TY  - JOUR
T1  - ON THE FUNDAMENTAL THEOREMS OF $(\alpha,\beta)$-PYTHAGOREAN FUZZY IDEALS OF RINGS
AU  - Ghorai, Ganesh
AU  - Bhunia, Supriya
PY  - 2025
DA  - October
Y2  - 2025
JF  - TWMS Journal of Applied and Engineering Mathematics
JO  - JAEM
PB  - Işık University Press
WT  - DergiPark
SN  - 2146-1147
SP  - 2530
EP  - 2542
VL  - 15
IS  - 10
LA  - en
AB  - 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.
KW  - $(\alpha
KW  - \beta)$-Pythagorean fuzzy set
KW  - $(\alpha
KW  - \beta)$-Pythagorean fuzzy coset
KW  - $(\alpha
KW  - \beta)$-Pythagorean fuzzy ideal
KW  - $(\alpha
KW  - \beta)$-Pythagorean fuzzy quotient ring
CR  - Reference1 Alghazzawi, D., Hanoon, W. H., Gulzar, M., Abbas, G. and Kausar, N., (2021), Certain properties of ω-Q-fuzzy subrings, Indonesian Journal of Electrical Engineering and Computer Science, 21(2), pp. 822-828.
CR  - Reference2 Atanassov, K., (1983), Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulg.). Reprinted: Int. J. Bioautomation,
2016, 20(S1), S1-S6.
CR  - Reference3 Banerjee, B. and Basnet, D., (2003), Intuitionistic fuzzy subrings and ideals, Journal of Fuzzy Mathematics, 11(1), pp. 139-155.
CR  - Reference4 Bhunia, S. and Ghorai, G., (2021), A New Approach to Fuzzy Group Theory Using (α, β)-Pythagorean Fuzzy Sets, Songklanakarin Journal of Science and Technology, 43(1), pp. 295-306.
CR  - Reference5 Bhunia, S., Ghorai, G. and Xin, Q., (2021), On the fuzzification of Lagrange’s theorem in (α, β)-Pythagorean fuzzy environment, AIMS Mathematics, 6(9), pp. 9290-9308.
CR  - Reference6 Bhunia, S., Ghorai, G., Xin, Q. and Gulzar, M., (2022), On the Algebraic Attributes of (α, β)-Pythagorean Fuzzy Subrings and (α, β)-Pythagorean Fuzzy Ideals of Rings, IEEE Access, 10, pp.
11048-11056.
CR  - Reference7 Bhunia, S. and Ghorai, G., (2024), An approach to Lagrange’s theorem in Pythagorean fuzzy subgroups, Kragujevac Journal of Mathematics, 48(6), pp. 893-906.
CR  - Reference8 Ceven, Y., (2012), N-Ideals of Rings, International Journal of Algebra, 6(25), pp. 1227-1232.
CR  - Reference9 Dixit, V. N., Kumar, R. and Ajmal, N., (1992), On fuzzy rings, Fuzzy Sets and Systems, 49(2), pp. 205-213.
CR  - Reference10 Gulzar, M., Alghazzawi, D., Mateen, M. H. and Premkumar, M., (2021), On some characterization of Q-complex fuzzy sub-rings, Journal of Mathematics and Comuter Science, 22(3), pp. 295-305.
CR  - Reference11 Hur, K., Kang, H. and Song, H., (2003), Intuitionistic fuzzy subgroups and subrings, Honam Mathematical Journal, 25(1), pp. 19-41.
CR  - Reference12 Hayat, K., Mahmood, T. and Cao, B, Y., (2017), On Bipolar Anti Fuzzy h-ideals in Hemi-rings, Fuzzy Information and Engineering, 9(1), pp. 1-19.
CR  - Reference13 Kim, S. D. and Kim, H. S., (1996), S. D. Kim and H. S. Kim, Bulletin of Korean Mathematical Society, 33(4), pp. 593-601.
CR  - Reference14 Liu, W., (1982), Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8(2), pp. 133-139.
CR  - Reference15 Liu, W., (1983), Operations On Fuzzy Ideals, Fuzzy Sets and Systems, 11(1), pp. 31-41.
CR  - Reference16 Mehmood, F., Shi, F. G. and Hayat, K., (2020), A new approach to the fuzzification of rings, Journal of Nonlinear and Convex Analysis, 21(12), pp. 2637-2646.
CR  - Reference17 Mehmood, F., Shi, F. G. and Hayat, K., (2020), The Homomorphism Theorems of M-Hazy Rings and Their Induced Fuzzifying Convexities, Mathematics, 8(3), pp. 411.
CR  - Reference18 Noether, E., (1921), Idealtheorie in Ringbereichen, Mathematische Annalen, 83(1), pp. 24-66.
CR  - Reference19 Peng, X. and Yang, Y., (2015), Some Results for Pythagorean Fuzzy Sets, International Journal of Intelligent System, 30(11), pp. 1133-1160.
CR  - Reference20 Rosenfeld, A., (1971), Fuzzy Groups, Journal of Mathematical Analysis and Application, 35(3), pp. 512-517.
CR  - Reference21 Ren, Y., (1985), Fuzzy ideals and quotient rings, Journal of Fuzzy Mathematics, 4(1), pp. 19-26.
CR  - Reference22 Yager, R. R., (2013), Pythagorean Fuzzy Subsets, 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), DOI: 10.1109/IFSA-NAFIPS.2013.6608375, pp. 57-61.
CR  - Reference23 Zadeh, L., (1965), Fuzzy sets, Information and Control, 8(3), pp. 338-353.
UR  - https://dergipark.org.tr/en/pub/twmsjaem/issue//1795504
L1  - https://dergipark.org.tr/en/download/article-file/5293854
ER  -