, the notion of $ε$-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.
Keywords: UP (BCC)-algebra; $ε$-Łukasiewicz fuzzy set; $ε$-Łukasiewicz fuzzy UP (BCC)-subalgebra