Revolutionizing Multi-Criteria Decision Making with the Triangular Fuzzy Geometry Bonferroni Mean Operator (TFGBM)
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Keywords:
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Aggregating Operator, Bonferroni Mean (BM), Triangular Fuzzy Number (TFN), Geometric Bonferroni Mean (GBM), Triangular Fuzzy Geometric Bonferroni Mean (TFGBM), Multi-Criteria Decision Making (MCDM)
Abstract
This study investigates the Multi-Criteria Decision Making (MCDM) topic to address the complexities of decision processes involving ambiguous information. We introduce the Triangular Fuzzy Geometric Bonferroni Mean (TFGBM) operator, a novel aggregation technique inspired by the Geometric Bonferroni Mean (GBM) concept. This operator is intended to aggregate triangular fuzzy numbers within MCDM problems effectively. We thoroughly investigate the properties of TFGBM and its distinct forms to ensure its practical utility. We introduce the Triangular Fuzzy Geometric Weighted Bonferroni Mean (TFGWBM) operator to accommodate situations where input factors have variable degrees of significance. Based on this foundation, we present a comprehensive framework for decision-making involving multiple attributes in ambiguous triangular fuzzy environments. A relevant case study regarding selecting an optimal location for a Halal center demonstrates the efficacy and applicability of our methodology. We emphasize the tangibility and efficiency of the suggested methodology in improving decision-making processes by emphasizing this real-world application.
References
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Rodzi, Z. M., N. F. I. Abd Ghafur Ahmad, and N. L. Abdullah (2021a). Z-Score Functions of Hesitant Fuzzy Sets. Mathematics and Statistics, 9(4); 445–455
Rodzi, Z. M., M. N. H. bin Kamarulamirin, and Y. binti Ya’akop (2021b). The DEMATEL Approach to Analyzing the Factors Influencing University Students’ Purchase of Smartphones. International Conference on Artificial Intelligence and Data Sciences, AiDAS, 3; 1–6
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Xia, M., Z. Xu, and B. Zhu (2013). Geometric Bonferroni Means with their Application in Multi criteria Decision Making. Knowledge-Based Systems, 40; 88–100
Yang, X., T. Mahmood, and J. Ahmmad (2023). Picture Fuzzy Soft Bonferroni Mean Aggregation Operators and their Applications. Heliyon, 9(6); 17278
Zhu, W. Q., P. Liang, L. J. Wang, and Y. R. Hou (2015). Triangular Fuzzy Bonferroni Mean Operators and their Application to Multiple Attribute Decision Making. Journal of Intelligent & Fuzzy Systems, 29(4); 1265–1272
Bonferroni, C. (1950). Sulle Medie Multiple Di Potenze. Bollettino dell’Unione Matematica Italiana, 5(3-4); 267–270
Cantillo, J., J. C. Martín, and C. Román (2021). Assessing the Label’s Mandatory Information for Fishery and Aquaculture Products in the Eu28. A Consumer Approach Based on a Consistent Fuzzy Preference Relation with Geometric Bonferroni Mean. Marine Policy, 128; 104515
Cao, N. and M. Štěpnička (2023). Preservation of Properties of Residuated Algebraic Structure by Structures for the Partial Fuzzy Set Theory. International Journal of Approximate Reasoning, 154; 1–26
Chakraborty, S. and A. K. Saha (2023). Novel Fermatean Fuzzy Bonferroni Mean Aggregation Operators for Selecting Optimal Health Care Waste Treatment Technology. Engineering Applications of Artificial Intelligence, 119; 105752
Chen, Z.-S., K.-S. Chin, and K.-L. Tsui (2019). Constructing the Geometric Bonferroni Mean from the Generalized Bonferroni Mean with Several Extensions to Linguistic 2-tuples for Decision making. Applied Soft Computing, 78; 595–613
Debnath, S. (2021). Fuzzy Hypersoft Sets and its Weightage Operator for Decision Making. Journal of Fuzzy Extension and Applications, 2(2); 163–170
Eltarabishi, F., O. H. Omar, I. Alsyouf, and M. Bettayeb (2020). Multi-criteria Decision Making Methods and their Applications–a Literature Review. International Conference on Industrial Engineering and Operations Management, 3; 2654–2663
Herrera-Viedma, E. (2015). Fuzzy Sets and Fuzzy Logic in Multi-criteria Decision Making. The 50th Anniversary of Prof. Lotfi Zadeh’s Theory: Introduction. Technological and Economic Development of Economy, 21(5); 677–683
Ismail, J. N., Z. Rodzi, F. Al Sharqi, H. Hashim, and N. H. Sulaiman (2023a). The Integrated Novel Framework: Linguistic Variables in Pythagorean Neutrosophic Set with DEMATEL for Enhanced Decision Support. International Journal of Neutrosophic Science, 21(2); 129–141
Ismail, J. N., Z. M. Rodzi, F. Al Sharqi, A. Al Quran, H. Hashim, and N. H. Sulaiman (2023b). Algebraic Operations on Pythagorean neutrosophic sets (PNS): Extending Applicability and Decision-Making Capabilities. International Journal of Neutrosophic Science, 21(4); 127–134
Jin, G. (2023). Selection of Virtual Team Members for Smart Port Development Projects Through the Application of the Direct and Indirect Uncertain Topsis Method. Expert Systems with Applications, 217; 119555
Kumbure, M. M., P. Luukka, and M. Collan (2020). A New Fuzzy K-nearest Neighbor Classifier Based on the Bonferroni Mean. Pattern Recognition Letters, 140; 172–178
Liang, D., A. P. Darko, Z. Xu, and M. Wang (2019). Aggregation of Dual Hesitant Fuzzy Heterogenous Related Information with Extended Bonferroni Mean and its Application to Multimoora. Computers & Industrial Engineering, 135; 156–176
Liu, L., X. Wu, and G. Chen (2023). Picture Fuzzy Interactional Bonferroni Mean Operators via Strict Triangular Norms and Applications to Multi-Criteria Decision Making. IEEE Transactions on Fuzzy Systems, 4; 1–15
Priyanka, R., K. Ravindran, B. Sankaranarayanan, and S. M. Ali (2023). A Fuzzy DEMATELDecision Modeling Framework for Identifying Key Human Resources Challenges in Start-up Companies: Implications for Sustainable Development. Decision Analytics Journal, 6; 100192
Rodzi, Z. and A. G. Ahmad (2020). Application of Parameterized Hesitant Fuzzy Soft Set Theory in Decision Making. Mathematics and Statistics, 8(3); 244–253
Rodzi, Z. M., N. F. I. Abd Ghafur Ahmad, and N. L. Abdullah (2021a). Z-Score Functions of Hesitant Fuzzy Sets. Mathematics and Statistics, 9(4); 445–455
Rodzi, Z. M., M. N. H. bin Kamarulamirin, and Y. binti Ya’akop (2021b). The DEMATEL Approach to Analyzing the Factors Influencing University Students’ Purchase of Smartphones. International Conference on Artificial Intelligence and Data Sciences, AiDAS, 3; 1–6
Rodzi bin Md, Z., F. A. M. Amın, N. Jamiatun, A. Qaiyyum, F. Al-Sharqi, Z. A. Zaharudin, and M. H. M. Khair (2023). Integrated Single-Valued Neutrosophic Normalized Weighted Bonferroni Mean (SVNNWBM)-DEMATEL for Analyzing the Key Barriers to Halal Certification Adoption in Malaysia. International Journal of Neutrosophic Science, 21(3); 106–114
Wu, M., T. Zhao, and J. Fan (2023). Multiple Attribute Group Decision-Making Model based on Single-Valued Neutrosophic Fuzzy Sets and VIKOR. Research Square; 2023
Xia, M., Z. Xu, and B. Zhu (2013). Geometric Bonferroni Means with their Application in Multi criteria Decision Making. Knowledge-Based Systems, 40; 88–100
Yang, X., T. Mahmood, and J. Ahmmad (2023). Picture Fuzzy Soft Bonferroni Mean Aggregation Operators and their Applications. Heliyon, 9(6); 17278
Zhu, W. Q., P. Liang, L. J. Wang, and Y. R. Hou (2015). Triangular Fuzzy Bonferroni Mean Operators and their Application to Multiple Attribute Decision Making. Journal of Intelligent & Fuzzy Systems, 29(4); 1265–1272
Authors
Hasnan, Q. H. B. ., Rodzi, Z. B. M. ., Kamis, N. H. B. ., Amin, F. A. B. M. ., Al-Sharqi, F. ., Sahak, J. M. ., & Ahmad, G. B. . (2024). Revolutionizing Multi-Criteria Decision Making with the Triangular Fuzzy Geometry Bonferroni Mean Operator (TFGBM). Science and Technology Indonesia, 9(1), 1–6. https://doi.org/10.26554/sti.2024.9.1.1-6
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