In this work, we introduce the concept of new approximate fuzzy structures, specifically Fermatean $ m $-polar fuzzy soft rough sets (FMPFSRSs), a novel hybrid structure that combines soft sets, rough sets, Fermatean fuzzy sets, and $ m $-polar fuzzy sets. The proposed FMPFSRS model effectively captures data uncertainty and imprecision through crisp soft and Fermatean $ m $-polar fuzzy soft approximation spaces. We establish the fundamental properties of these approximation spaces (demonstrating 92% uncertainty reduction in test cases) and provide illustrative examples. Our medical case study on coronary artery disease diagnosis achieves 89.2% diagnostic accuracy, significantly outperforming traditional fuzzy set approaches (76.5% accuracy) while reducing decision time by 44% (2.3 sec vs 4.1 sec). The methodology classifies patients using multidimensional data analysis with score ($ S = 0.725 $ for severe cases), precision ($ H = 0.650 $), and certainty ($ C = 0.504 $) functions. Clinical validation shows strong parameter sensitivity (cholesterol $ \beta = 0.42 $, $ p < 0.001 $; blood pressure $ \beta = 0.38 $, $ p < 0.001 $), confirming the model's reliability. The framework's versatility is demonstrated through successful application to complex multi-criteria decision-making scenarios in healthcare, with particular effectiveness in handling cases showing 62% inherent data uncertainty.
Citation: Hilah Awad Alharbi, Kholood Mohammad Alsager. Fermatean $ m $-polar fuzzy soft rough sets with application to medical diagnosis[J]. AIMS Mathematics, 2025, 10(6): 14314-14346. doi: 10.3934/math.2025645
In this work, we introduce the concept of new approximate fuzzy structures, specifically Fermatean $ m $-polar fuzzy soft rough sets (FMPFSRSs), a novel hybrid structure that combines soft sets, rough sets, Fermatean fuzzy sets, and $ m $-polar fuzzy sets. The proposed FMPFSRS model effectively captures data uncertainty and imprecision through crisp soft and Fermatean $ m $-polar fuzzy soft approximation spaces. We establish the fundamental properties of these approximation spaces (demonstrating 92% uncertainty reduction in test cases) and provide illustrative examples. Our medical case study on coronary artery disease diagnosis achieves 89.2% diagnostic accuracy, significantly outperforming traditional fuzzy set approaches (76.5% accuracy) while reducing decision time by 44% (2.3 sec vs 4.1 sec). The methodology classifies patients using multidimensional data analysis with score ($ S = 0.725 $ for severe cases), precision ($ H = 0.650 $), and certainty ($ C = 0.504 $) functions. Clinical validation shows strong parameter sensitivity (cholesterol $ \beta = 0.42 $, $ p < 0.001 $; blood pressure $ \beta = 0.38 $, $ p < 0.001 $), confirming the model's reliability. The framework's versatility is demonstrated through successful application to complex multi-criteria decision-making scenarios in healthcare, with particular effectiveness in handling cases showing 62% inherent data uncertainty.
| [1] |
L. A. Zadeh, Fuzzy sets, Inform. Contr., 8 (1965), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X doi: 10.1016/S0019-9958(65)90241-X
|
| [2] |
Z. Pawlak, Rough sets, Int. J. Comput. Inform. Sci., 11 (1982), 341–356. https://doi.org/10.1007/BF01001956 doi: 10.1007/BF01001956
|
| [3] |
D. Molodtsov, Soft set theory—First results, Comput. Math. Appl., 37 (1999), 19–31. https://doi.org/10.1016/S0898-1221(99)00056-5 doi: 10.1016/S0898-1221(99)00056-5
|
| [4] |
F. Feng, X. Liu, V. Leoreanu-Fotea, Y. B. Jun, Soft sets and soft rough sets, Inform. Sciences, 181 (2011), 1125–1137. https://doi.org/10.1016/j.ins.2010.11.004 doi: 10.1016/j.ins.2010.11.004
|
| [5] |
K. M. Alsager, Decision‐making framework based on multineutrosophic soft rough sets, Math. Probl. Eng., 2022 (2022), 2868970. https://doi.org/10.1155/2022/2868970 doi: 10.1155/2022/2868970
|
| [6] |
M. A. Alshayea, K. Alsager, $ m $-polar Q-hesitant anti-fuzzy set in BCK/BCI-algebras, Eur. J. Pure Appl. Math., 17 (2024), 338–355. https://doi.org/10.29020/nybg.ejpam.v17i1.4952 doi: 10.29020/nybg.ejpam.v17i1.4952
|
| [7] |
K. M. Alsager, A contemporary algebraic attributes of $ m $-polar Q-hesitant fuzzy sets in BCK/BCI algebras and applications of career determination, Symmetry, 17 (2025), 535. https://doi.org/10.3390/sym17040535 doi: 10.3390/sym17040535
|
| [8] |
G. Ali, K. Alsager, Novel Heronian mean-based $m$-polar fuzzy power geometric aggregation operators and their application to urban transportation management, AIMS Math., 9 (2024), 34109–34146. https://doi.org/10.3934/math.20241626 doi: 10.3934/math.20241626
|
| [9] |
T. Senapati, R. R. Yager, Fermatean fuzzy sets, J. Ambient Intell. Humaniz. Comput., 11 (2020), 663–674. https://doi.org/10.1007/s12652-019-01377-0 doi: 10.1007/s12652-019-01377-0
|
| [10] |
T. Senapati, R. R. Yager, Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision making, Informatica, 30 (2019), 391–412. https://doi.org/10.15388/Informatica.2019.211 doi: 10.15388/Informatica.2019.211
|
| [11] |
A. Hussain, M. I. Ali, T. Mahmood, Pythagorean fuzzy soft rough sets and their applications in decision-making, J. Taibah Univ. Sci., 14 (2020), 101–113. https://doi.org/10.1080/16583655.2019.1708541 doi: 10.1080/16583655.2019.1708541
|
| [12] | W. R. Zhang, Bipolar fuzzy sets and relations: A computational framework for cognitive modeling and multiagent decision analysis, In: Proceedings of the first international joint conference of the north American fuzzy information processing society biannual conference, 1994,305–309. https://doi.org/10.1109/IJCF.1994.375115 |
| [13] |
J. Chen, S. Li, S. Ma, X. Wang, m‐Polar fuzzy sets: an extension of bipolar fuzzy sets, Sci. World J., 2014 (2014), 416530. https://doi.org/10.1155/2014/416530 doi: 10.1155/2014/416530
|
| [14] |
M. Akram, G. Ali, N. O. Alshehri, A new multi-attribute decision-making method based on $ m $-polar fuzzy soft rough sets, Symmetry, 9 (2017), 271. https://doi.org/10.3390/sym9110271 doi: 10.3390/sym9110271
|
| [15] |
M. Akram, N. Waseem, P. Liu, Novel approach in decision making with $ m $-polar fuzzy ELECTRE-Ⅰ, Int. J. Fuzzy Syst., 21 (2019), 1117–1129. https://doi.org/10.1007/s40815-019-00608-y doi: 10.1007/s40815-019-00608-y
|
| [16] |
M. Riaz, M. R. Hashmi, Soft rough Pythagorean $ m $-polar fuzzy sets and Pythagorean $ m $-polar fuzzy soft rough sets with application to decision-making, Comput. Appl. Math., 39 (2020), 16. https://doi.org/10.1007/s40314-019-0989-z doi: 10.1007/s40314-019-0989-z
|
| [17] | H. Zhang, L. Xiong, W. Ma, Generalized intuitionistic fuzzy soft rough set and its application in decision making, J. Comput. Anal. Appl., 20 (2016), 1. |
| [18] | K. M. Alsager, N. O. Alshehri, Single valued neutrosophic hesitant fuzzy rough set and its application, Infinite Study, 2019. |
| [19] | M. Kirişci, Fermatean fuzzy soft matrices approach for diagnosis of infectious diseases and lung cancer, Available at SSRN 4233981. |
| [20] |
M. Riaz, F. Qamar, S. Tariq, K. M. Alsager, AI-driven LOPCOW-AROMAN framework and topological data analysis using circular intuitionistic fuzzy information: Healthcare supply chain innovation, Mathematics, 12 (2024), 3593. https://doi.org/10.3390/math12223593 doi: 10.3390/math12223593
|
| [21] |
R. Gul, An extension of VIKOR approach for MCDM using bipolar fuzzy preference $\delta$-covering based bipolar fuzzy rough set model, Spectrum Oper. Res., 2 (2025), 72–91. https://doi.org/10.31181/sor21202511 doi: 10.31181/sor21202511
|
| [22] |
M. E. M. Abdalla, A. Uzair, A. Ishtiaq, M. Tahir, M. Kamran, Algebraic structures and practical implications of interval-valued Fermatean neutrosophic super hypersoft sets in healthcare, Spectrum Oper. Res., 2 (2025), 199–218. https://doi.org/10.31181/sor21202523 doi: 10.31181/sor21202523
|
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Hilah Awad Alharbi, Kholood Mohammad Alsager. Fermatean $ m $-polar fuzzy soft rough sets with application to medical diagnosis[J]. AIMS Mathematics, 2025, 10(6): 14314-14346. doi: 10.3934/math.2025645
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