An Alternative Approach for Enhanced Decision-Making using Fermatean Fuzzy Sets
DOI:
https://doi.org/10.31181/sems21202411jKeywords:
Fermatean Fuzzy Sets, Multi-Criteria Decision-Making, Score function, Function Aggregation, Uncertainty, Decision-makersAbstract
This paper explores an innovative approach to solving multi-criteria decision-making (MCDM) problems by focusing on the aggregation of membership and non-membership values using score functions of Fermatean fuzzy sets. Fermatean fuzzy sets have been used to provide a more complex and flexible framework for decision-making because of their ability to handle higher levels of uncertainty and ambiguity. The suggested approach makes use of the unique characteristics of Fermatean fuzzy sets to enhance the aggregation procedure and guarantee a more accurate representation of uncertainty in scenarios involving decision-making. The study begins with a comprehensive review of existing fuzzy set theories and their applications in MCDM, highlighting the limitations of traditional methods. The novel part of this work is to provide a score function designed for Fermatean fuzzy sets that improves the accuracy and consistency of the aggregation procedure. Such score function offers a reliable method for combining several criteria since they are carefully put together to represent the varied relationships between membership and non-membership values. To validate the effectiveness of the proposed approach, the methodology is applied to a hypothetical case study in software design. The results underscore the potential of Fermatean fuzzy sets in addressing the complexities of MCDM, particularly in fields requiring high levels of precision and adaptability. This research presents a novel and effective alternative to traditional MCDM approaches, offering significant improvements in the handling of uncertainty and ambiguity. Experimental results of the study are presented and compared with the existing literature.
Downloads
References
Dong, Y.C., Liu, Y.T., Liang, H.M., Chiclana, F., & Herrera-Viedma, E. (2018). Strategic weight manipulation in multiple attribute decision making. Omega, 75, 154-164. https://doi.org/10.1016/j.omega.2017.02.008.
Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X.
Atanassov, K.T., Vassilev, P.M., & Tsvetkov, R.T. (2013). Intuitionistic Fuzzy Sets, Measures and Integrals. Professor Marin Drinov Academic Publishing House.
Atanassov, K.T. (2016). Geometrical interpretation of the elements of the intuitionistic fuzzy objects. International Journal of Bioautomation, 20(S1), S27-S42.
Yager, R.R. (2013). Pythagorean fuzzy subsets. In Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting (pp. 57-61), Edmonton, AB, Canada. IEEE. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375.
Yager, R.R. (2014). Pythagorean membership grades in multicriteria decision making. IEEE Transactions on Fuzzy Systems, 22, 958-965. https://doi.org/10.1109/10.1109/TFUZZ.2013.2278989.
Peng, X., & Yang, Y. (2015). Some results for Pythagorean fuzzy sets. International Journal of Intelligent Systems, 30, 1133-1160. https://doi.org/10.1002/int.21738.
Gou, X., Xu, Z., & Ren, P. (2016). The properties of continuous Pythagorean fuzzy information. International Journal of Intelligent Systems, 31, 401-424. https://doi.org/10.1002/int.21788.
Senapati, T., & Yager, R.R. (2019). Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision making. Informatica, 30(2), 391-412. https://doi.org/10.15388/Informatica.2019.211.
Senapati, T., & Yager, R.R. (2019). Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods. Engineering Applications of Artificial Intelligence, 85, 112-121. https://doi.org/10.1016/j.engappai.2019.05.012.
Senapati, T., & Yager, R.R. (2020). Fermatean fuzzy sets. Journal of Ambient Intelligence and Humanized Computing, 11, 663-674. https://doi.org/10.1007/s12652-019-01377-0.
Salehi, K. (2015). A hybrid fuzzy MCDM approach for project selection problem. Decision Science Letters, 4(1), 109-116. https://doi.org/10.5267/j.dsl.2014.8.003.
Huang, X. (2007). Optimal project selection with random fuzzy parameters. International Journal of Production Economics, 106(2), 513-522. https://doi.org/10.1016/j.ijpe.2006.06.011.
Carlsson, C., Fullér, R., Heikkilä, M., & Majlender, P. (2007). A fuzzy approach to R&D project portfolio selection. International Journal of Approximate Reasoning, 44(2), 93-105. https://doi.org/10.1016/j.ijar.2006.07.003.
Mohanty, R.P. (1992). Project selection by a multiple-criteria decision-making method: an example from a developing country. International Journal of Project Management, 10(1), 31-38. https://doi.org/10.1016/0263-7863(92)90070-P.
Enea, M., & Piazza, T. (2004). Project selection by constrained fuzzy AHP. Fuzzy Optimization and Decision Making, 3(1), 39-62. https://doi.org/10.1023/B:FODM.0000013071.63614.3d.
Mahmoodzadeh, S., Shahrabi, J., Pariazar, M., & Zaeri, M. S. (2007). Project selection by using fuzzy AHP and TOPSIS technique. World Academy of Science, Engineering and Technology, 30, 333-338.
Amiri, M. P. (2010). Project selection for oil-fields development by using the AHP and fuzzy TOPSIS methods. Expert Systems with Applications, 37(9), 6218-6224. https://doi.org/10.1016/j.eswa.2010.02.103.
Daneshvar Rouyendegh, B., & Erol, S. (2012). Selecting the best project using the Fuzzy ELECTRE Method. Mathematical Problems in Engineering, 2012. https://doi.org/10.1155/2012/790142.
Chu, M. T., Shyu, J., Tzeng, G. H., & Khosla, R. (2007). Comparison among three analytical methods for knowledge communities’ group-decision analysis. Expert Systems with Applications, 33(4), 1011-1024. https://doi.org/10.1016/j.eswa.2006.08.026.
Opricovic, S., & Tzeng, G. H. (2004). Compromise solution by MCDM methods: A comparative analysis of VIKOR and TOPSIS. European Journal of Operational Research, 156(2), 445-455. https://doi.org/10.1016/S0377-2217(03)00020-1.
Raei, R., & Jahromi, M. (2012). Portfolio optimization using a hybrid of fuzzy ANP, VIKOR and TOPSIS. Management Science Letters, 2(7), 2473-2484. https://doi.org/10.5267/j.msl.2012.07.019.
Sahoo, L., Rana, A., Senapati, T., & Yager, R.R. (2022). Score function-based effective ranking of interval-valued Fermatean fuzzy sets and its applications to multi-criteria decision-making problem. In Real Life Applications of Multiple Criteria Decision-Making Techniques in Fuzzy Domain (pp. 435-451). Singapore: Springer Nature Singapore. https://doi.org/10.1007/978-981-19-4929-6_20.
Yager, R.R. (1988). On ordered weighted averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man, and Cybernetics, 18, 183-190. https://doi.org/10.1109/21.87068.
Grabisch, M., Marichal, J.L., Mesiar, R., & Pap, E. (2011). Aggregation functions: Means. Information Sciences, 181, 1-22. https://doi.org/10.1016/j.ins.2010.08.043.
Dombi, J. (1982). A general class of fuzzy operators, the DeMorgan class of fuzzy operators and fuzziness measures induced by fuzzy operators. Fuzzy Sets and Systems, 8(2), 149-163. https://doi.org/10.1016/0165-0114(82)90005-7.
Garg, H. (2016). A new generalized Pythagorean fuzzy information aggregation using Einstein operations and its application to decision making. International Journal of Intelligent Systems, 31, 886-920. https://doi.org/10.1002/int.21809.
Liu, P. (2014). Some Hamacher aggregation operators based on the interval-valued intuitionistic fuzzy numbers and their application to group decision making. IEEE Transactions on Fuzzy Systems, 22(1), 83-97. https://doi.org/10.1109/TFUZZ.2013.2248736.
Decky, M., Mesiar, R., & Stupnanová, A. (2018). Deviation-based aggregation functions. Fuzzy Sets and Systems, 332, 29-36. https://doi.org/10.1016/j.fss.2017.03.016.
Durante, F., & Ricci, R.G. (2018). Supermigrativity of aggregation functions. Fuzzy Sets and Systems, 335, 55-66. https://doi.org/10.1016/j.fss.2017.05.015.
Dong, Y. C., Zha, Q., Zhang, H., Kou, G., Fujita, H., Chiclana, F., & Herrera-Viedma, E. (2018). Consensus reaching in social network group decision making: Research paradigms and challenges. Knowledge-Based Systems, 162, 3-13. https://doi.org/10.1016/j.knosys.2018.06.036.
Sahoo, L. (2021). A new score function based Fermatean fuzzy transportation problem. Results in Control and Optimization, 4, 100040. https://doi.org/10.1016/j.rico.2021.100040.
Sahoo, L. (2021). Some score functions on Fermatean fuzzy sets and its application to bride selection based on TOPSIS method. International Journal of Fuzzy System Applications, 10(3), 18-29.
Shannon, C.E. (1948). A mathematical theory of communication. The Bell System Technical Journal, 27(3), 379-423. https://doi.org/10.1002/j.1538-7305.1948.tb01338.x.
Downloads
Published
Issue
Section
License
Copyright (c) 2024 Spectrum of Engineering and Management Sciences
This work is licensed under a Creative Commons Attribution 4.0 International License.
