A New Approach to Fuzzy a-Ideals of BCI-Algebras

To strengthen the ideal theory in BCI-algebras, the more general concept [Formula: see text]-fuzzy [Formula: see text]-ideals in BCI-algebras is proposed. It is shown that [Formula: see text]-fuzzy [Formula: see text]-ideals are [Formula: see text]-fuzzy [Formula: see text]-ideals; however, the converse is not valid. Following that, the concept of [Formula: see text]-fuzzy [Formula: see text]-ideals is introduced. We demonstrate that [Formula: see text]-fuzzy [Formula: see text]-ideals are [Formula: see text]-fuzzy [Formula: see text]-ideals. The converse is not true, and an example is given to support it. An equivalent condition for [Formula: see text]-fuzzy [Formula: see text]-ideals is provided. We prove that the [Formula: see text]-fuzzy [Formula: see text]-ideals are [Formula: see text]-fuzzy [Formula: see text]-ideals and [Formula: see text]-fuzzy [Formula: see text]-ideals. Furthermore, [Formula: see text]-fuzzy [Formula: see text]-ideals are characterized in terms [Formula: see text]-ideals.