Abstract
In this paper, we study the primary intuitionistic fuzzy ideal, the intuitionistic fuzzy ideal expansion and [Formula: see text]-primary intuitionistic fuzzy ideal which assemble prime intuitionistic fuzzy ideals and primary intuitionistic fuzzy ideals. Some properties of them are investigated. Also, we scrutinize the relationships of [Formula: see text]-primary intuitionistic fuzzy ideal and [Formula: see text]-primary ideal of a commutative ring [Formula: see text]. Moreover, we give a fundamental result about correspondence theorem for [Formula: see text]-primary intuitionistic fuzzy ideals. Further, we introduce 2-absorbing [Formula: see text]-primary intuitionistic fuzzy ideals which are the generalization of 2-absorbing intuitionistic fuzzy ideals and 2-absorbing primary intuitionistic fuzzy ideals. Some properties of them are obtained.