Picture Fuzzy Aczel-Alsina Power Geometric Aggregation Operators and Their Application to Multi Criteria Decision-Making
DOI:
https://doi.org/10.52783/jns.v14.2104Keywords:
Multi criteria decision-making, picture fuzzy set, Aczel-Alsina t-norms and t-conorms, Power aggregation operator, Food industryAbstract
This paper develops a robust picture fuzzy (PF) decision-making framework by integrating power aggregation operators derived from Aczél-Alsina operations. The proposed power aggregation operators effectively capture intricate interrelationships among multiple criteria, thereby enhancing the precision and reliability of decision-making processes. In this study, the familiarity of decision makers with the evaluated objects is systematically incorporated into the PF framework alongside primary data, ensuring a more comprehensive assessment. Motivated by the operational principles of Aczél-Alsina functions, this research advances the theoretical foundation of PF Aczél-Alsina power-weighted and ordered-weighted geometric operators, seamlessly integrating decision makers’ expertise into the aggregation process. The structural properties and mathematical characteristics of these newly developed operators are rigorously analyzed. To validate their practical applicability, we employ the proposed operators to solve a complex multi-criteria decision-making (MCDM) problem within the food industry, a domain where uncertainty and nuanced judgments play a critical role. A comparative evaluation against existing operators highlights the superior performance of our approach in effectively managing uncertainty, refining decision accuracy, and enhancing adaptability to real-world decision-making challenges.
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Atanassov, K. T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87-96.
Ates, F., & Akay, D. (2020). Some picture fuzzy Bonferroni mean operators with their application to multicriteria decision making, International Journal of Intelligent Systems, 35(4), 625-649.
Biswas, A., & Deb, N. (2021). Pythagorean fuzzy Dombi power aggregation operators for solving multi-attribute decision making problems, Granular Computing, 6, 991–1007.
Cuong, B. C., & Kreinovich, V. (2013). Picture fuzzy sets-a new concept for computational intelligence problems. In 2013 third world congress on information and communication tech- nologies (WICT 2013), 1-6. IEEE.
Cuong, B. C., Kreinovitch, V., & Ngan, R. T. (2016). A classification of representable t-norm operators for picture fuzzy sets. In 2016 eighth international conference on knowledge and systems engineering (KSE), 19-24. IEEE.
Garg, H. (2017). Some picture fuzzy aggregation operators and their applications to multicriteria decision-making. , Arabian Journal for Science and Engineering, 42(12), 5275-5290.
Garg, H., Tiwari, P., & Prasad, V. (2023). Dombi prioritized aggregation operators for intuitionistic fuzzy information and their application in multi-attribute decision making, Alexandria Engineering Journal, 67, 229–240.
Hussain, A., Latif, S., & Ullah, K. (2022). A novel approach of picture fuzzy sets with unknown degree of weights based on Dombi aggregation operators, Journal of Innovative Research in Mathematical and Computational Sciences, 1(2), 18–39.
Jana, C., & Pal, M. (2019). Assessment of enterprise performance based on picture fuzzy Hamacher aggregation operators, Symmetry, 11(1), 75.
Jana chiranjibe, Tapan Senapati, Madhumangal Pal, and Ronald R. Yager. Picture fuzzy Dombi aggregation operators: application to MADM process, Applied Soft Computing, 74, 99-109.
Khan, S., Abdullah, S., & Ashraf, S. (2019). Picture fuzzy aggregation information based on Einstein operations and their application in decision making, Mathematical Sciences, 13(3), 213-229.
Khan, Q., Riaz, M., & Latif, S. (2022). Multiple attribute group decision making based on intuitionistic fuzzy Dombi generalized power aggregation operators, Mathematical Problems in Engineering, 2022(1), 4634411.
Lin, M., Li, X., Chen, R., Fujita, H., & Lin, J. (2022). Picture fuzzy interactional partitioned Heronian mean aggregation operators: an application to MCDM process. Artificial Intelligence Review, 1-38.
Liu, P. D., & Liu, X. (2017). Multiattribute group decision-making methods based on linguistic intuitionistic fuzzy power Bonferroni mean operators. Complexity, 3571459(1), 1-15.
Ma, L., Zhang, T., & Wang, Y. (2024). Decision algorithm for q-rung orthopair fuzzy information based on Dombi aggregation operators with applications in agricultural systems, IEEE Access, 12, 25762–25778.
Qin, Y., Cui, X., Huang, M., Zhong, Y., Tang, Z., & Shi, P. (2021). Multiple-attribute decision-making based on picture fuzzy Archimedean power Maclaurin symmetric mean operators. Granular Computing, 6(3), 737-761.
Qiyas, M., Khan, M. A., Khan, S., & Abdullah, S. (2020). Concept of Yager operators with the picture fuzzy set environment and its application to emergency program selection. International Journal of Intelligent Computing and Cybernetics, 13(4), 455-483.
Rahman, K., Ayub, S., & Abdullah, S. (2021). Generalized intuitionistic fuzzy aggregation operators based on levels for group decision making. Granular Computing, 6, 867-886.
Seikh, M. R., & Mandal, U. (2021). Some Picture Fuzzy Aggregation Operators based on Frank t-norm and t-conorm: Application to MCDM Process. Informatica, 45(3).
Senapati, T. (2022). Approaches to multi-attribute decision-making based on picture fuzzy Aczel–Alsina geometric aggregation operators. Computational and Applied Mathematics, 41(1), 40.
Ullah, K. (2021). Picture fuzzy maclaurin symmetric mean operators and their applications in solving multiattribute decision-making problems. Mathematical Problems in Engineering, 1-13.
Ullah, K., Naeem, M., Hussain, A., Waqas, M., & Haleemzai, I. (2023). Evaluation of electric motor cars based frank power aggregation operators under picture fuzzy information and a multi-attribute group decision-making process. IEEE Access, 11, 67201-67219.
Wang, R., Wang, J., Gao, H., & Wei, G. (2018). Methods for MCDM with picture fuzzy muirhead mean operators and their application for evaluating the financial investment risk, Symmetry, 11(1), 6.
Wei, G. (2017). Picture fuzzy aggregation operators and their application to multiple attribute decision making, Journal of Intelligent & Fuzzy Systems, 33(2), 713-724.
Wei, G. (2018). Picture fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. , Fundamenta Informaticae, 157(3), 271-320.
Wei, D., Liu, X., & Ma, Z. (2022). Fermatean fuzzy Dombi operators and BWM-entropy-based combined compromise solution approach: an application to green supplier selection, Entropy, 24(6), 776.
Yager, R. R. (1988). On ordered weighted geometric aggregation operators in multi criteria decision making. IEEE Transactions on systems Man and Cybernetics, 18(1)(1), 183-190.
Yager, R. R (2001). The power geometric operator. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 31 (6), 724-731.
Zadeh, L. A. (1965). Fuzzy sets. Information and control, 8(3), 338-353.
Zhang, H., Zhang, R., Huang, H., & Wang, J. (2018). Some picture fuzzy Dombi Heronian mean operators with their application to multi-attribute decision-making, Symmetry, 10(11), 593.
Naeem, M. Khan, Y. Ashraf, S. Weera, W. and Batool, B. (2022). A novel picture fuzzy Aczel-Alsina geometric aggregation information: Application to determining the factors affecting mango crops, AIMS Math, 7(7), 12264-12288.
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