Provide A New Solution to Multi-Criteria Decision Problems in A Hesitant Fuzzy Space Environment

Document Type : Original Article

Author

20.1001.1.27174409.1399.3.1.5.0/DOR

Abstract

Hesitant Fuzzy Sets (HFS), an extension of fuzzy sets, are useful in solving decision problems where decision makers are unable to choose between multiple values ​​when expressing their opinions. Multi-criteria decision making (MCDM) is a way to rank solutions and find the best one when making two or more criteria decisions. AHP, ELECTRE and TOPSIS are the most popular and accepted MCDM methods. In this paper, we first present a new distance for hesitant fuzzy sets and then use it to solve the MCDM problem with hesitant fuzzy data using the popular TOPSIS method. Finally, with the help of two practical examples, we examined our proposed method.

Keywords


[1] Akram, M., & Adeel, A. TOPSIS approach for MAGDM based on interval-valued hesitant fuzzy N-soft environment. International Journal of Fuzzy Systems. (2019) 21(3), 993-1009.
 
[2] Ding, Z., & Wu, Y. An improved interval-valued hesitant fuzzy multi-criteria group decision-making method and applications. Mathematical and Computational Applications (2016) 21(2), 2-34.
 
[3] Farhadinia, B., Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inf. Sci. (2013) 240, 129-144.
 
[4] Farhadinia, B., Distance and similarity measures for higher order hesitant fuzzy sets. Knowl.-Based Syst. (2014) 55, 43–48.
 
[5] Farhadinia, B., Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets. Int. J. Intell. Syst. (2014) 29, 184–205.
 
[6] Gitinavard, Hossein, S. Meysam Mousavi, and Behnam Vahdani. Soft computing-based new interval-valued hesitant fuzzy multi-criteria group assessment method with last aggregation to industrial decision problems. Soft Computing (2017) 21(12), 3247-3265.
 
[7] Garg, Harish, and Gagandeep Kaur. Algorithm for probabilistic dual hesitant fuzzy multi-criteria decision-making based on aggregation operators with new distance measures. Mathematics (2018) 6(12), 280-295.
 
[8] Joshi, D., & Kumar, S. Interval-valued intuitionistic hesitant fuzzy Choquet integral based TOPSIS method for multi-criteria group decision making. European Journal of Operational Research (2016) 248(1), 183-191.
 
[9] Liao, H.C., Xu, Z.C., Xia, M.M., Multiplicative consistency of hesitant fuzzy preference relation and its application in group decision making, Int. J. Inform. Technol. Decis. Mak. (2014) 13, 47-76.
 
[10] Liao, H.C., Xu, Z.C., Xia, M.M., Distance and similarity measures for hesitant fuzzy linguistic term sets and their application in multi-criteria decision making, Inform. Sci. (2014) 271, 125–142.
 
[11] Mei, Ye, Juanjuan Peng, and Junjie Yang. "Convex aggregation operators and their applications to multi-hesitant fuzzy multi-criteria decision-making.” Information (2018) 9(9), 207-217.
 
[12] Meng, F.Y., Chen, X.H., Zhang, Q. Multi-attribute decision analysis under a linguistic hesitant fuzzy environment, Inform. Sci. (2014) 267, 287–305.
 
[13] Peng, d.h., Gao, C.Y., Gao, Z.F., Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision making, Appl. Math. Model. (2013) 37, 5837–5850.
 
[14] Qian, G., Wang, H., Feng, X., Generalized hesitant fuzzy sets and their application in decision support system, Knowl.-Based Syst. (2013) 37, 357-365.
 
[15] Rodrguez, R.M., Martinez, L., Herrera, F., Hesitant fuzzy linguistic term sets for decision making, IEEE Trans. Fuzzy Syst. (2012) 20, 109–119.
 
[16] Rodrguez, R.M., Martinez, L., Herrera, F., A group decision making model dealing with comparative linguistic expressions based on hesitant fuzzy linguistic term sets, Inform. Sci. (2013) 241, 28-42.
 
[17] Rodriguez, R.M., Martinez, L., Torra, V., Xu, Z.S., Herrera, F.:Hesitant fuzzy sets: state of the art and future directions. Int. J. Intell. Syst. (2014) 29, 495–524.
 
[18] Torra, V., Hesitant fuzzy sets. Int. J. Intell. Syst. (2010), 25, 529–539.
 
[19] Torra, V., Narukawa, Y., On hesitant fuzzy sets and decision. In: The 18th IEEE International Conference on Fuzzy Systems, Jeju Island, Kerea (2009), 1378–1382.
 
[20] Wu, Z., Xu, J., Jiang, X., & Zhong, L. Two MAGDM models based on hesitant fuzzy linguistic term sets with possibility distributions: VIKOR and TOPSIS. Information Sciences. (2019) 473, 101-120.
 
[21] Xu, Z.S., Xia, M.M., On distance and correlation measures of hesitant fuzzy information. Int. J. Intell. Syst. (2011) 26, 410–425.
 
[22] Xu, Z.S., Xia, M.M., Distance and similarity measures for hesitant fuzzy sets. Inf. Sci. (2011) 181, 2128-2138.
 
[23] Zadeh, L.A. Fuzzy sets. Inf. Control (1965), 8, 338–353.
 
[24] Zhang, Zhiming. Hesitant fuzzy multi-criteria group decision making with unknown weight information. International Journal of Fuzzy Systems, (2017) 19(3), 615-636.
 
[25] Zhou, Huan, et al. Linguistic hesitant fuzzy multi-criteria decision-making method based on evidential reasoning. International Journal of Systems Science (2016) 47(2), 314-327.
 
[26] B. O'Neill, Semi-Riemannian geometry, Academic Press, 1986.
 
[27] J. Oprea, Differential geometry and its applications, Prentice Hall, second ed., 2004.