Generalizations of Fuzzy q-Ideals of BCI-Algebras

In this paper, we introduce the notion of ∈,∈∨κ∗,qκ-fuzzy q-ideals of BCI-algebras to propose a more general form of fuzzy q-ideals of BCI-algebras. We prove that ∈,∈∨q-fuzzy q-ideals and ∈∨κ∗,qκ,∈∨κ∗,qκ-fuzzy q-ideals are ∈,∈∨κ∗,qκ-fuzzy q-ideals, but the converse assertion is not valid and examples are given to support this. It is proved that every ∈,∈∨κ∗,qκ-fuzzy q-ideal is an ∈,∈∨κ∗,qκ-fuzzy ideal, but the converse need not be true in general and an example is provided. In addition, correspondence between ∈,∈∨κ∗,qκ-fuzzy q-ideals and q-ideals of BCI-algebras is considered.