In this paper, we introduce some new structures such as soft primary int-ideal and soft 1-absorbing primary int-ideal, which are different generalizations of the soft prime int-ideal. We study these new structures theoretically and practically. We examine the relationship between these new structures. One of our most important results is that a soft prime int-ideal is both soft primary int-ideal and soft 1-absorbing primary int-ideal. It is shown with the help of examples that opposites are not always true. Moreover, We show that every soft primary int-ideal is a soft 1-absorbing primary int-ideal, but the opposite of this situation is not validated. Then, another result is the behavior of the soft radical on these structures. Besides, we strengthen this structure through various problems. Moreover, we determine that soft homomorphic images and pre-images of these new structures are guarded under onto ring homomorphisms.
Çıtak et al. (Mon,) studied this question.