Fuzzy subalgebras with thresholds in BCK/BCI-algebras
Commun. Korean Math. Soc. 2007 Vol. 22, No. 2, 173-181 Printed June 1, 2007
Young Bae Jun Gyeongsang National University
Abstract : Using the \emph{belongs to} relation ($\in$) and \emph{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 $\{\in,$ ${\rm q},$ $\in \!\vee \, {\rm q},$ $\in \!\wedge \, {\rm q}\}$ with $\alpha \ne \, \in \!\wedge \, {\rm q}$ was introduced, and related properties were investigated in \cite{BKMS42-703}. As a continuation of the paper \cite{BKMS42-703}, 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 $(\in, \in\! \vee \, {\rm q})$-fuzzy subalgebra are provided.
Keywords : belong to, quasi-coincident with, $(\alpha, \beta)$-fuzzy subalgebra, fuzzy subalgebra with thresholds, fuzzifying subalgebra, $t$-implication-based subalgebra
