Confidence Level-Based Hamacher Aggregation Operators for Sustainable Furniture Supplier Selection using p,q-Quasirung Orthopair Fuzzy Sets

Utpal Mandal ¹ ( )
Arnab Kumar De ² ( )
Mijanur Rahaman Seikh ³ ( )

Submited date : 2025-03-23 Accepted date : 2025-09-18

Keywords: Multi-criteria group decision-making, p, q-QOFSs, Hamacher aggregation operators, Confidence levels, Supplier selection.,

Abstract :

Selecting sustainable furniture suppliers for universities is a complex decision-making problem that must balance environmental, economic, and social factors under conditions of uncertainty. As higher education institutions increasingly adopt green procurement policies, the need for structured, data-driven evaluation methods becomes more pressing. This necessitates robust models capable of handling imprecision and reflecting the trustworthiness of expert opinions. Traditional methods often fall short in handling the vagueness inherent in expert evaluations. To address this, we adopt the recently introduced p,q-quasirung orthopair fuzzy sets (p,q-QOFSs), which provide a more flexible framework for modeling imprecise information. This study proposes novel confidence level-based Hamacher weighted averaging and geometric aggregation operators for p,q-QOFSs to incorporate the reliability of expert judgments into the decision-making process. Using these operators, we develop a robust multi-criteria group decision-making (MCGDM) model for sustainable supplier selection. The model is validated through a real-world case study involving three experts assessing four suppliers against eight sustainability criteria. Comparative analysis with existing methods highlights the superior performance of the proposed approach, while sensitivity analysis confirms its stability and robustness across varying parameter settings. The incorporation of confidence levels not only enhances the credibility of the aggregated evaluations but also allows for more informed and nuanced decision outcomes.

References:

[1] Zadeh LA. Fuzzy sets. Information and Control. 1965; 8(3): 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
[2] Seikh MR, Mandal U. Multiple attribute group decision making based on quasirung orthopair fuzzy sets: Application to electric vehicle charging station site selection problem. Engineering Applications of Artificial Intelligence. 2022; 115: 105299. DOI: https://doi.org/10.1016/j.engappai.2022.105299
[3] Rahim M, Akhtar Y, Yang M-S, Ali HEM, Elhag AA. Improved COPRAS method with unknown weights under p, q-quasirung orthopair fuzzy environment: Application to green supplier selection. IEEE Access. 2024; 12: 69783-69795. DOI: https://doi.org/10.1109/ACCESS.2024.3400016
[4] Rahim M, Tag Eldin EM, Khan S, Ghamry NA, Alanzi AM, Khalifa HAE-W. Multi-criteria group decision-making based on Dombi aggregation operators under p, q-quasirung orthopair fuzzy sets. Journal of Intelligent & Fuzzy Systems. 2023; 46(1): 53-74. DOI: https://doi.org/10.3233/JIFS-233327
[5] Rahim M, Younis BA, Ahmad S, Ahmed MM, Egami RH. Multiple attribute group decision making based on p, q-quasirung orthopair Bonferroni mean operators and their applications. Evolving Systems. 2025; 16(1): 9. DOI: https://doi.org/10.1007/s12530-024-09638-w
[6] Ali J, Naeem M. Analysis and application of p,q-quasirung orthopair fuzzy AczelAlsina aggregation operators in multiple criteria decision-making. IEEE Access. 2023; 11: 49081-49101. DOI: https://doi.org/10.1109/ACCESS.2023.3274494
[7] Arya P, Pal AK. MCDM model using Jaccard and cosine similarity-driven aggregation operators in (n, m)-rung orthopair fuzzy environment: A case study on government medical facilities in Indian states. International Journal of Information Technology. 2025; 17(1): 225-236. DOI:
https://doi.org/10.1007/s41870-024-02233-x
[8] Hamacher H. ber logische Verknpfungen unscharfer Aussagen und deren zugehrige Bewertungsfunktionen. Progress in Cybernetics and Systems Research. 1978; 3: 267288.
[9] Meher BB, Jeevaraj S, Alrasheedi M. Dombi weighted geometric aggregation operators on the class of trapezoidal-valued intuitionistic fuzzy numbers and their applications to multi-attribute group decisionmaking. Artificial Intelligence Review. 2025; 58(7): 205. DOI: https://doi.org/10.1007/s10462-025-11200-2
[10] Rong Y, Yu L. An extended MARCOS approach and generalized Dombi aggregation operators-based group decision-making for emergency logistics suppliers selection utilizing q-rung picture fuzzy information. Granular Computing. 2024; 9(1): 22. DOI: https://doi.org/10.1007/s41066-023-00439-1
[11] Jin J, Pamucar D, Shi S, Zhang H, Teng W. Generalized picture fuzzy Frank aggregation operators and their applications. Alexandria Engineering Journal. 2024; 109: 726-739. DOI: https://doi.org/10.1016/j.aej.2024.09.081
[12] Deb N, Sarkar A, Biswas A. Multicriteria group decision-making using Archimedean t-norm and tconorm-based linguistic q-rung orthopair fuzzy generalized operators. Granular Computing. 2024; 9(2): 52. DOI: https://doi.org/10.1007/s41066-024-00465-7
[13] Shao Y, Wang N, Gong Z. Multi-criteria q-rung orthopair fuzzy decision analysis: A novel approach based on Archimedean aggregation operator with the confidence level. Soft Computing. 2020; 26(9): 4375-4394. DOI: https://doi.org/10.1007/s00500-022-06776-8
[14] Huang JY. Intuitionistic fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems. 2014; 27(1): 505-513. DOI: https://doi.org/10.3233/IFS-131019
[15] Senapati T, Chen G. Some novel interval-valued Pythagorean fuzzy aggregation operator based on Hamacher triangular norms and their application in MADM issues. Computational and Applied Mathematics. 2021; 40(4): 109. DOI: https://doi.org/10.1007/s40314-021-01502-w
[16] Asif M, Ishtiaq U, Argyros IK. Hamacher aggregation operators for Pythagorean fuzzy set and its application in multi-attribute decision-making problem. Spectrum of Operational Research. 2025; 2(1): 27-40. DOI: https://doi.org/10.31181/sor2120258
[17] Hadi A, Khan W, Khan A. A novel approach to MADM problems using Fermatean fuzzy Hamacher aggregation operators. International Journal of Intelligent Systems. 2021; 36(7): 3464-3499. DOI: https://doi.org/10.1002/int.22423
[18] Jan A, Khan A, Khan W, Afridi M. A novel approach to MADM problems using Fermatean fuzzy Hamacher prioritized aggregation operators. Soft Computing. 2021; 25: 13897-13910. DOI: https://doi.org/10.1007/s00500-021-0630-w
[19] Akram M, Alsulami S, Karaaslan F, Khan A. Q-Rung orthopair fuzzy graphs under Hamacher operators. Journal of Intelligent & Fuzzy Systems. 2021; 40(1): 1367-1390. DOI: https://doi.org/10.3233/JIFS201700
[20] Gayen S, Sarkar A, Biswas A. Development of q-rung orthopair trapezoidal fuzzy Hamacher aggregation operators and its application in MCGDM problems. Computational and Applied Mathematics. 2022; 41(6): 1-39. DOI: https://doi.org/10.1007/s40314-022-01955-7
[21] Ali Z, Yang MS. Circular Pythagorean fuzzy Hamacher aggregation operators with application in the assessment of goldmines. IEEE Access. 2024; 12: 13070-13087. DOI: https://doi.org/10.1109/ACCESS.2024.3354823
[22] Ahmad T, Rahim M, Yang J, Alharbi R, Khalifa HAE-W. Development of p,q-quasirung orthopair fuzzy Hamacher aggregation operators and its application in decision-making problems. Heliyon. 2024; 10(3): e24726. DOI: https://doi.org/10.1016/j.heliyon.2024.e24726
[23] Qiyaas M, Khan N, Khan S, Khan F. Confidence levels bipolar complex fuzzy aggregation operators and their application in decision making problem. IEEE Access. 2024; 12: 6204-6214. DOI: https://doi.org/10.1109/ACCESS.2023.3347043
[24] Rahaman K, Muhammad J. Enhanced decision making induced confidence level complex polytopic fuzzy aggregation operator. International Journal of Knowledge and Innovation Studies. 2024; 2(1): 11-18. DOI: https://doi.org/10.56578/ijkis020102
[25] Punetha T, Komal. Confidence Picture fuzzy hybrid aggregation operators and its application in multi criteria group decision making. OPSEARCH. 2024; 61(3): 1404-1440. DOI: https://doi.org/10.1007/s12597-023-00720-6
[26] Rizwan khan M, Ullah K, Reza A, Senapati T, Moslem S. Multi-attribute decision-making method based on complex T-spherical fuzzy frank prioritized aggregation operators. Heliyon. 2024; 10(3): e25368. DOI: https://doi.org/10.1016/j.heliyon.2024.e25368
[27] Chatterjee P, Seikh MR. Evaluating municipal solid waste management with a confidence level-based decision-making approach in q-rung orthopair picture fuzzy environment. Journal of Industrial Information Integration. 2024; 42: 100708. DOI: https://doi.org/10.1016/j.jii.2024.100708
[28] Mahmood T, Ali Z, Yang M. Confidence level aggregation operators based on intuitionistic fuzzy rough sets with application in medical diagnosis. IEEE Access. 2023; 8674-8688. DOI: https://doi.org/10.1109/ACCESS.2023.3236410
[29] Lin H, Ullah I, Ali A, Abbas S. Analysis of cost and profit using aggregation operator on spherical fuzzy sets with confidence level. Journal of Intelligent and Fuzzy Systems. 2023; 45(1): 675-686. DOI: https://doi.org/10.3233/JIFS-220102
[30] Seikh MR, Chatterjee P. Sustainable strategies for electric vehicle adoption: A confidence level-based interval-valued spherical fuzzy MEREC-VIKOR approach. Information Sciences. 2025; 699: 121814. DOI: https://doi.org/10.1016/j.ins.2024.121814
[31] Seikh MR, Chatterjee P. Determination of best renewable energy sources in India using SWARA-ARAS in confidence level based interval-valued Fermatean fuzzy environment. Applied Soft Computing. 2024; 155: 111495. DOI: https://doi.org/10.1016/j.asoc.2024.111495
[32] Sivadas A, John SJ, Athira TM. (p, q)-fuzzy aggregation operators and their applications to decisionmaking. The Journal of Analysis. 2024; 1-30. DOI: https://doi.org/10.1007/s41478-023-00693-1
[33] Tronnebati I, Jawab F, Frichi Y, Arif J. Green supplier selection using fuzzy AHP, fuzzy TOSIS, and fuzzy WASPAS: A case study of the moroccan automotive industry. Sustainability. 2024; 16(11), 4580. DOI: https://doi.org/10.3390/su16114580
[34] Kara K, Acar AZ, Polat M, nden , Yaln GC. Developing a hybrid methodology for green-based supplier selection: Application in the automotive industry. Expert Systems with Applications. 2024; 249, 123668. DOI: https://doi.org/10.1016/j.eswa.2024.123668
[35] Pinar A. An integrated sentiment analysis and q-rung orthopair fuzzy MCDM model for supplier selection in E-commerce: a comprehensive approach. Electronic Commerce Research. 2025; 25: 13111342. DOI: https://doi.org/10.1007/s10660-023-09768-4
[36] Banerjee A, Ries JM, Wiertz C. The impact of social media signals on supplier selection: insights from two experiments. International Journal of Operations & Production Management. 2020; 40(5): 531-552. DOI: https://doi.org/10.1108/IJOPM-05-2019-0413
[37] Wu Z, Gu L. A hybrid decision-making framework for hydrogen energy supplier selection: Enhancing economic viability and energy security. International Journal of Hydrogen Energy. 2025; 144: 133-142. DOI: https://doi.org/10.1016/j.ijhydene.2025.05.243
[38] Magableh GM. An integrated model for rice supplier selection strategies and a comparative analysis of fuzzy multicriteria decision-making approaches based on the fuzzy entropy weight method for evaluating rice suppliers. PLOS One. 2024; 19(4): e0301930. DOI: https://doi.org/10.1371/journal.pone.0301930
[39] Kamran MA, Afsharfar S, Al Mawali F, Babazadeh R, Al Balushi M. Application of Fuzzy MCDM Methods to Optimize Supplier Selection in Oil and Gas Industry of Oman. International Journal of Industrial Engineering. 2025; 36(2): 52-67. DOI: https://doi.org/10.22068/ijiepr.36.2.2234
[40] Abdulla A, Baryannis G. A hybrid multi-criteria decision-making and machine learning approach for explainable supplier selection. Supply Chain Analytics. 2024; 7: 100074. DOI: https://doi.org/10.1016/j.sca.2024.100074
[41] Baki R, Ecer B, Aktas A. A decision framework for supplier selection in digital supply chains of e-commerce platforms using interval-valued intuitionistic fuzzy VIKOR methodology. Journal of Theoretical and Applied Electronic Commerce Research. 2025; 20(1): 23. DOI:
https://doi.org/10.3390/jtaer20010023
[42] Wang Y, Wang W, Wang Z, Deveci M, Roy SK, Kadry S. Selection of sustainable food suppliers using the Pythagorean fuzzy CRITIC-MARCOS method. Information Sciences. 2024; 664: 120326. DOI: https://doi.org/10.1016/j.ins.2024.120326
[43] Pamucar D, Uluta A, Topal A, Karamaa , Ecer F. Fermatean fuzzy framework based on preference selection index and combined compromise solution methods for green supplier selection in textile industry. International Journal of Systems Science: Operations & Logistics. 2024; 11(1): 2319786. DOI:
https://doi.org/10.1080/23302674.2024.2319786
[44] Rahim M, Shah K, Abdeljawad T, Aphane M, Alburaikan A, Khalifa HAE-W. Confidence levels-based p, q-quasirung orthopair fuzzy operators and its applications to criteria group decision making problems. IEEE Access. 2023; 11, 109983-109996. DOI: https://doi.org/10.1109/ACCESS.2023.3321876
[45] Joshi BP, Gegov A. Confidence levels qrung orthopair fuzzy aggregation operators and its applications to MCDM problems. International Journal of Intelligent Systems. 2020; 35(1): 125-149. DOI: https://doi.org/10.1002/int.22203
[46] Mandal U, Seikh MR. Confidence level-driven Dombi aggregation operators within the p,q-quasirung orthopair fuzzy environment for sustainable supplier evaluation in automotive industry. Decision Making Advances. 2025; 3(1): 285-309. DOI: https://doi.org/10.31181/dma312025101
[47] Li Z, Wei G, Wang R, Wu J, Wei C, Wei Y. EDAS method for multiple attribute group decision making under q-rung orthopair fuzzy environment. Technological and Economic Development of Economy. 2020; 26(1): 86-102. DOI: https://doi.org/10.3846/tede.2019.11333