Fuzzy ideals of BCI-algebras with respect to t-norm

In this paper, we introduce and define the concepts of fuzzy implicative ideals, fuzzy closed implicative ideals and fuzzy commutative ideals of BCI-algebras with respect to T-norms and we investigate some good examples. Next, we present some fundamental properties of them. Also, we link them with implicative ideals, closed implicative ideals and commutative ideals of BCI-algebras such that every fuzzy implicative ideal, fuzzy closed implicative ideals and fuzzy commutative ideals of BCI-algebras with respect to T-norms will be implicative ideals, closed implicative ideals and commutative ideals of BCI-algebras, respectively and we indicate some examples. Later we investigate and generalize the concepts as intersection and cartesian product of them and we show that the intersection and cartesian product of fuzzy implicative ideals, fuzzy closed implicative ideals and fuzzy commutative ideals of BCI-algebras with respect to T-norms are also fuzzy implicative ideals, fuzzy closed implicative ideals and fuzzy commutative ideals of BCI-algebras with respect to T-norms, respectively and characterize their properties of them with examples. Finally, we prove some properties about them under homomorphisms (image and pre-image) of BCI-algebras.