\((\bar{\varepsilon},\overline{\varepsilon\wedge q_k})\)-fuzzy Subalgebras In BCK/BCI-algebras

Abstract

In this paper, the notion of not quasi-coincidence \(\bar{q}\) of a fuzzy point with a fuzzy set is considered. We introduce the notion of \((\bar{\varepsilon},\overline{\varepsilon\wedge q_k})\)-fuzzy \((\bar{\varepsilon},\overline{ q_k})\)-fuzzy subalgebra in a BCK/BCI-algebra X and several properties are investigated. Specially, we show that under certain conditions an \((\bar{\varepsilon},\overline{\varepsilon\wedge q_k})\) -fuzzy subalgebra can be expressed such that consist of a union of two proper non-equivalent \((\bar{\varepsilon},\overline{\varepsilon\wedge q_k})\) - fuzzy subalgebras.