A Detailed Study of Mathematical Rings in q-Rung Orthopair Fuzzy Framework

Symmetry-related problems can be addressed by means of group theory, and ring theory seen as an extension additive theory. Ring a significant topic in abstract algebra, is currently active diverse range study domains across the disciplines mathematics, theoretical physics coding The ideals vital to rings wide ways. uncertainties present information are well q-rung orthopair fuzzy set (q-ROFS). Considering significance q-ROFS, this article defines (q-ROFIs) conventional investigates its various algebraic features. We introduce notion cosets (q-ROFCs) q-ROFI demonstrate that, under certain binary operations, collection all q-ROFCs forms ring. In addition, we provide analog fundamental theorem homomorphism. Furthermore, semi-prime (q-ROFSPIs) comprehensive explanation their many properties. Finally, regular were characterized using q-ROFIs.