An Interval-Valued T-Spherical Fuzzy SWARA Approach with Sugeno–Weber Operators for Artificial Intelligence Selection

Rashid Kakis; Szabolcs Fischer; Dmytro Kurhan

Authors

Rashid Kakis Department of Mathematics, Riphah International University Lahore, Lahore, Pakistan Author https://orcid.org/0009-0004-1377-0503
Szabolcs Fischer Department of Transport Infrastructure and Water Resources Engineering, Faculty of Civil Engineering, Széchenyi István University, Hungary Author https://orcid.org/0000-0001-7298-9960
Dmytro Kurhan Department of Transport Infrastructure, Ukrainian State University of Science and Technologies, Ukraine Author https://orcid.org/0000-0002-9448-5269

Keywords:

T-spherical fuzzy set, Sugeno–Weber, T-SFS, Multi-Attribute Decision-Making, MADM, Artificial Intelligence

Abstract

The T-spherical fuzzy set (T-SFS) has emerged as a powerful and flexible framework for modelling uncertainty and ambiguity in decision-making processes. In this study, we examine the integration of Sugeno–Weber (SW) t-norms within an interval-valued T-spherical fuzzy (IVT-SF) environment. Based on this framework, a novel family of aggregation operators is developed, including the interval-valued T-spherical fuzzy Sugeno–Weber power averaging (IVT-SFSWPA), power geometric (IVT-SFSWPG), power-weighted averaging (IVT-SFSWPWA), and power-weighted geometric (IVT-SFSWPWG) operators. The proposed operators are analyzed in terms of their fundamental properties and special cases, demonstrating their flexibility and effectiveness in handling complex decision-making problems. In addition, a new multi-attribute decision-making (MADM) method is developed within the IVT-SF environment. Furthermore, a comparative analysis with existing approaches is conducted to highlight the superiority, robustness, and practicality of the proposed aggregation operators. The results indicate that the proposed method provides more consistent and reliable decision-making outcomes. This study advances fuzzy decision-making methodologies and offers a promising approach to addressing real-world problems in dynamic, complex environments.

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References

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/S0019-9958(65)90241-X

Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96. https://doi.org/10.1016/S0165-0114(86)80034-3

Yager, R. (2013). Pythagorean fuzzy subsets. 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS). https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375

Yager, R. R. (2017). Generalized Orthopair Fuzzy Sets. IEEE Transactions on Fuzzy Systems, 25(5), 1222–1230. https://doi.org/10.1109/TFUZZ.2016.2604005

Cường, B. C. (2014). Picture fuzzy sets. Journal of Computer Science and Cybernetics, 30(4), 409–409. https://doi.org/10.15625/1813-9663/30/4/5032

Mahmood, T., Ullah, K., Khan, Q., & Jan, N. (2019). An approach toward decision-making and medical diagnosis problems using the concept of spherical fuzzy sets. Neural Comput & Applic, 31(11), 7041–7053. https://doi.org/10.1007/s00521-018-3521-2

Lundström, A., & Hellström, F. (2015). Getting to know electric cars through an app. In Proceedings of the 7th International Conference on Automotive User Interfaces and Interactive Vehicular Applications (pp. 289–296). Association for Computing Machinery. https://doi.org/10.1145/2799250.2799272

Kalifa, M., Özdemir, A., Özkan, A., & Banar, M. (2022). Application of Multi‐Criteria Decision analysis including sustainable indicators for prioritization of public transport system. Integrated Environmental Assessment and Management, 18(1), 25–38. https://doi.org/10.1002/ieam.4486

Sarfraz, M., & Gul, R. (2025). An Aczel-Alsina T-Spherical Fuzzy Framework for the Electric Vehicle Selection. Spectrum of Engineering and Management Sciences, 3(1), 158–174. https://doi.org/10.31181/sems31202543s

Vitta, S. (2021). Electric cars – Assessment of “green” nature vis-à-vis conventional fuel driven cars. Sustainable Materials and Technologies, 30, e00339. https://doi.org/10.1016/j.susmat.2021.e00339

Onat, N. C., Kucukvar, M., Tatari, O., & Zheng, Q. P. (2016). Combined application of multi-criteria optimization and life-cycle sustainability assessment for optimal distribution of alternative passenger cars in U.S. Journal of Cleaner Production, 112, 291–307. https://doi.org/10.1016/j.jclepro.2015.09.021

Lim, M. C. H., Ayoko, G. A., Morawska, L., Ristovski, Z. D., Jayaratne, E. R., & Kokot, S. (2006). A comparative study of the elemental composition of the exhaust emissions of cars powered by liquefied petroleum gas and unleaded petrol. Atmospheric Environment, 40(17), 3111–3122. https://doi.org/10.1016/j.atmosenv.2006.01.007

Hao, X., Zhang, X., Cao, X., Shen, X., Shi, J., & Yao, Z. (2018). Characterization and carcinogenic risk assessment of polycyclic aromatic and nitro-polycyclic aromatic hydrocarbons in exhaust emission from gasoline passenger cars using on-road measurements in Beijing, China. Science of The Total Environment, 645, 347–355. https://doi.org/10.1016/j.scitotenv.2018.07.113

Ternel, C., Bouter, A., & Melgar, J. (2021). Life cycle assessment of mid-range passenger cars powered by liquid and gaseous biofuels: Comparison with greenhouse gas emissions of electric vehicles and forecast to 2030. Transportation Research Part D: Transport and Environment, 97, 102897. https://doi.org/10.1016/j.trd.2021.102897

Bauer, C., Hofer, J., Althaus, H.-J., Del Duce, A., & Simons, A. (2015). The environmental performance of current and future passenger vehicles: Life cycle assessment based on a novel scenario analysis framework. Applied Energy, 157, 871–883. https://doi.org/10.1016/j.apenergy.2015.01.019

Sarfraz, M., Ullah, K., Akram, M., Pamucar, D., & Božanić, D. (2022). Prioritized Aggregation Operators for Intuitionistic Fuzzy Information Based on Aczel–Alsina T-Norm and T-Conorm and Their Applications in Group Decision-Making. Symmetry, 14(12), Article 12. https://doi.org/10.3390/sym14122655

Zhou, L., Abdullah, S., Zafar, H., Muhammad, S., Qadir, A., & Huang, H. (2025). Analysis of artificial neural network based on pq-rung orthopair fuzzy linguistic muirhead mean operators. Expert Systems with Applications, 276, 127157. https://doi.org/10.1016/j.eswa.2025.127157

Shan, T., Tay, F. R., & Gu, L. (2021). Application of Artificial Intelligence in Dentistry. J Dent Res, 100(3), 232–244. https://doi.org/10.1177/0022034520969115

Zhou, X.-Y., Guo, Y., Shen, M., & Yang, G.-Z. (2020). Application of artificial intelligence in surgery. Front. Med., 14(4), 417–430. https://doi.org/10.1007/s11684-020-0770-0

Yang, Y. J., & Bang, C. S. (2019). Application of artificial intelligence in gastroenterology. World J Gastroenterol, 25(14), 1666–1683. https://doi.org/10.3748/wjg.v25.i14.1666

Liu, P., Lu, L., Zhang, J., Huo, T., Liu, S., & Ye, Z. (2021). Application of Artificial Intelligence in Medicine: An Overview. CURR MED SCI, 41(6), 1105–1115. https://doi.org/10.1007/s11596-021-2474-3

Wan, H., Liu, G., & Zhang, L. (2021). Research on the Application of Artificial Intelligence in Computer Network Technology. In Proceedings of the 2021 5th International Conference on Electronic Information Technology and Computer Engineering (pp. 704–707). ACM. https://doi.org/10.1145/3501409.3501536

Ghodousian, A., Ahmadi, A., & Dehghani, A. (2017). Solving a non-convex non-linear optimization problem constrained by fuzzy relational equations and Sugeno-Weber family of t-norms. Journal of Algorithms and Computation, 49(2), 63–101. https://doi.org/10.22059/jac.2017.7978

Kauers, M., Pillwein, V., & Saminger-Platz, S. (2011). Dominance in the family of Sugeno–Weber t-norms. Fuzzy Sets and Systems, 181(1), 74–87. https://doi.org/10.1016/j.fss.2011.04.007

Farahbod, F. (2012). Comparison of Different T-Norm Operators in Classification Problems. International Journal of Fuzzy Logic Systems, 2(3), 33–39. https://doi.org/10.5121/ijfls.2012.2303

Troiano, L., Rodríguez-Muñiz, L. J., Marinaro, P., & Díaz, I. (2014). Statistical analysis of parametric t-norms. Information Sciences, 257, 138–162. https://doi.org/10.1016/j.ins.2013.09.041

Ghodousian, A. (2019). Optimization of linear problems subjected to the intersection of two fuzzy relational inequalities defined by Dubois-Prade family of t-norms. Information Sciences, 503, 291–306. https://doi.org/10.1016/j.ins.2019.06.058

Wang, L., & Li, N. (2020). Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making. Int J Intell Syst, 35(1), 150–183. https://doi.org/10.1002/int.22204

Senapati, T., Chen, G., Mesiar, R., & Yager, R. R. (2023). Intuitionistic fuzzy geometric aggregation operators in the framework of Aczel-Alsina triangular norms and their application to multiple attribute decision making. Expert Systems with Applications, 212, 118832. https://doi.org/10.1016/j.eswa.2022.118832

Sarfraz, M., Gul, R., & Esztergár-Kiss, D. (2026). A Multi-Attribute Group Decision-Making Scheme Under q-Rung Orthopair Fuzzy Rough Aczel-Alsina Geometric Aggregation Operators with Applications in Sustainable Transportation. Int J Comput Intell Syst, 19(1), 54. https://doi.org/10.1007/s44196-025-01090-1

Senapati, T., Sarkar, A., & Chen, G. (2024). Enhancing healthcare supply chain management through artificial intelligence-driven group decision-making with Sugeno–Weber triangular norms in a dual hesitant q-rung orthopair fuzzy context. Engineering Applications of Artificial Intelligence, 135, 108794. https://doi.org/10.1016/j.engappai.2024.108794

Ullah, K., Hassan, N., Mahmood, T., Jan, N., & Hassan, M. (2019). Evaluation of Investment Policy Based on Multi-Attribute Decision-Making Using Interval Valued T-Spherical Fuzzy Aggregation Operators. Symmetry, 11(3), Article 3. https://doi.org/10.3390/sym11030357

Wang, H., & Liu, J. (2025). Some Spherical Uncertain Linguistic Aggregation Operators and their Application in Multi-Attribute Decision-Making. Journal of Intelligent Decision Making and Granular Computing, 1(1), 106-126. https://doi.org/10.31181/jidmgc11202511