$\varepsilon$-Lukasiewicz fuzzy UP (BCC)-subalgebras of UP (BCC)-algebras
DOI:
https://doi.org/10.29020/nybg.ejpam.v17i3.5311Keywords:
UP (BCC)-algebra, $\varepsilon$-{\L}ukasiewicz fuzzy set, $\varepsilon$-{\L}ukasiewicz fuzzy UP (BCC)-subalgebraAbstract
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.
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