Algebraic Structures and Practical Implications of Interval-Valued Fermatean Neutrosophic Super HyperSoft Sets in Healthcare

Manal Elzain Mohamed Abdalla; Anns Uzair; AiIman Ishtiaq; Muhammad Tahir; Muhammad Kamran

doi:10.31181/sor21202523

Authors

Manal Elzain Mohamed Abdalla Department of Mathematics, Applied College Mahayil, King Khalid University, Saudi Arabia Author https://orcid.org/0009-0001-8951-8185
Anns Uzair Department of Mathematics, Govt College University Faisalabad, Pakistan Author https://orcid.org/0009-0007-3703-0384
AiIman Ishtiaq Department of Mathematics, Govt College University Faisalabad, Pakistan Author https://orcid.org/0009-0005-1538-2907
Muhammad Tahir Department of Mathematics, Institute of Numerical Sciences, Gomal University, Dera Ismail Khan, Pakistan Author https://orcid.org/0009-0003-6542-6264
Muhammad Kamran Department of Mathematics, Thal University Bhakkar, Pakistan Author https://orcid.org/0009-0000-5467-0497

DOI:

https://doi.org/10.31181/sor21202523

Keywords:

Super HyperSoft sets, Interval-Valued Fermatean Neutrosophic sets, Fuzzy Algebra, Healthcare, Decision Making

Abstract

Healthcare workers, including doctors and medical staff, must consistently make informed decisions that significantly affect patients on individual, community, national, and global scales. Healthcare practitioners must occasionally make judgments with constrained information, resources, and knowledge, yet it is anticipated that these choices are meticulously measured and precise. Familiarizing oneself with precise concepts pertaining to medical decision-making is essential. The complexity of decision-making (DM) arises from the environment’s ambiguous, imprecise, and uncertain characteristics, especially when several attributes are present and further categorized. We have used the hypersoft set concept to address such complex challenges. This article defines interval-valued Fermatean neutrosophic super hyper-soft sets. Its fundamental operations are subsets, equality, null sets, complements, unions, and intersections. Using these algebraic procedures, we establish a numerical example for the prioritization of patients awaiting organ transplantation. This hybrid environment may effectively manage uncertainty and yield distinctive results.

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References

Ghosh, A. K., & Joshi, S. (2020). Tools to manage medical uncertainty. Diabetes & Metabolic Syndrome: Clinical Research & Reviews, 14(5), 1529-1533. https://doi.org/10.1016/j.dsx.2020.07.055.

Falkum, E., & Førde, R. (2001). Paternalism, patient autonomy, and moral deliberation in the physician–patient relationship: Attitudes among Norwegian physicians. Social science & medicine, 52(2), 239-248. https://doi.org/10.1016/S0277-9536(00)00224-0.

Wang, J., Ma, X., Xu, Z., & Zhan, J. (2022). Regret theory-based three-way decision model in hesitant fuzzy environments and its application to medical decision. IEEE Transactions on Fuzzy Systems, 30(12), 5361-5375. https://doi.org/10.1109/TFUZZ.2022.3176686.

Griffin, L., & Baverstock, A. (2023). Medical student perceptions and experiences of incivility: a qualitative study. BMC medical education, 23(1), 404. https://doi.org/10.1186/s12909-023-04354-6.

Davda, L. S., Gallagher, J. E., Short, S. D., & Balasubramanian, M. (2024). Migrant dentists, health system responses and future challenges: a case study of the United Kingdom and Australia. Journal of Ethnic and Migration Studies, 50(5), 1177-1201. https://doi.org/10.1080/1369183X.2023.2279738.

Alizadehsani, R., Roshanzamir, M., Hussain, S., Khosravi, A., Koohestani, A., Zangooei, M. H., ... & Acharya, U. R. (2021). Handling of uncertainty in medical data using machine learning and probability theory techniques: A review of 30 years (1991–2020). Annals of Operations Research, 1-42. https://doi.org/10.1007/s10479-021-04006-2.

Chaukos, D., Genus, S., & Mylopoulos, M. (2023). Uncertainty in the clinic: The importance of adaptive expertise for dealing with complexity. Academic Psychiatry, 47(6), 680-683. https://doi.org/10.1007/s40596-023-01849-8.

Zadeh, L. A. (1965). Fuzzy sets. Information and Control. https://doi.org/10.1016/S0019-9958(65)90241-X.

Moraga, C., Trillas, E., & Guadarrama, S. (2003). Multiple-valued logic and artificial intelligence fundamentals of fuzzy control revisited. Artificial Intelligence Review, 20, 169-197. https://doi.org/10.1023/B:AIRE.0000006610.94970.1d.

Zhang, W. R. (1994, December). Bipolar fuzzy sets and relations: a computational framework for cognitive modeling and multiagent decision analysis. In NAFIPS/IFIS/NASA'94. Proceedings of the First International Joint Conference of The North American Fuzzy Information Processing Society Biannual Conference. The Industrial Fuzzy Control and Intelligence (pp. 305-309). IEEE. https://doi.org/10.1109/IJCF.1994.375115.

Turksen, I. B. (1992). Interval-valued fuzzy sets and ‘compensatory AND’. Fuzzy Sets and Systems, 51(3), 295-307. https://doi.org/10.1016/0165-0114(92)90020-5.

Saqlain, M., & Xin, X. L. (2020). Interval valued, m-polar and m-polar interval valued neutrosophic hypersoft sets. Infinite Study.

Yao, Y. Y. (1998). A comparative study of fuzzy sets and rough sets. Information sciences, 109(1-4), 227-242. https://doi.org/10.1016/S0020-0255(98)10023-3.

Atanassov, K. T. (1999). Intuitionistic fuzzy sets (pp. 1-137). Physica-Verlag HD. https://doi.org/10.1016/S0165-0114(86)80034-3.

Zhang, X., & Xu, Z. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International journal of intelligent systems, 29(12), 1061-1078. https://doi.org/10.1002/int.21676.

Smarandache, F. (1998). Neutrosophy: neutrosophic probability, set, and logic: analytic synthesis & synthetic analysis.

Deli, I., Ali, M., & Smarandache, F. (2015, August). Bipolar neutrosophic sets and their application based on multi-criteria decision making problems. In 2015 International conference on advanced mechatronic systems (ICAMechS) (pp. 249-254). IEEE. https://doi.org/10.1109/ICAMechS.2015.7287068.

Wang, H., Smarandache, F., Zhang, Y., & Sunderraman, R. (2010). Single valued neutrosophic sets. Infinite study.

Peng, J. J., & Wang, J. Q. (2015). Multi-valued neutrosophic sets and its application in multi-criteria decision-making problems. Neutrosophic Sets and Systems, 10(1), 6.

Zhang, H., Wang, J., & Chen, X. (2016). An outranking approach for multi-criteria decision-making problems with interval-valued neutrosophic sets. Neural Computing and Applications, 27, 615-627. https://doi.org/10.1007/s00521-015-1882-3.

Yang, W., & Pang, Y. (2018). New multiple attribute decision making method based on DEMATEL and TOPSIS for multi-valued interval neutrosophic sets. Symmetry, 10(4), 115. https://doi.org/10.3390/sym10040115.

Kamran, M., Nadeem, M., Zywiolek, J., Abdalla, M. E. M., Uzair, A., & Ishtiaq, A. (2024). Enhancing Transportation Efficiency with Interval-Valued Fermatean Neutrosophic Numbers: A Multi-Item Optimization Approach. Symmetry, 16(6), 766. https://doi.org/10.3390/sym16060766.

Edalatpanah, S. A., Hassani, F. S., Smarandache, F., Sorourkhah, A., Pamucar, D., & Cui, B. (2024). A hybrid time series forecasting method based on neutrosophic logic with applications in financial issues. Engineering applications of artificial intelligence, 129, 107531. https://doi.org/10.1016/j.engappai.2023.107531.

Palanikumar, M., Jana, C., Hezam, I. M., Foul, A., Simic, V., & Pamucar, D. (2024). Multiple attribute decision-making model for artificially intelligent last-mile delivery robots selection in neutrosophic square root environment. Engineering applications of artificial intelligence, 136, 108878. https://doi.org/10.1016/j.engappai.2024.108878.

Zulqarnain, R. M., Xin, X. L., Saqlain, M., Smarandache, F., & Ahamad, M. I. (2021). An integrated model of neutrosophic TOPSIS with application in multi-criteria decision-making problem. Neutrosophic Sets and Systems, 40, 253-269.

Kamran, M., Salamat, N., Ashraf, S., Hassan, A. M., & Karamti, W. (2024). Quaternion Framework of Neutrosophic Information with its Distance Measures and Decision-Making Model. International Journal of Neutrosophic Science (IJNS), 23(2). https://doi.org/10.54216/IJNS.230220.

Kamran, M., Ashraf, S., Salamat, N., Naeem, M., & Hameed, M. S. (2023). Smart city design plan selection through single-valued neutrosophic probabilistic hesitant fuzzy rough aggregation information. Journal of Intelligent & Fuzzy Systems, (Preprint), 1-45. DOI: 10.3233/JIFS-224364.

Baser, Z., & Ulucay, V. (2025). Energy of a neutrosophic soft set and its applications to multi-criteria decision-making problems. Neutrosophic Sets and Systems, 79, 479-492.

Saeed, M., Shafique, I., & Gunerhan, H. (2025). Fundamentals of Fermatean Neutrosophic Soft Set with Application in Decision Making Problem. International Journal of Mathematics, Statistics, and Computer Science, 3, 294-312. https://doi.org/10.59543/ijmscs.v3i.10625.

Kamran, M., Ashraf, S., Salamat, N., Naeem, M., & Botmart, T. (2023). Cyber security control selection based decision. https://doi.org/10.3934/math.2023280.

Molodtsov, D. (1999). Soft set theory—first results. Computers & mathematics with applications, 37(4-5), 19-31. https://doi.org/10.1016/S0898-1221(99)00056-5.

Maji, P. K. (2013). Neutrosophic soft set. Infinite Study.

Deli, I. (2017). Interval-valued neutrosophic soft sets and its decision making. International Journal of Machine Learning and Cybernetics, 8, 665-676. https://doi.org/10.1007/s13042-015-0461-3.

Saqlain, M., Kumam, P., & Kumam, W. (2024). Neutrosophic linguistic valued hypersoft set with application: Medical diagnosis and treatment. Neutrosophic Sets and Systems, 63, 130-152.

Smarandache, F. (2018). Extension of soft set to hypersoft set, and then to plithogenic hypersoft set. Neutrosophic sets and systems, 22(1), 168-170.

Arshad, M., Saeed, M., Rahman, A. U., Mohammed, M. A., Abdulkareem, K. H., Nedoma, J., ... & Deveci, M. (2024). A robust framework for the selection of optimal COVID-19 mask based on aggregations of interval-valued multi-fuzzy hypersoft sets. Expert systems with applications, 238, 121944. https://doi.org/10.1016/j.eswa.2023.121944.

Saqlain, M., Kumam, P., & Kumam, W. (2024). Neutrosophic linguistic valued hypersoft set with application: Medical diagnosis and treatment. Neutrosophic Sets and Systems, 63, 130-152.

Saqlain, M., Garg, H., Kumam, P., & Kumam, W. (2023). Uncertainty and decision-making with multi-polar interval-valued neutrosophic hypersoft set: A distance, similarity measure and machine learning approach. Alexandria Engineering Journal, 84, 323-332.

Jafar, M. N., & Saeed, M. (2024). Some New Aggregation Operations of Intuitionistic Fuzzy Hypersoft Set. HyperSoft Set Methods in Engineering, 2, 83-95.

Rahman, A. U., Saeed, M., & Abd El-Wahed Khalifa, H. (2024). Multi-attribute decision-making based on aggregations and similarity measures of neutrosophic hypersoft sets with possibility setting. Journal of Experimental & Theoretical Artificial Intelligence, 36(2), 161-186.

Asaad, B. A., Musa, S. Y., & Ameen, Z. A. (2024). Fuzzy bipolar hypersoft sets: a novel approach for decision-making applications. Mathematical and Computational Applications, 29(4), 50. https://doi.org/10.3390/mca29040050.

Kamran, M., Salamat, N., Jana, C., & Xin, Q. (2025). Decision-making technique with neutrosophic Z-rough set approach for sustainable industry evaluation using sine trigonometric operators. Applied Soft Computing, 169, 112539. https://doi.org/10.1016/j.asoc.2024.112539.

Harl, M. I., Saeed, M., Saeed, M. H., Bajri, S. A., Alburaikan, A., & Khalifa, H. A. E. W. (2024). Development of an Investment Sector Selector Using a TOPSIS Method Based on Novel Distances and Similarity Measures for Picture Fuzzy Hypersoft Sets. IEEE Access. https://doi.org/10.1109/ACCESS.2024.3380025.

Surya, A. N., Vimala, J., & Vizhi, M. (2024). Bonferroni mean aggregation operators under q-rung linear diophantine fuzzy hypersoft set environment and its application in multi-attribute decision making. International Journal of Information Technology, 1-24. https://doi.org/10.1007/s41870-024-01837-7.

Zulqarnain, R. M., Xin, X. L., Ali, B., Broumi, S., Abdal, S., & Ahamad, M. I. (2021). Decision-making approach based on correlation coefficient with its properties under interval-valued neutrosophic hypersoft set environment. Infinite Study.

Saeed, A., Jian, M., Imran, M., & Freen, G. (2024). Green-resilient model for smartphone closed-loop supply chain network design: A novel four-valued refined neutrosophic optimization. Computers & Industrial Engineering, 190, 110087.

Cordeiro, T. A., Ferreira, F. A., Spahr, R. W., Sunderman, M. A., & Ferreira, N. C. (2024). Enhanced planning capacity in urban renewal: Addressing complex challenges using neutrosophic logic and DEMATEL. Cities, 150, 105006.

Irfan, D. E. L. İ., & ULUÇAY, V. (2025). Some harmonic aggregation operators for N-valued neutrosophic trapezoidal numbers and their application to multi-criteria decision-making. Neutrosophic Sets and Systems, 79, 355-375.

Khan, K. A., Asghar, A., Rahman, A. U., & Mabela, R. M. (2024). An algorithmic multiple attribute decision-making context to model uncertainty associated with hospital site selection problem using complex sv-neutrosophic soft information. Applied artificial intelligence, 38(1), 2375110.