FUZZY SUBALGEBRAS WITH THRESHOLDS IN BCK/BCI-ALGEBRAS

FUZZY SUBALGEBRAS WITH THRESHOLDS IN BCK/BCI-ALGEBRAS

Using the belongs to relation ($\in$) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of ($\alpha,\;\beta$)-fuzzy subalgebras where $\alpha,\;\beta$ are any two of $\{{\in},\;q,\;{\in}\;{\vee}\;q,\;{\in}\;{\wedge}\;q\}$ with ${\alpha}\;{\neq}\;{\in}\;{\wedge}\;q$ was introduced, and related properties were investigated in [3]. As a continuation of the paper [3], in this paper, the notion of a fuzzy subalgebra with thresholds is introduced, and its characterizations are obtained. Relations between a fuzzy subalgebra with thresholds and an (${\in},\;{\in}\;{\vee}\;q$)-fuzzy subalgebra are provided.