Subalgebras of type (<i>α, β</i>) based on <i>m</i>-polar fuzzy points in <i>BCK/BCI</i>-algebras

Abstract

In this article, we present the idea of quasi-coincidence of an $m$-polar fuzzy point with an $m$-polar fuzzy subset. By utilizing this new idea, we further introduce the notion of $m$-polar $(\alpha, \beta)$-fuzzy subalgebras in $BCK/BCI$-algebras which is a generalization of the idea of $(\alpha, \beta)$-bipolar fuzzy subalgebras in $BCK/BCI$-algebras. Some interesting results of the $BCK/BCI$-algebras in terms of $m$-polar $(\alpha, \beta)$-fuzzy subalgebras are given. By using $m$-polar $(\in, \in \vee q)$-fuzzy subalgebras, some interesting results are obtained. Conditions for an $m$-polar fuzzy set to be an $m$-polar $(q, \in \vee q)$-fuzzy subalgebra and an $m$-polar $(\in, \in \vee q)$-fuzzy subalgebra are provided. Characterizations of $m$-polar $(\in, \in \vee q)$-fuzzy subalgebras in $BCK/BCI$-algebras by using level cut subsets are explored.