This study presents the innovative concept of roughness in semirings built on intuitionistic fuzzy frameworks. Specifically, this research introduces the concept of rough intuitionistic fuzzy ideals within the framework of semirings and systematically investigates their properties. The aim of this study is to extend the existing concepts of 2-absorbing, 2-absorbing primary, intuitionistic fuzzy 2-absorbing, and intuitionistic fuzzy 2-absorbing primary ideals of semirings by incorporating the notion of roughness. This extension provides a more comprehensive and refined framework for analyzing ideals and intuitionistic fuzzy ideals in semirings. Furthermore, we explore the conditions that establish a connection between the upper and lower rough 2-absorbing primary ideals and the upper and lower approximations of their homomorphic images.
Ali et al. (Wed,) studied this question.