Confidence Level-Driven Dombi Aggregation Operators within the p,q-Quasirung Orthopair Fuzzy Environment for Sustainable Supplier Evaluation in Automotive Industry

Utpal Mandal; Mijanur Rahaman Seikh

doi:10.31181/dma312025101

Authors

Utpal Mandal Department of Mathematics & Statistics, Banasthali Vidyapith, Rajasthan-304 022, India https://orcid.org/0000-0002-1479-5516
Mijanur Rahaman Seikh Department of Mathematics, Kazi Nazrul University, Asansol 713340, India https://orcid.org/0000-0003-4746-5369

DOI:

https://doi.org/10.31181/dma312025101

Keywords:

Multi-criteria group decision-making, p,q-quasirung orthopair fuzzy sets, Confidence levels, Dombi aggregation operator, Supplier selection

Abstract

Selecting sustainable suppliers in the automotive industry is crucial for fostering environmental responsibility, cost efficiency, and ethical sourcing, all of which enhance long-term competitiveness and compliance with global sustainability standards. However, this process is a complex decision-making problem due to vague, uncertain, and imprecise data stemming from subjective expert judgments, incomplete information, dynamic market conditions, evolving regulations, and diverse stakeholder expectations. Traditional methods often fail to adequately capture these intricacies, necessitating more flexible and intelligent evaluation frameworks. To address this challenge, this study leverages p,q-quasirung orthopair fuzzy sets (p,q-QOFSs) to effectively model hesitation and ambiguity in expert assessments, while incorporating confidence levels to enhance reliability by accounting for varying decision-maker expertise. We propose confidence level-based Dombi weighted averaging (geometric) aggregation operators for p,q-QOFSs and develop a multi-criteria group decision-making model, with attribute weights determined using the Analytic Hierarchy Process (AHP). The model is validated through a case study in which three experts evaluate five automotive suppliers across eight sustainability criteria. A comparative analysis with existing methods demonstrates the superiority of the proposed approach, while sensitivity analysis confirms its robustness and stability under parameter variations.

Downloads

Download data is not yet available.

References

Kolour, H. R., Momayezi, V., & Momayezi, F. (2025). Enhancing supplier selection in public manufacturing: A hybrid multi-criteria decision-making approach. Spectrum of Decision Making and Applications, 3(1), 1–20. https://doi.org/10.31181/sdmap31202629

Wang, Y., Yang, H., & Han, X. (2024). Study on the method of selecting sustainable food suppliers considering interactive factors. Journal of Operations Intelligence, 2(1), 202–218. https://doi.org/10.31181/jopi21202420

Mandal, U., & Seikh, M. R. (2023a). An integrated weighted distance-based approximation method for interval-valued spherical fuzzy MAGDM. In C. Jana, M. Pal, G. Muhiuddin, & P. Liu (Eds.), Fuzzy optimization, decision-making and operations research (pp. 1–20). Springer. https://doi.org/10.1007/978-3-031-35668-1_24

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

Seikh, M. R., & Mandal, U. (2022). 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, 115, 105299. https://doi.org/10.1016/j.engappai.2022.105299

Rahim, M., Abosuliman, S. S., Alroobaea, R., Shah, K., & Abdeljawad, T. (2024). Cosine similarity and distance measures for p, q-quasirung orthopair fuzzy sets: Applications in investment decision-making. Heliyon, 10(11), e32107. https://doi.org/10.1016/j.heliyon.2024.e32107

Rahim, M., Akhtar, Y., Yang, M. S., Ali, H. E., & Elhag, A. A. (2024). Improved COPRAS method with unknown weights under p, q-quasirung orthopair fuzzy environment: Application to green supplier selection. IEEE Access, 12, 69783–69795. https://doi.org/10.1109/ACCESS.2024.3400016

Alballa, T., Rahim, M., Aloraini, N. M., & Khalifa, H. A. E. W. (2024). An extension of the CODAS method using p,q-quasirung orthopair fuzzy information: Application in location selection for retail store. International Journal of Fuzzy Systems, 1–17. https://doi.org/10.1007/s40815-024-01870-5

Rahim, M., Tag Eldin, E. M., Khan, S., Ghamry, N. A., Alanzi, A. M., & Khalifa, H. A. E. W. (2024). Multi-criteria group decision-making based on Dombi aggregation operators under p,q-quasirung orthopair fuzzy sets. Journal of Intelligent & Fuzzy Systems, 46(1), 53–74. https://doi.org/10.3233/JIFS-233327

Rahim, M., Ahmad, S., Younis, B. A., Egami, R. H., & Ahmed, M. M. (2025). Multiple attribute group decision making based on p, q-quasirung orthopair Bonferroni mean operators and their applications. Evolving Systems, 16(1), 9. https://doi.org/10.1007/s12530-024-09638-w

Ali, J., & Naeem, M. (2023). Analysis and application of p, q-quasirung orthopair fuzzy Aczel–Alsina aggregation operators in multiple criteria decision-making. IEEE Access, 11, 49081–49101. https://doi.org/10.1109/ACCESS.2023.3274494

Arya, P., & Pal, A. K. (2025). 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, 17(1), 225–236. https://doi.org/10.1007/s41870-024-02233-x

Dombi, J. (1982). A general class of fuzzy operators, the De Morgan class of fuzzy operators and fuzziness measure included by fuzzy operators. Fuzzy Sets and Systems, 8(2), 149–163. https://doi.org/10.1016/0165-0114(82)90005-7

Seikh, M. R., & Mandal, U. (2021). Intuitionistic fuzzy Dombi aggregation operators and their application to multiple attribute decision-making. Granular Computing, 6, 473–488. https://doi.org/10.1007/s41066-019-00209-y

Alolaiyan, H., Kalsoom, U., Shuaib, U., Razaq, A., Baidar, A. W., & Xin, Q. (2024). Precision measurement for effective pollution mitigation by evaluating air quality monitoring systems in linguistic Pythagorean fuzzy Dombi environment. Scientific Reports, 14(1), 31944. https://doi.org/10.1038/s41598-024-83478-1

Saha, A., Dabic-Miletic, S., Senapati, T., Simic, V., Pamucar, D., Ala, A., & Arya, L. (2024). Fermatean fuzzy Dombi generalized Maclaurin symmetric mean operators for prioritizing bulk material handling technologies. Cognitive Computation, 16, 3096–3121. https://doi.org/10.1007/s12559-024-10323-y

Seikh, M. R., & Mandal, U. (2023). Interval-valued Fermatean fuzzy Dombi aggregation operators and SWARA-based PROMETHEE II method to bio-medical waste management. Expert Systems with Applications, 226, 120082. https://doi.org/10.1016/j.eswa.2023.120082

Senapati, T., Chen, G., Ullah, I., Khan, M. S. A., & Hussain, F. (2024). A novel approach towards multiattribute decision making using q-rung orthopair fuzzy Dombi–Archimedean aggregation operators. Heliyon, 10(6), e27969. https://doi.org/10.1016/j.heliyon.2024.e27969

Mandal, U., & Seikh, M. R. (2023b). Interval-valued spherical fuzzy MABAC method based on Dombi aggregation operators with unknown attribute weights to select plastic waste management process. Applied Soft Computing, 145, 110516. https://doi.org/10.1016/j.asoc.2023.110516

Kavitha, S., Janani, K., Mohanrasu, S. S., Satheeshkumar, J., Amudha, T., & Rakkiyappan, R. (2024). Ensemble feature selection using q-rung orthopair hesitant fuzzy Hamacher, Einstein and Dombi aggregation operators. Applied Soft Computing, 161, 111752. https://doi.org/10.1016/j.asoc.2024.111752

Seikh, M. R., & Chatterjee, P. (2025). Sustainable strategies for electric vehicle adoption: A confidence level-based interval-valued spherical fuzzy MEREC-VIKOR approach. Information Sciences, 699, 121814. https://doi.org/10.1016/j.ins.2024.121814

Seikh, M. R., & Chatterjee, P. (2024). Evaluation and selection of e-learning websites using intuitionistic fuzzy confidence level-based Dombi aggregation operators with unknown weight information. Applied Soft Computing, 163, 111850. https://doi.org/10.1016/j.asoc.2024.111850

Chatterjee, P., & Seikh, M. R. (2024). 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, 42, 100708. https://doi.org/10.1016/j.jii.2024.100708

Joshi, B. P., & Gegov, A. (2020). Confidence levels q-rung orthopair fuzzy aggregation operators and its applications to MCDM problems. International Journal of Intelligent Systems, 35(1), 125–149. https://doi.org/10.1002/int.22203

Mahmood, T., Ali, Z., & Yang, M. (2023). Confidence level aggregation operators based on intuitionistic fuzzy rough sets with application in medical diagnosis. IEEE Access, 11, 8674–8688. https://doi.org/10.1109/ACCESS.2023.3236410

Lin, H., Ullah, I., Ali, A., & Abbas, S. (2023). Analysis of cost and profit using aggregation operator on spherical fuzzy sets with confidence level. Journal of Intelligent and Fuzzy Systems, 45(1), 675–686. https://doi.org/10.3233/JIFS-220102

Punetha, T., & Komal. (2024). Confidence picture fuzzy hybrid aggregation operators and its application in MCGDM. OPSEARCH, 1–37. https://doi.org/10.1007/s12597-023-00720-6

Qiyaas, M., Khan, N., Khan, S., & Khan, F. (2024). Confidence levels bipolar complex fuzzy aggregation operators and their application in decision making problem. IEEE Access, 12, 6204–6214. https://doi.org/10.1109/ACCESS.2023.3347043

Sivadas, A., John, S. J., & Athira, T. (2024). (p, q)-fuzzy aggregation operators and their applications to decision-making. The Journal of Analysis, 1–30. https://doi.org/10.1007/s41478-023-00693-1

Saaty, T. L. (1980). The analytic hierarchy process (AHP). The Journal of the Operational Research Society, 41(11), 1073–1076.

Tronnebati, I., Jawab, F., Frichi, Y., & Arif, J. (2024). Green supplier selection using fuzzy AHP, fuzzy TOPSIS, and fuzzy WASPAS: A case study of the Moroccan automotive industry. Sustainability, 16(11), 4580. https://doi.org/10.3390/su16114580

Kara, K., Acar, A. Z., Polat, M., Önden, İ., & Yalçın, G. C. (2024). Developing a hybrid methodology for green-based supplier selection: Application in the automotive industry. Expert Systems with Applications, 249, 123668. https://doi.org/10.1016/j.eswa.2024.123668

Bas, S. A. (2024). A hybrid approach based on consensus decision making for green supplier selection in automotive industry. Sustainability, 16(7), 3096. https://doi.org/10.3390/su16073096

Gergin, R. E., Peker, İ., & Kısa, A. C. G. (2022). Supplier selection by integrated IFDEMATEL-IFTOPSIS method: A case study of automotive supply industry. Decision Making: Applications in Management and Engineering, 5(1), 169–193. https://doi.org/10.31181/dmame211221075g

Bah, M. K., & Tulkinov, S. (2022). Evaluation of automotive parts suppliers through ordinal priority approach and TOPSIS. Management Science and Business Decisions, 2(1), 5–17. https://doi.org/10.52812/msbd.37

Dweiri, F., Kumar, S., Khan, S. A., & Jain, V. (2016). Designing an integrated AHP based decision support system for supplier selection in automotive industry. Expert Systems with Applications, 62, 273–283. https://doi.org/10.1016/j.eswa.2016.06.030

Dang, T. T., Nguyen, N. A. T., Nguyen, V. T. T., & Dang, L. T. H. (2022). A two-stage multi-criteria supplier selection model for sustainable automotive supply chain under uncertainty. Axioms, 11(5), 228. https://doi.org/10.3390/axioms11050228

Zimmer, K., Fröhling, M., & Schultmann, F. (2016). Sustainable supplier management–a review of models supporting sustainable supplier selection, monitoring and development. International Journal of Production Research, 54(5), 1412–1442. https://doi.org/10.1080/00207543.2015.1079340

Masudin, I., Habibah, I. Z., Wardana, R. W., Restuputri, D. P., & Shariff, S. S. R. (2024). Enhancing supplier selection for sustainable raw materials: A comprehensive analysis using analytical network process (ANP) and TOPSIS methods. Logistics, 8(3), 74. https://doi.org/10.3390/logistics8030074

Amindoust, A., Ahmed, S., Saghafinia, A., & Bahreininejad, A. (2012). Sustainable supplier selection: A ranking model based on fuzzy inference system. Applied Soft Computing, 12(6), 1668–1677. https://doi.org/10.1016/j.asoc.2012.01.023

Rahim, M., Shah, K., Abdeljawad, T., Aphane, M., Alburaikan, A., & Khalifa, H. A. E. W. (2023). Confidence levels-based p, q-quasirung orthopair fuzzy operators and its applications to criteria group decision making problems. IEEE Access, 11, 109983–109996. https://doi.org/10.1109/ACCESS.2023.3321876