Abstract
The Fermatean fuzzy set (FFS) presented is a stronger and usefulness uncertain information representation model for portraying the potential nondeterminacy of data, and the combined compromise solution (COCOSO) method can comprehensively attain a more robust decision outcome through taking into consideration three information fusion strategies. By taking the merits of FFS and COCOSO method, we advance a newly multiple expert multiple criteria decision-making (MEMCDM) technique in light of COCOSO and coefficient of variation methods with Fermatean fuzzy information. Firstly, we review several fundamental conceptions of FFS, including the score function and aggregation operators. Secondly, we put forward an innovative MEMCDM approach through synthesizing the COCOSO method and coefficient of variation method under Fermatean fuzzy environment, where the criterion weight is ascertained through improved Fermatean fuzzy coefficient of variation (COV) method from the visual angle of decision information objectivity. Afterward, a case concerning the assessment of investment enterprises is employed to further confirm the practicability and feasibility of the propounded MEMCDM method, as well as the contrast analysis is conducted to sticking out the flexibility and efficiency of the proffered MEMCDM technique.
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References
Tzeng, G.H., Huang, J.J.: Multiple Attribute Decision Making: Methods and Applications, p. 1981. Springer-Verlag, New York (2011)
Liu, Y., Qin, Y., Liu, F., Rong, Y.: GIBWM-MABAC approach for MAGDM under multi-granularity intuitionistic 2-tuple linguistic information model. J. Ambient Intell. Humaniz. Comput., 1–17 (2021). https://doi.org/10.1007/s12652-021-03476-3
Liu, Y., Wei, G., Liu, H., Xu, L.: Group decision making for internet public opinion emergency based upon linguistic intuitionistic fuzzy information. Int. J. Mach. Learn. Cybern. 1–16. https://doi.org/10.1007/s13042-020-01262-9
Rong, Y., Liu, Y., Pei, Z.: Complex q-rung orthopair fuzzy 2-tuple linguistic Maclaurin symmetric mean operators and its application to emergency program selection. Int. J. Intell. Syst. 35(11), 1749–1790 (2020)
Rong Y, Liu Y, Pei Z.: A novel multiple attribute decision-making approach for evaluation of emergency management schemes under picture fuzzy environment.Int. J. Mach. Learn. Cybern. (2021). https://doi.org/10.1007/s13042-021-01280-1
Mardani, A., Saraji, M.K., Mishra, A.R., Rani, P.: A novel extended approach under hesitant fuzzy sets to design a framework for assessing the key challenges of digital health interventions adoption during the COVID-19 outbreak. Appl. Soft Comput. 96, 106613 (2020)
Saraji, M.K., Mardani, A., Köppen, M., Mishra, A.R., Rani, P.:An extended hesitant fuzzy set using SWARA-MULTIMOORA approach to adapt online education for the control of the pandemic spread of COVID-19 in higher education institutions. Artif. Intell. Rev. 1–26 (2021).https://doi.org/10.1007/s10462-021-10029-9
Zadeh, L.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)
Atanssov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20(1), 87–96 (1986)
Ejegwa, P.A.: Novel correlation coefficient for intuitionistic fuzzy sets and its application to multi-criteria decision-making problems. Int. J. Fuzzy Syst. Appl. 10(2), 39–58 (2021)
Yager, R.R.: Pythagorean membership grades in multicriteria decision making. IEEE Trans. Fuzzy Syst. 22(4), 958–965 (2013)
Yager, R.R.: Pythagorean fuzzy subsets. In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), pp. 57–61. IEEE, June 2013
Ejegwa, P.A., Jana C., Some new weighted correlation coefficients between Pythagorean fuzzy sets and their applications, In: Garg, H. (eds.) Pythagorean Fuzzy Sets, pp. 39–64, Springer (2021). https://doi.org/10.1007/978-981-16-1989-2-2
Ejegwa, P.A., Feng, Y., Zhang, W.: Pattern recognition based on an improved Szmidt and Kacprzyk’s correlation coefficient in Pythagorean fuzzy environment, In: Min, H., Sitian, Q., Nian, Z. (eds.) Advances in Neural Networks—17th International Symposium on Neural Networks (ISNN 2020), Lecture Notes in Computer Science (LNCS) 12557, pp. 190–206. Springer (2020). https://doi.org/10.1007/978-3-030-64221-1-17
Senapati, T., Yager, R.R.: Fermatean fuzzy sets. J. Ambient Intell. Humaniz. Comput. 11(2), 663–674 (2020)
Senapati, T., Yager, R.R.: Fermatean fuzzy weighted averaging/geometric operators and its application in multi-criteria decision-making methods. Eng. Appl. Artif. Intell. 85, 112–121 (2019)
Senapati, T., Yager, R.R.: Some new operations over Fermatean fuzzy numbers and application of Fermatean fuzzy WPM in multiple criteria decision making. Informatica 30(2), 391–412 (2019)
Garg, H., Shahzadi, G., Akram, M.: Decision-making analysis based on Fermatean fuzzy Yager aggregation operators with application in COVID-19 testing facility. Math. Prob. Eng. 2020 (2020). https://doi.org/10.1155/2020/7279027
Shahzadi, G., Muhiuddin, G., Arif Butt, M., Ashraf, A.: Hamacher interactive hybrid weighted averaging operators under Fermatean fuzzy numbers. J. Math. 2021 (2021). https://doi.org/10.1155/2021/5556017
Shahzadi, G., Zafar, F., Alghamdi, M.A.: Multiple-attribute decision-making using Fermatean fuzzy Hamacher interactive geometric operators. Math. Prob. Eng. 2021 (2021). https://doi.org/10.1155/2021/5150933
Shit, C., Ghorai, G.: Multiple attribute decision-making based on different types of Dombi aggregation operators under Fermatean fuzzy information. Soft. Comput. 25(22), 13869–13880 (2021)
Ejegwa, P.A., Nwankwo, K.N., Ahmad, M., Ghazal, T.M., Khan, M.A.: Composite relation under Fermatean fuzzy context and its application in disease diagnosis. Informatica 32(10), 87–101 (2021)
Liu, D., Liu, Y., Chen, X.: Fermatean fuzzy linguistic set and its application in multicriteria decision making. Int. J. Intell. Syst. 34(5), 878–894 (2019)
Liu, D., Liu, Y., Wang, L.: Distance measure for Fermatean fuzzy linguistic term sets based on linguistic scale function: An illustration of the TODIM and TOPSIS methods. Int. J. Intell. Syst. 34(11), 2807–2834 (2019)
Jeevaraj, S.: Ordering of interval-valued Fermatean fuzzy sets and its applications. Expert Syst. Appl. 185 (2021). https://doi.org/10.1016/j.eswa.2021.115613
Keshavarz-Ghorabaee, M., Amiri, M., Hashemi-Tabatabaei, M., Zavadskas, E.K., Kaklauskas, A.: A new decision-making approach based on Fermatean fuzzy sets and WASPAS for green construction supplier evaluation. Mathematics 8, 2202 (2020). https://doi.org/10.3390/math8122202
Mishra, A.R., Rani, P.: Multi-criteria healthcare waste disposal location selection based on Fermatean fuzzy WASPAS method. Complex Intell. Syst. 7(5), 2469–2484 (2021)
Gul, M., Lo, H.-W., Yucesan, M.: Fermatean fuzzy TOPSIS-based approach for occupational risk assessment in manufacturing. Complex Intell. Syst. 7(5), 2635–2653 (2021)
Aydemir, S.B., Gunduz, S.Y.: Fermatean fuzzy TOPSIS method with Dombi aggregation operators and its application in multi-criteria decision making. J. Intell. Fuzzy Syst. 39(1), 851–869 (2020)
Gul, S.: Fermatean fuzzy set extensions of SAW, ARAS, and VIKOR with applications in COVID-19 testing laboratory selection problem. Expert Syst. 38(8), e12769 (2021). https://doi.org/10.1111/exsy.12769
Mishra, A.R., Rani, P., Pandey, K.: Fermatean fuzzy CRITIC-EDAS approach for the selection of sustainable third-party reverse logistics providers using improved generalized score function. J. Ambient Intell. Humaniz. Comput. (2021). https://doi.org/10.1007/s12652-021-02902-w
Rani, P., Mishra, A.R.: Fermatean fuzzy Einstein aggregation operators-based MULTIMOORA method for electric vehicle charging station selection. Expert Syst. Appl. 182, 115267 (2021). https://doi.org/10.1016/j.eswa.2021.115267
Kamali Saraji, M., Streimikiene, D., Kyriakopoulos, G.L.: Fermatean fuzzy CRITIC-COPRAS method for evaluating the challenges to industry 4.0 adoption for a sustainable digital transformation. Sustainability 13(17), 9577 (2021)
Deng, Z., Wang, J.: Evidential Fermatean fuzzy multicriteria decision-making based on Fermatean fuzzy entropy. Int. J. Intell. Syst. 36(10), 5866–5886 (2021)
Yazdani, M., Zarate, P., Zavadskas, E.K., Turskis, Z.: A combined compromise solution (CoCoSo) method for multi-criteria decision-making problems. Manag. Decis. 57(9), 2501–2519 (2019)
Yazdani, M., Wen, Z., Liao, H., Banaitis, A., Turskis, Z.: A grey combined compromise solution (COCOSO-G) method for supplier selection in construction management. J. Civ. Eng. Manag. 25(8), 858–874 (2019)
Peng, X., Zhang, X., Luo, Z.: Pythagorean fuzzy MCDM method based on CoCoSo and CRITIC with score function for 5G industry evaluation. Artif. Intell. Rev. 53(5), 3813–3847 (2020)
Ecer, F., Pamucar, D.: Sustainable supplier selection: A novel integrated fuzzy best worst method (F-BWM) and fuzzy CoCoSo with Bonferroni (CoCoSo’B) multi-criteria model. J. Cleaner Prod. 266, 121981 (2020). https://doi.org/10.1016/j.jclepro.2020.121981
Rani, P., Ali, J., Krishankumar, R., Mishra, A.R., Cavallaro, F., Ravichandran, K.S.: An integrated single-valued neutrosophic combined compromise solution methodology for renewable energy resource selection problem. Energies 14(15), 4594 (2021). https://doi.org/10.3390/en14154594
Yazdani, M., Chatterjee, P., Pamucar, D., Chakraborty, S.: Development of an integrated decision making model for location selection of logistics centers in the Spanish autonomous communities. Expert Syst. Appl. 148, 113208 (2020). https://doi.org/10.1016/j.eswa.2020.113208
Rani, P., Mishra, A.R., Saha, A., Hezam, I.M., Pamucar, D.: Fermatean fuzzy Heronian mean operators and MEREC-based additive ratio assessment method: An application to food waste treatment technology selection. Int. J. Intell. Syst. 1–36 (2021). https://doi.org/10.1002/int.22787
Mishra, A.R., Rani, P., Pandey, K., et al.: Novel multi-criteria intuitionistic fuzzy SWARA-COPRAS approach for sustainability evaluation of the bioenergy production process. Sustainability 12(10), 4155 (2020)
Roubens, M.: Fuzzy sets and decision analysis. Fuzzy Sets Syst. 90, 199–206 (1997)
Liu, B.S., Zhou, Q., Ding, R.X., Palomares, I., Herrera, F.: Large-scale group decision making model based on social network analysis: Trust relationship-based conflict detection and elimination. Eur. J. Oper. Res. 275(2), 737–754 (2019). https://doi.org/10.1016/j.ejor.2018.11.075
Zhang, Y., Chen, X., Gao, L., Dong, Y., Pedryczc, W.: Consensus reaching with trust evolution in social network group decision making. Expert Syst. Appl. (2021). https://doi.org/10.1016/j.eswa.2021.116022
Wang, X., Triantaphyllou, E.: Ranking irregularities when evaluating alternatives by using some ELECTRE methods. Omega 36(1), 45–63 (2008)
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The research was funded by the General Program of National Natural Science Foundation of China (No: 12071280).
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Rong, Y., Yu, L., Liu, Y. (2023). Fermatean Fuzzy Combined Compromise Solution Multiple Expert Multiple Criteria Decision-Making Approach. In: Sahoo, L., Senapati, T., Yager, R.R. (eds) Real Life Applications of Multiple Criteria Decision Making Techniques in Fuzzy Domain. Studies in Fuzziness and Soft Computing, vol 420. Springer, Singapore. https://doi.org/10.1007/978-981-19-4929-6_4
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