A Consensus-Based MULTIMOORA Framework under Probabilistic Hesitant Fuzzy Environment for Manufacturing Vendor Selection

Saha, Abhijit; Rage, Kiranmai; Senapati, Tapan; Chatterjee, Prasenjit; Zavadskas, Edmundas Kazimieras; Sliogerienė, Jūratė

doi:10.15388/24-INFOR581

Informatica

A Consensus-Based MULTIMOORA Framework under Probabilistic Hesitant Fuzzy Environment for Manufacturing Vendor Selection

Abhijit Saha Kiranmai Rage Tapan Senapati Prasenjit Chatterjee

Edmundas Kazimieras Zavadskas Jūratė Sliogerienė

https://doi.org/10.15388/24-INFOR581

Pub. online: 6 January 2025 Type: Research Article

Open Access

Received
1 August 2024

Accepted
1 December 2024

Published
6 January 2025

Abstract

Multi-criteria group decision-making has gained considerable attention due to its ability to aggregate diverse expert opinions and establish a preference order among alternatives. While probabilistic hesitant fuzzy (PHF) sets offer increased flexibility and generality for representing criteria values compared to traditional fuzzy and hesitant fuzzy set theories, existing aggregation techniques often fail to enhance consensus among biased expert judgments. Motivated by the need for more effective consensus-based decision-making, this paper proposes a new framework that integrates PHF set theory with Aczel-Alsina weighted averaging and geometric aggregation operators. These operators, known for their flexibility and the inclusion of an adjustable parameter, are particularly well-suited for addressing real-world decision-making challenges. The framework employs a cross-entropy based model to determine criteria weights and multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) method to establish priority orders of alternatives. The proposed framework is demonstrated through a case study on manufacturing outsourcing vendor selection. The results show that Bertrandt is the most suitable vendor, with a score of 0.2390, and resources consumption is identified as the most critical criterion, with a weight of 0.20. To validate the robustness of the proposed framework, sensitivity and comparison analyses have also been conducted.

References

Ali, J., Naeem, M. (2022). Complex q-rung orthopair fuzzy Aczel–Alsina aggregation operators and its application to multiple criteria decision-making with unknown weight information. IEEE Access, 10, 85315–85342.

Athar Farid, H.A., Riaz, M. (2023). q-rung orthopair fuzzy Aczel–Alsina aggregation operators with multi-criteria decision-making. Engineering Applications of Artificial Intelligence, 122, 106105.

Brauers, W.K.M., Zavadskas, E.K. (2006). The MOORA method and its application to privatization in a transition economy. Control and Cybernetics, 35, 445–469.

Brauers, W.K.M., Zavadskas, E.K. (2010). Project management by MULTIMOORA as an instrument for transition economies. Technological and Economic Development of Economy, 16, 5–24.

Borkhade, R., Bhat, S.K., Mahesha, G.T. (2022). Implementation of sustainable reforms in the Indian automotive industry: from vehicle emissions perspective. Cogent Engineering, 9. 2014024.

Chen, L., Zhou, X., Wu, M., Shi, Y., Wang, Y. (2023). Aczel-Alsina aggregation operators on complex Fermatean fuzzy information with application to multi-attribute decision-making. IEEE Access, 11, 141703–141722.

Ding, J., Xu, Z.S., Zhao, N. (2017). An interactive approach to probabilistic hesitant fuzzy multi-attribute group decision making with incomplete weight information. Journal of Intelligent and Fuzzy Systems, 32, 2523–2536.

Gai, L., Liu, H.C., Wang, Y., Xing, Y. (2023). Green supplier selection and order allocation using linguistic Z-numbers MULTIMOORA method and bi-objective non-linear programming. Fuzzy Optimization and Decision Making, 22(2), 267–288.

Ghaemi-Zadeh, N., Eghbali-Zarch, M. (2024). Evaluation of business strategies based on the financial performance of the corporation and investors’ behavior using D-CRITIC and fuzzy MULTI-MOORA techniques: a real case study. Expert Systems with Applications, 247, 123183.

Gula, R., Al-shamib, T.M., Ayuba, S., Shabira, M., Hosnye, M. (2024). Development of Aczel-Alsina t-norm based linear Diophantine fuzzy aggregation operators and their applications in multi-criteria decision-making with unknown weight information. Helion, 10, e35942.

Guo, J., Yin, J., Zhang, L., Lin, Z., Li, X. (2020). Extended TODIM method for CCUS storage site selection under probabilistic hesitant fuzzy environment. Applied Soft Computing, 93, 106381.

He, Y., Xu, Z.S. (2019). Multi-attribute decision-making methods based on reference ideal theory with probabilistic hesitant information. Expert Systems With Applications, 118, 459–469.

Jaisankar, R., Murugesan, V., Narayanamoorthy, S., Ahmadian, A., Suvitha, K., Ferrara, M., Kang, Integrated, D. (2023). MCDM approaches for exploring the ideal therapeutic plastic disposal technology: probabilistic hesitant fuzzy domain. Water, Air and Soil Pollution, 234, 71.

Jin, F., Garg, H., Pei, L., Liu, J., Chen, H. (2020). Multiplicative consistency adjustment model and data envelopment analysis-driven decision-making process with probabilistic hesitant fuzzy preference relations. International Journal of Fuzzy Systems, 22, 2319–2332.

Krishankumar, R., Garg, H., Arun, K., Saha, A., Ravichandran, K.S. (2022). An integrated decision-making COPRAS approach to probabilistic hesitant fuzzy set information. Complex and Intelligent Systems, 7(5), 2281–2298.

Li, J., Wang, J.Q. (2017). Multi-criteria outranking methods with hesitant probabilistic fuzzy sets. Cognitive Computation, 9, 611–625.

Li, W., Ye, J., Türkarslan, E. (2023). MAGDM model using the Aczel-Alsina aggregation operators of neutrosophic entropy elements in the case of neutrosophic multi-valued sets. Neutrosophic Sets and Systems, 57, 1–17.

Li, J., Wang, J.Q., Hu, J.H. (2019). Multi-criteria decision-making method based on dominance degree and BWM with probabilistic hesitant fuzzy information. International Journal of Machine Learning and Cybernetics, 10, 1671–1685.

Li, J., Chen, Q., Li, L., Wang, Z.X. (2020). An ORESTE approach for multi-criteria decision-making with probabilistic hesitant fuzzy information. International Journal of Machine Learning and Cybernetics, 11, 1591–1609.

Liao, N., Wei, G., Xu, X., Chen, X., Guo, Y. (2022a). CODAS method with probabilistic hesitant fuzzy information and its application to environmentally, and economically balanced supplier selection. Technological and Economic Development of Economy, 28, 1419–1438.

Liao, N., Wei, G., Xu, X., Chen, X. (2022b). TODIM method based on cumulative prospect theory for multiple attributes group decision making under probabilistic hesitant fuzzy setting. International Journal of Fuzzy Systems, 24, 322–339.

Lin, M., Zhan, Q., Xu, Z.S. (2020a). Decision making with probabilistic hesitant fuzzy information based on multiplicative consistency. International Journal of Intelligent Systems, 35, 1233–1261.

Lin, Z.M., Huang, C., Lin, M.W. (2020b). Probabilistic hesitant fuzzy methods for prioritizing distributed stream processing frameworks for IoT applications. Mathematical Problems in Engineering, 2021, 6655477.

Liu, Q., Hou, J., Dong, Q. (2023a). Modified MARCOS method for industrial competitiveness evaluation of regional cultural tourism with probabilistic hesitant fuzzy information. Journal of Intelligent and Fuzzy Systems, 45, 93–103.

Liu, P., Ali, Z., Mahmood, T., Geng, Y. (2023b). Prioritized aggregation operators for complex intuitionistic fuzzy sets based on Aczel-Alsina T-norm and T-conorm and their applications in decision-making. International Journal of Fuzzy Systems, 25, 2590–2608.

Liu, X., Wang, Z., Zhang, S., Liu, J. (2020). Probabilistic hesitant fuzzy multiple attribute decision-making based on regret theory for the evaluation of venture capital projects. Economic Research, 33, 672–697.

Liu, J.P., Huang, C., Song, J.S., Du, P.C., Jin, F.F., Chen, H.Y. (2021). Group decision making based on the modified probability calculation method and DEA cross-efficiency with probabilistic hesitant fuzzy preference relations. Computers and Industrial Engineering, 156, 107262.

Liu, D., Xu, J., Du, Y. (2024). An integrated HPF-TODIM-MULTIMOORA approach for car selection through online reviews. Annals of Operations Research. https://doi.org/10.1007/s10479-024-05972-z.

Luthra, S., Garg, D., Haleem, A. (2016). The impacts of critical success factors for implementing green supply chain management towards sustainability: an empirical investigation of Indian automobile industry. Journal of Cleaner Production, 121, 142–158.

Mahmood, T., Ali, Z., Baupradist, S., Chinram, R. (2022). Complex intuitionistic fuzzy Aczel-Alsina aggregation operators and their application in multi-attribute decision-making. Symmetry, 14, 2255.

Mathivathanan, D., Kannan, D., Haq, A.N. (2018). Sustainable supply chain management practices in Indian automotive industry: a multi-stakeholder view. Resources, Conservation and Recycle, 128, 284–305.

Miglani, S. (2019). The growth of the Indian automobile industry: analysis of the roles of government policy and other enabling factors. In: ARCIALA Series on Intellectual Assets and Law in Asia. https://doi.org/10.1007/978-981-13-8102-7_19.

Mishra, A.R., Rani, P., Saha, A., Pamucar, D. (2023). Entropy and discrimination measures based q-rung orthopair fuzzy MULTIMOORA framework for selecting solid waste disposal method. Environmental Science and Pollution Research, 30(5), 12988–13011.

Qi, Q. (2023). TOPSIS methods for probabilistic hesitant fuzzy MAGDM and application to performance evaluation of public charging service quality. Informatica, 34(2), 317–336. https://doi.org/10.15388/22-INFOR501.

Rani, P., Mishra, A.R. (2021). Fermatean fuzzy Einstein aggregation operators based MULTIMOORA method for electric vehicle charging station selection. Expert Systems with Applications, 182, 115267.

Rani, P., Mishra, A.R., Krishankumar, R., Mardani, A., Ravichandran, K.S., Kar, S. (2021). Multi-criteria food waste treatment method selection using single-valued neutrosophic-CRITIC-MULTIMOORA framework. Applied Soft Computing, 111, 107657.

Rodriguez, R.M., Martinez, L., Torra, V., Xu, Z.S., Herrera, F. (2014). Hesitant fuzzy sets: state of the art and future directions. International Journal of Intelligent Systems, 29, 495–524.

Stanujkic, D., Karabasevic, D., Zavadskas, E.K., Smarandache, F., &Brauers, W.K. (2019). A bipolar fuzzy extension of the MULTIMOORA method. Informatica, 30(1), 135–152. https://doi.org/10.15388/Informatica.2019.201.

Sahin, Y., Aydemir, E. (2022). A comprehensive solution approach for CNC machine tool selection problem. Informatica, 33(1), 81–108. https://doi.org/10.15388/21-INFOR461.

Saha, A., Simic, V., Senapati, T., Dabic-Miletic, S., Ala, A. (2023). A dual hesitant fuzzy sets-based methodology for advantage prioritization of zero-emission last-mile delivery solutions for sustainable city logistics. IEEE Transactions on Fuzzy Systems, 31(2), 407–420. https://doi.org/10.1109/TFUZZ.2022.3164053.

Saluja, R.S., Singh, V. (2023). An improved fuzzy MULTIMOORA approach and its application in welding process selection. International Journal of Fuzzy Systems, 25(4), 1707–1726.

Senapati, T. (2024). An Aczel-Alsina aggregation-based outranking method for multiple attribute decision-making using single-valued neutrosophic numbers. Complex and Intelligent Systems, 10, 1185–1199.

Senapati, T., Chen, G., Mesiar, R., Yager, R.R., Saha, A. (2022a). Novel Aczel-Alsina operations-based hesitant fuzzy aggregation operators and their applications in cyclone disaster assessment. International Journal of General Systems, 51(5), 511–546.

Senapati, T., Mishra, A.R., Saha, A., Simic, V., Rani, P., Ali, R. (2022b). Construction of interval-valued Pythagorean fuzzy Aczel-Alsina aggregation operators for decision making: a case study in emerging IT software company selection. Sådhanå, 47, 255.

Senapati, T., Chen, G., Mesiar, R., Yager, R.R. (2023a). 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.

Senapati, T., Simic, V., Saha, A., Dobrodolac, M., Rong, Y., Tirkolaee, E.B. (2023b). Intuitionistic fuzzy power Aczel-Alsina model for prioritization of sustainable transportation sharing practices. Engineering Applications of Artificial Intelligence, 119, 105716.

Torra, V. (2010). Hesitant fuzzy sets. International Journal of Intelligent Systems, 25, 529–539.

Vaezi, A., Rabbani, E., Yazdian, S.A. (2024). Blockchain-integrated sustainable supplier selection and order allocation: a hybrid BWM-MULTIMOORA and bi-objective programming approach. Journal of Cleaner Production, 444, 141216.

Wang, H., Xu, T., Feng, L., Mahmood, T., Ullah, K. (2023). Aczel–Alsina Hamy mean aggregation operators in T-spherical fuzzy multi-criteria decision-making. Axioms, 12, 224.

Xu, Z.S., Zhou, W. (2016). Consensus building with a group of decision makers under the hesitant probabilistic fuzzy environment. Fuzzy Optimization and Decision Making, 16, 481–503.

Yu, J., Zeng, Q., Yu, Y., Wu, S., Ding, H., Ma, W., Yang, J. (2023). Failure mode and effects analysis based on rough cloud model and MULTIMOORA method: application to single-point mooring system. Applied Soft Computing, 132, 109841.

Yucesan, M., Özkan, B., Mete, S., Gul, M., Özceylan, E. (2024). Evaluating sustainability of urban mobility of Asian cities: An integrated approach of interval type-2 fuzzy best-worst method and MULTIMOORA. Engineering Applications of Artificial Intelligence, 127, 107266.

Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.

Zhang, C., Wang, B., Li, W., Li, D. (2024). Incorporating artificial intelligence in detecting crop diseases: Agricultural decision-making based on group consensus model with MULTIMOORA and evidence theory. Crop Protection, 179, 106632.

Zhou, Q., Ye, C., Geng, X. (2024). A decision framework of offshore wind power station site selection using a MULTIMOORA method under Pythagorean hesitant fuzzy environment. Ocean Engineering, 291, 116416.

Biographies

Saha Abhijit

abhijit84.math@gmail.com

A. Saha is an Assistant Professor (Research) in the Department of Computing Technologies at SRMIST, Tamil Nadu, India. Dr. Saha has published 40 research articles in various journals of international repute. His areas of research interest are fuzzy set theory, soft set theory, optimization and decision-making. He is serving as an editorial board member of various Scopus indexed journals including International Journal of Neutrosophic Sciences and Decision <aking: Applications in Engineering and Management.

Rage Kiranmai

kiranmai.r@bvrit.ac.in

K. Rage is an assistant professor in the Department of Computer Science and Engineering at B V Raju Institute of Technology, Narsapur, Telangana, India. She has published numerous research papers in Decision Sciences, Convolutional Neural Networks, Decision Trees, Deep Belief Networks, Deep Learning, and Reinforcement Learning.

Senapati Tapan

math.tapan@gmail.com

T. Senapati received the BSc, MSc and PhD degrees in mathematics from the Vidyasagar University, India, in 2006, 2008 and 2013 respectively. He has published two books and 65 papers in peer-reviewed international journals. His current research interests include fuzzy sets, fuzzy optimization, soft computing, multi-attribute decision making and aggregation operators.

Chatterjee Prasenjit

https://orcid.org/0000-0002-7994-4252

p.chatterjee@mckvie.edu.in

Zavadskas Edmundas Kazimieras

zavadskas@vilniustech.lt

Sliogerienė Jūratė

jurate.sliogeriene@vilniustech.lt