Hamacher Aggregation Operators for Pythagorean Fuzzy Set and its Application in Multi-Attribute Decision-Making Problem
DOI:
https://doi.org/10.31181/sor2120258Keywords:
Fuzzy set, Pythagorean fuzzy set, Hamacher t-Norms, Aggregation Operators, MADMAbstract
Pythagorean fuzzy set is a useful expansion of intuitionistic fuzzy set for dealing with ambiguities, which mostly occur in real-life problems. Hamacher t-norm also has important and compatible norms that incorporate a parameter that offers various options to decision-makers during the information fusion process, thereby enhancing their ability to model decision-making problems effectively compared to alternative methods. In this study, Hamacher operators are being used to introduce several Pythagorean fuzzy Hamacher interactive weighted averaging (PFHIWA), Pythagorean fuzzy Hamacher interactive ordered weighted averaging (PFHIOWA), Pythagorean fuzzy Hamacher interactive weighted geometric (PFHIWG), and Pythagorean fuzzy Hamacher interactive ordered weighted geometric (PFHIOWG) operators. The properties of these operators are examined in detail. The benefit of using progressive operators is that they deliver more understanding of the scenario to the decision-makers. Proposed operators are utilized to elaborate multi-attribute decision-making (MADM). By showing the sensitivity analysis, our proposed operator has high stability related to multi-attribute decision-making (MADM) under the Pythagorean fuzzy data set.
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References
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. (1999). Intuitionistic fuzzy sets (pp. 1-137). Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-1870-3_1
Yager, R. R. (2013). Pythagorean membership grades in multicriteria decision making. IEEE Transactions on fuzzy systems, 22(4), 958-965. https://doi.org/10.1109/TFUZZ.2013.2278989
Yager, R. R. (2013). Pythagorean fuzzy subsets. In 2013 joint IFSA world congress and NAFIPS annual meeting (IFSA/NAFIPS) (pp. 57-61). IEEE. https://doi.org/10.1109/IFSA-NAFIPS.2013.6608375
Peng, X., & Yang, Y. (2015). Some results for Pythagorean fuzzy sets. International Journal of Intelligent Systems, 30(11), 1133-1160. https://doi.org/10.1002/int.21738
Yager, R. R., & Abbasov, A. M. (2013). Pythagorean membership grades, complex numbers, and decision making. International journal of intelligent systems, 28(5), 436-452. https://doi.org/10.1002/int.21584
Zhang, X., & Xu, Z. (2014). Extension of TOPSIS to multiple criteria decision making with Pythagorean fuzzy sets. International journal of intelligent systems, 29(12), 1061-1078. https://doi.org/10.1002/int.21676
Lin, M., Chen, Y., & Chen, R. (2021). Bibliometric analysis on Pythagorean fuzzy sets during 2013–2020. International Journal of Intelligent Computing and Cybernetics, 14(2), 104-121. https://doi.org/10.1108/ijicc-06-2020-0067
Li, Z., & Lu, M. (2019). Some novel similarity and distance measures of pythagorean fuzzy sets and their applications. Journal of Intelligent & Fuzzy Systems, 37(2), 1781-1799. https://doi.org/10.3233/JIFS-179241
Olgun, M., & Ünver, M. (2023). Circular Pythagorean fuzzy sets and applications to multi-criteria decision making. Informatica, 34(4), 713-742. https://doi.org/10.15388/23-INFOR529
Akram, M., Zahid, K., & Kahraman, C. (2023). New optimization technique for group decision analysis with complex Pythagorean fuzzy sets. Journal of Intelligent & Fuzzy Systems, 44(3), 3621-3645. https://doi.org/10.3233/JIFS-220764
Aldring, J., & Ajay, D. (2023). Multicriteria group decision making based on projection measures on complex Pythagorean fuzzy sets. Granular Computing, 8, 137-155. https://doi.org/10.1007/s41066-022-00321-6
Wu, D. L., Zhu, Z., Ullah, K., Liu, L., Wu, X., & Zhang, X. (2023). Analysis of Hamming and Hausdorff 3D distance measures for complex pythagorean fuzzy sets and their applications in pattern recognition and medical diagnosis. Complex & Intelligent Systems, 9, 4147-4158. https://doi.org/10.1007/s40747-022-00939-8
Chaurasiya, R., & Jain, D. (2023). Hybrid MCDM method on pythagorean fuzzy set and its application. Decision Making: Applications in Management and Engineering, 6(1), 379-398. https://doi.org/10.31181/dmame0306102022c
Al-shami, T. M. (2023). (2, 1)-Fuzzy sets: properties, weighted aggregated operators and their applications to multi-criteria decision-making methods. Complex & Intelligent Systems, 9, 1687-1705. https://doi.org/10.1007/s40747-022-00878-4
Alhamzi, G., Javaid, S., Shuaib, U., Razaq, A., Garg, H., & Razzaque, A. (2023). Enhancing interval-valued Pythagorean fuzzy decision-making through Dombi-based aggregation operators. Symmetry, 15(3), 765. https://doi.org/10.3390/sym15030765
Ullah, K., Mahmood, T., Ali, Z., & Jan, N. (2020). On some distance measures of complex Pythagorean fuzzy sets and their applications in pattern recognition. Complex & Intelligent Systems, 6, 15-27. https://doi.org/10.1007/s40747-019-0103-6
Wang, W., & Liu, X. (2012). Intuitionistic fuzzy information aggregation using Einstein operations. IEEE Transactions on Fuzzy Systems, 20(5), 923-938. http://doi.org/10.1109/tfuzz.2012.2189405
Klir, G., & Yuan, B. (1995). Fuzzy sets and fuzzy logic (Vol. 4, pp. 1-12). New Jersey: Prentice hall.
Garg, H. (2016). Novel single-valued neutrosophic aggregated operators under Frank norm operation and its application to decision-making process. International Journal for Uncertainty Quantification, 6(4). http://doi.org/10.1615/Int.J.UncertaintyQuantification.2016018603
Sarfraz, M. (2024). Application of Interval-valued T-spherical Fuzzy Dombi Hamy Mean Operators in the antiviral mask selection against COVID-19. Journal of Decision Analytics and Intelligent Computing, 4(1), 67-98. https://doi.org/10.31181/jdaic10030042024s
Tešić, D., & Marinković, D. (2023). Application of fermatean fuzzy weight operators and MCDM model DIBR-DIBR II-NWBM-BM for efficiency-based selection of a complex combat system. Journal of Decision Analytics and Intelligent Computing, 3(1), 243-256. https://doi.org/10.31181/10002122023t
Garg, H. (2016). Some series of intuitionistic fuzzy interactive averaging aggregation operators. SpringerPlus, 5(1), 999. https://doi.org/10.1186/s40064-016-2591-9
Huang, J. Y. (2014). Intuitionistic fuzzy Hamacher aggregation operators and their application to multiple attribute decision making. Journal of Intelligent & Fuzzy Systems, 27(1), 505-513. http://doi.org/10.3233/IFS-131019
Tang, X., Fu, C., Xu, D. L., & Yang, S. (2017). Analysis of fuzzy Hamacher aggregation functions for uncertain multiple attribute decision making. Information Sciences, 387, 19-33. https://doi.org/10.1016/j.ins.2016.12.045
Deb, N., Sarkar, A., & Biswas, A. (2022). Linguistic q-rung orthopair fuzzy prioritized aggregation operators based on Hamacher t-norm and t-conorm and their applications to multicriteria group decision making. Archives of Control Sciences, 451-484. http://doi.org/10.24425/acs.2022.141720
Garg, H. (2019). Intuitionistic fuzzy hamacher aggregation operators with entropy weight and their applications to multi-criteria decision-making problems. Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 43, 597-613. http://doi.org/10.1007/s40998-018-0167-0
Dong, H., Ali, Z., Mahmood, T., & Liu, P. (2023). Power aggregation operators based on Hamacher t-norm and t-conorm for complex intuitionistic fuzzy information and their application in decision-making problems. Journal of Intelligent & Fuzzy Systems, (Preprint), 1-21. https://doi.org/10.3233/JIFS-230323
Liu, P. (2013). 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. http://doi.org/10.1109/TFUZZ.2013.2248736
Gál, L., Lovassy, R., Rudas, I. J., & Kóczy, L. T. (2014). Learning the optimal parameter of the Hamacher t-norm applied for fuzzy-rule-based model extraction. Neural Computing and Applications, 24, 133-142. http://dx.doi.org/10.1007/s00521-013-1499-3
Silambarasan, I., & Sriram, S. (2021). Some operations over intuitionistic fuzzy matrices based on Hamacher t-norm and t-conorm. TWMS Journal of Applied and Engineering Mathematics, 11(2), 541-551.
Zhu, J., & Li, Y. (2018). Hesitant Fuzzy Linguistic Aggregation Operators Based on the Hamacher t-norm and t-conorm. Symmetry, 10(6), 189. https://doi.org/10.3390/sym10060189
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