A Novel Study Based on Fuzzy p-Ideals of BCI-Algebras

Abstract

In this paper, we propose the concept of $\left(\in ,\in \vee \left(j^{\ast },q_j\right)\right)$ -fuzzy p-ideals in “ $BCI$ -algebras.” We show that “ $\left.\left(\in ,\in \vee q\right)\right)$ -fuzzy p-ideals” and “ $\left(\in \vee \left(j^{\ast },q_j\right),\in \vee \left(j^{\ast },q_j\right)\right)$ -fuzzy $p$ -ideals” are “ $\left(\in ,\in \vee \left(j^{\ast },q_j\right)\right)$ -fuzzy $p$ -ideals.” However, the converse is not true, then presented examples. For a BCI-algebra $\widehat{Y}$ , it has been shown that every $\left(\in ,\in \vee \left(j^{\ast },q_j\right)\right)$ -fuzzy p-ideal of $\widehat{Y}$ is an $\left(\in ,\in \vee \left(j^{\ast },q_j\right)\right)$ -fuzzy ideals of $\widehat{Y}$ but not conversely, and then, an example is given. Furthermore in $\widehat{Y}$ , a connection between $\left(\in ,\in \vee \left(j^{\ast },q_j\right)\right)$ -fuzzy p-ideals and p-ideals is established.