A Novel 〈p,q〉-Rung Orthopair Fuzzy Aczel–Alsina AHP Framework for Multi-Attribute Decision-Making with Application to Smart Water Management System Selection

Mehwish Sarfraz

doi:10.65069/smart2120267

Authors

Mehwish Sarfraz Department of Mathematics, Riphah International University (Lahore Campus), Lahore, Pakistan. Author https://orcid.org/0009-0006-0154-3199

DOI:

https://doi.org/10.65069/smart2120267

Keywords:

Aczel-Alsina geometric, MADM, Aczel-Alsina, 〈p,q〉-Rung Orthopair fuzzy Aczel-Alsina averaging, 〈p,q〉-Rung Orthopair fuzzy

Abstract

Water scarcity, rapid urbanization, and increasing environmentally demanding conditions highlight the need for a green, sustainable smart water management system. Selection of the most suitable system. To face this problem, there is a novel approach for selecting smart water management structures: a fuzzy analytical hierarchy system (AHP)-based multi-attribute decision-making (MADM) framework. Based on operation laws of Aczel–Alsina (AA) aggregation operators (AOs), especially 〈p,q〉-ROFAAWA and 〈p,q〉-ROFAAWG operators, are proposed to efficiently aggregate uncertain and fuzzy information. The AHP method is used to define the input objectives. A numerical example regarding the selection of smart water management systems is provided to demonstrate the applicability and operation of the proposed framework. Furthermore, comparative evaluation with existing techniques confirms that the proposed technique provides an additional flexible, reliable, and regular alternative under a 〈p, q〉-rung orthopair fuzzy environment. The proposed framework is intelligent and green for sustainable hydropower generation and feedstock control selection utility

References

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

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

[3] Yager, R. (2013). Pythagorean fuzzy subsets. 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 57–61. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375

[4] 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

[5] 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. International Journal of Computational Intelligence Systems, 19(1), 54. https://doi.org/10.1007/s44196-025-01090-1

[6] Raja, M. S., Hayat, K., Munshi, A., Mahmood, T., Sheraz, R., & Matloob, I. (2024). Aggregation operators on group-based generalized q-rung orthopair fuzzy N-soft sets and applications in solar panel evaluation. Heliyon, 10(5), e27323. https://doi.org/10.1016/j.heliyon.2024.e27323

[7] 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

[8] Aczél, J., & Alsina, C. (1982). Characterizations of some classes of quasilinear functions with applications to triangular norms and to synthesizing judgements. Aequationes Mathematicae, 25(1), 313–315. https://doi.org/10.1007/BF02189626

[9] 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

[10] Senapati, T., Chen, G., & Yager, R. R. (2022). Aczel–Alsina aggregation operators and their application to intuitionistic fuzzy multiple attribute decision making. International Journal of Intelligent Systems, 37(2), 1529–1551. https://doi.org/10.1002/int.22684

[11] Akram, M., Ullah, K., Ćirović, G., & Pamucar, D. (2023). Algorithm for Energy Resource Selection Using Priority Degree-Based Aggregation Operators with Generalized Orthopair Fuzzy Information and Aczel–Alsina Aggregation Operators. Energies, 16(6), 2816. https://doi.org/10.3390/en16062816

[12] Asif, M., Ishtiaq, U., & Argyros, I. K. (2025). Hamacher Aggregation Operators for Pythagorean Fuzzy Set and its Application in Multi-Attribute Decision-Making Problem. Spectrum of Operational Research, 2(1), 27–40. https://doi.org/10.31181/sor2120258

[13] Akram, M., Zahid, S., & Al-Kenani, A. N. (2024). Multi-criteria group decision-making for evaluating efficient and smart mobility sharing systems using Pythagorean fuzzy rough numbers. Granular Computing, 9(2), 50. https://doi.org/10.1007/s41066-024-00466-6

[14] Garg, H. (2020). Neutrality operations-based Pythagorean fuzzy aggregation operators and its applications to multiple attribute group decision-making process. Journal of Ambient Intelligence and Humanized Computing, 11(7), 3021–3041. https://doi.org/10.1007/s12652-019-01448-2

[15] Wang, P., Zhu, B., Yan, K., Zhang, Z., Ali, Z., & Pamucar, D. (2025). Power aggregation operators based on Aczel–Alsina T-norm and T-conorm for intuitionistic hesitant fuzzy information and their application to logistics service provider selection. Artificial Intelligence Review, 58(7), 204. https://doi.org/10.1007/s10462-025-11155-4

[16] Batool, B., Abdullah, S., Ashraf, S., & Ahmad, M. (2022). Pythagorean probabilistic hesitant fuzzy aggregation operators and their application in decision-making. Kybernetes, 51(4), 1626–1652. https://doi.org/10.1108/K-11-2020-0747

[17] Garg, H. (2021). Sine trigonometric operational laws and its based Pythagorean fuzzy aggregation operators for group decision-making process. Artificial Intelligence Review, 54(6), 4421–4447. https://doi.org/10.1007/s10462-021-10002-6

[18] Sarfraz, M., & Alharbi, T. (2026). Optimal Decision Model for Sustainable Green Industry Using AHP and TOPSIS with Picture Fuzzy Soft Aczel-Alsina Operators. Journal of Statistics Applications & Probability, 14(6), 637–667. https://doi.org/10.18576/jsap/140611

[19] Naeem, M., & Ali, J. (2022). A novel multi-criteria group decision-making method based on Aczel–Alsina spherical fuzzy aggregation operators: Application to evaluation of solar energy cells. Physica Scripta, 97(8), 085203. https://doi.org/10.1088/1402-4896/ac7980

[20] Khan, A. U., & Ali, Y. (2020). Analytical Hierarchy Process (AHP) and Analytic Network Process Methods and Their Applications: A Twenty Year Review from 2000–2019. International Journal of the Analytic Hierarchy Process, 12(3). https://doi.org/10.13033/ijahp.v12i3.822

[21] Nadeem, R., Singh, R., Patidar, A., Yusliza, M. Y., Ramayah, T., & Azmi, F. T. (2025). Prioritizing determinants of employees’ green behavior in the Indian hotel industry: An analytic hierarchy process (AHP) and fuzzy AHP approach. Journal of Hospitality and Tourism Insights, 8(8), 2900–2919. https://doi.org/10.1108/JHTI-07-2024-0737

[22] Bošnjaković, M., Santa, R., Vučić, A., & Crnac, Z. (2025). Analysis of Biodiesel from Algae Using the SWOT-AHP Method: Strategic Insights for a Green Energy Future. Clean Technologies, 7(3), 69. https://doi.org/10.3390/cleantechnol7030069

[23] Xu, C., Xu, C., Zhan, L., & Li, G. (2025). Establishment and validation of a novel composite index for energy efficiency evaluation of data center chilled water systems based on AHP and Entropy Weight Method. Energy and Buildings, 337, 115677. https://doi.org/10.1016/j.enbuild.2025.115677

[24] Ju, Y., Liang, Y., Luo, C., Dong, P., Gonzalez, E. D., & Wang, A. (2021). T-spherical fuzzy TODIM method for multi-criteria group decision-making problem with incomplete weight information. Soft Computing, 25(4), 2981–3001. https://doi.org/10.1007/s00500-020-05357-x