A novel structure of $q$-rung orthopair fuzzy sets in ring theory

The q-rung orthopair fuzzy atmosphere is an innovative approach for handling unclear circumstances in a range of decision making problems. As compare to intuitionistic fuzzy sets, this one is more appropriate and adaptable because it evaluates the significance of ring theory while retaining the features of q-rung orthopair fuzzy sets. In this study, we characterize $q$-rung orthopair fuzzy subring as a modification of the pythagorean fuzzy subring. We introduce the novel idea of $q$-rung orthopair fuzzy subring and investigate the algebraic characteristics for the $q$-rung orthopair fuzzy subrings. Furthermore, we establish the concept of $q$-rung orthopair fuzzy quotient ring and $q$-rung orthopair fuzzy left and right ideals. Also, we describe the $q$-rung orthopair fuzzy level subring and associate axioms. Finally, we investigate how ring homomorphism influences the q-rung orthopair fuzzy subring and investigate there pre-images homomorphism on $q$-ROFSR and different aspects of images.