Enhancing Artificial Intelligence Models with Interval-Valued Picture Fuzzy Sets and Sugeno-Weber Triangular Norms
DOI:
https://doi.org/10.31181/sems31202540gKeywords:
Picture Fuzzy Sets, Aggregation Operators, Sugeno-Weber Triangular Norms, Multi-Attribute Decision-MakingAbstract
This work aims to improve intelligence decision-making using interval-valued picture fuzzy sets (IVPFS). In particular, it explores using Sugeno-Weber (SW) norms in IVPFS data recording, providing reliable estimates important for decision-making. This paper introduces a new class of aggregation operators such as the interval-valued picture fuzzy Sugeno-Weber power average (IVPFSWPA), interval-valued picture fuzzy Sugeno-Weber power geometric (IVPFSWPG), interval-valued picture fuzzy Sugeno-Weber power weighted average (IVPFSWPWA), and interval-valued picture fuzzy Sugeno-Weber power weighted geometric (IVPFSWPWG) operators. The real-life characteristics and specific situations of these operators are described as well as how they adapt to real-life situations. The new multi-attribute decision-making method suitable for many practical applications with different requirements or functions is proposed. An example of an intelligent selection process is given to demonstrate its effectiveness. In addition, a general comparative method is proposed to demonstrate the effectiveness and suitability of the collective strategy by comparing its results with existing methods. The study concludes by summarizing its findings and discussing its prospects, highlighting the potential contribution of the proposed studies to the advancement of cutting-edge technology in a dynamic and complex environment.
References
Biswas, A., Gazi, K.H., & Mondal, S.P. (2024). Finding Effective Factor for Circular Economy Using Uncertain MCDM Approach. Management Science Advances, 1(1), 31-52. https://doi.org/10.31181/msa1120245.
Bouraima, M.B., Qian, S., Qiu, Y., Badi, I., & Sangaré-Oumar, M.M. (2025). Addressing Human Capital Development Challenges in Developing Countries Using an Interval-spherical Fuzzy Environment. Management Science Advances, 2(1), 59-68. https://doi.org/10.31181/msa2120258.
L. A. 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.
Atanassov, K.T. (2012). On intuitionistic fuzzy sets theory (vol. 283). Springer.
Yager, R. (2013). Pythagorean fuzzy subsets. In 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS). https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375.
Sarfraz, M. (2024). Interval-value Pythagorean Fuzzy Prioritized Aggregation Operators for Selecting an Eco-Friendly Transportation Mode Selection. Spectrum of Engineering and Management Sciences, 2(1), 172-201. https://doi.org/10.31181/sems21202422g.
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.
Cuong, B.C. (2015). Picture fuzzy sets. JCC, 30(4), 409. https://doi.org/10.15625/1813-9663/30/4/5032.
Sarfraz, M. (2024). Maclaurin Symmetric Mean Aggregation Operators Based on Novel Frank T-Norm and T-Conorm for Picture Fuzzy Multiple-Attribute Group Decision-Making. Decision Making Advances, 2(1), 163-185. https://doi.org/10.31181/dma2120242.
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), 2655. https://doi.org/10.3390/sym14122655.
Ullah, K., Sarfraz, M., Akram, M., Ali, Z. (2023). Identification and Classification of Prioritized Aczel-Alsina Aggregation Operators Based on Complex Intuitionistic Fuzzy Information and Their Applications in Decision-Making Problem. In: Jana, C., Pal, M., Muhiuddin, G., Liu, P. (eds) Fuzzy Optimization, Decision-making and Operations Research. Springer, Cham. https://doi.org/10.1007/978-3-031-35668-1_17.
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.
Sarkar, A., Senapati, T., Jin, L., Mesiar, R., Biswas, A., & Yager, R.R. (2023). Sugeno–Weber triangular norm-based aggregation operators under T-spherical fuzzy hypersoft context. Information Sciences, 645, 119305. https://doi.org/10.1016/j.ins.2023.119305.
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.
Klement, E.P., Mesiar, R., & Pap, E. (2000). Families of t-norms. Triangular Norms, 101-119.
Hadžić, O., Pap, E., & Budinčević, M. (2002). Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces. Kybernetika, 38(3), 363-382.
Arya, V., & Kumar, S. (2020). A new picture fuzzy information measure based on Shannon entropy with applications in opinion polls using extended VIKOR–TODIM approach. Computational and Applied Mathematics, 39(3), 197. https://doi.org/10.1007/s40314-020-01228-1.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Rizwan Gul, Mehwish Sarfraz (Author)
This work is licensed under a Creative Commons Attribution 4.0 International License.
All site content, except where otherwise noted, is licensed under the 