@article{article_1795504, title={ON THE FUNDAMENTAL THEOREMS OF $(\alpha,\beta)$-PYTHAGOREAN FUZZY IDEALS OF RINGS}, journal={TWMS Journal of Applied and Engineering Mathematics}, volume={15}, pages={2530–2542}, year={2025}, author={Bhunia, Supriya and Ghorai, Ganesh}, keywords={$(\alpha,\beta)$-Pythagorean fuzzy set, $(\alpha,\beta)$-Pythagorean fuzzy coset, $(\alpha,\beta)$-Pythagorean fuzzy ideal, $(\alpha,\beta)$-Pythagorean fuzzy quotient ring}, abstract={An $(\alpha,\beta)$-Pythagorean fuzzy set is a modern approach to handling ambiguity. This article represents the perception of an $(\alpha,\beta)$-Pythagorean fuzzy coset of any $(\alpha,\beta)$-Pythagorean fuzzy ideal of rings. We demonstrate several characteristics of $(\alpha,\beta)$-Pythagorean fuzzy cosets. Moreover, we explain the $(\alpha,\beta)$-Pythagorean fuzzy quotient ring of $(\alpha,\beta)$-Pythagorean fuzzy ideals of any ring. Furthermore, we present the isomorphism theorems of $(\alpha,\beta)$-Pythagorean fuzzy ideals.}, number={10}, publisher={Işık University Press}