An Innovative Perspective on Bipolar Fuzzy Fantastic Ideals in BCK/BCI-Algebras.

In this paper, we propose the concept of (∈, ∈ v(...))-bipolar fuzzy ideals in BCK/BCI-algebras. We show that an (∈, ∈ ...)-bipolar fuzzy ideal is an (∈, ∈ v(...))-bipolar fuzzy ideal. For a BCK/BCI-algebra, it has been shown that an (∈, ∈ v(...)-bipolar fuzzy ideal is an (∈, ∈ ...)-bipolar fuzzy ideal of ..., but not conversely, and then an example is given. We introduce the concept of (∈, ∈ v(...))-bipolar fuzzy fantastic ideals in BCK/BCI-algebras. It has been shown that an (∈, ∈ v(...))-bipolar fuzzy fantastic ideal is an (∈, ∈)-bipolar fuzzy ideal in BCK/BCI-algebras. Furthermore, the connection between (∈, ∈ v(...))-bipolar fuzzy fantastic ideals and fantastic ideals are established. [ABSTRACT FROM AUTHOR]