New types of fuzzy ideals of BCI-algebras

The concepts of $$(\in_{\gamma},\in_{\gamma} \! \vee\,{\rm q}_{\delta})$$-fuzzy (p-, q- and a-) ideals and $$(\overline{\in}_{\gamma},\overline{\in}_{\gamma} \! \vee\,{\rm \overline{q}}_{\delta})$$-fuzzy (p-, q- and a-) ideals in BCI-algebras are introduced. Some new characterizations are investigated. In particular, we prove that a fuzzy set μ of a BCI-algebra X is an $$(\in_{\gamma},\in_{\gamma} \! \vee\,{\rm q}_{\delta})$$-fuzzy a-ideal of X if and only if it is both an $$(\in_{\gamma},\in_{\gamma} \! \vee\,{\rm q}_{\delta})$$-fuzzy p-ideal and an $$(\in_{\gamma},\in_{\gamma} \! \vee\,{\rm q}_{\delta})$$-fuzzy q-ideal.

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