Generalization of Fuzzy Soft BCK / BCI -Algebras

Abstract

In this paper, the notions of $\left(\in ,\in \vee q\right)$ -fuzzy soft $\text{BCK}/\text{BCI}$ -algebras and $\left(\in ,\in \vee q\right)$ -fuzzy soft sub- $\text{BCK}/\text{BCI}$ -algebras are introduced, and related properties are investigated. Furthermore, relations between fuzzy soft $\text{BCK}/\text{BCI}$ -algebras and $\left(\in ,\in \vee q\right)$ -fuzzy soft $\text{BCK}/\text{BCI}$ -algebras are displayed. Moreover, conditions for an $\left(\in ,\in \vee q\right)$ -fuzzy soft $\text{BCK}/\text{BCI}$ -algebra to be a fuzzy soft $\text{BCK}/\text{BCI}$ -algebra are provided. Also, the union, the extended intersection, and the “AND”-operation of two $\left(\in ,\in \vee q\right)$ -fuzzy soft (sub-) $\text{BCK}/\text{BCI}$ -algebras are discussed, and a characterization of an $\left(\in ,\in \vee q\right)$ -fuzzy soft $\text{BCK}/\text{BCI}$ -algebra is established.