Lukasiewicz fuzzy subalgebras in BCK-algebras and BCI-algebras

초록

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

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