This article first aims to critically review the existing literature on entropy measures for hesitant fuzzy elements (HFEs), and then introduces the concept of interval-transformed HFE (ITHFE) which bridges HFEs and interval-valued fuzzy sets (IVFSs). As discussed later, this bridge will also benefit researchers in terms of opening up more directions for future work, concentrating on HFE entropy measures. By taking the concept of ITHFE into account, we here exploit three features of an interval value including its lower and upper bounds, and the range of possible values to define a new class of entropy measures for HFEs. Then, we introduce the axiomatic framework of the new measures of entropy for HFEs, and two families of HFE entropy measures are also constructed. A comparison results shows that the proposed entropy measures for HFEs are more confident in distinguishing different HFEs rather than the most existing entropy measures. Finally, a multiple attribute decision making problem based on TOPSIS is applied to a case study of the health-care waste management.
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Bedregal B, Reiser R, Bustince H, Lopez-Molina C, Torra V. Aggregation functions for typical hesitant fuzzy elements and the action of automorphisms. Inform Sci. 2014;255:82–9.
Chen N, Xu ZS, Xia M. Correlation coefficients of hesitant fuzzy sets and their applications to clustering analysis. Appl Math Modell. 2013;37:2197–11.
De S K, Biswas R, Roy A R. Some operations on intuitionistic fuzzy sets. Fuzzy Set Syst. 2000;114: 477–84.
Farhadinia B. A novel method of ranking hesitant fuzzy values for multiple attribute decision-making problems. Int J Intell Syst 2014;29:184–205.
Farhadinia B. A series of score functions for hesitant fuzzy sets. Inform Sci. 2014;277:102–10.
Farhadinia B. Information measures for hesitant fuzzy sets and interval-valued hesitant fuzzy sets. Inform Sci. 2013;240:129–44.
Farhadinia B. Distance and similarity measures for higher order hesitant fuzzy sets. Knowl-Based Syst. 2014; 55:43–8.
Farhadinia B. Correlation for dual hesitant fuzzy sets and dual interval-valued hesitant fuzzy sets. Int J Intell Syst. 2014;29:184–205.
Farhadinia B. 2014. Multi criteria decision making method based on the higher order hesitant fuzzy soft set. Int Scholar Res Not. doi:10.1155/2014/873454.
Farhadinia B, Xu Z. 2017. Distance and aggregation-based methodologies for hesitant fuzzy decision making. Cogn Comput. doi:10.1007/s12559-016-9436-2.
Havrda M E, Charavat F. Quantification method of classification processes: concept of structural a-entropy. Kybernetica 1967;3:30–5.
Hu J, Zhang X, Chen X, Liu Y. Hesitant fuzzy information measures and their applications in multi-criteria decision making. Int J Syst Sci. 2016;47:62–76.
Meng FY, Chen XH. Correlation coefficients of hesitant fuzzy sets and their application based on fuzzy measures. Cogn Comput. 2015;7:445–63.
Meng FY, Wang C, Chen XH. Linguistic interval hesitant fuzzy sets and their application in decision making. Cogn Comput 2016;8:52–68.
Renyi A. On measures of entropy and information. Proc Fourth Berkeley Symp Math Stat Prob. 1961;1:547–61.
Rodriguez R M, Bedregal B, Bustince H, Dong Y C, Farhadinia B, Kahraman C, Martinez L, Torra V, Xu Y J, Xu Z S, Herrera F, position A. perspective analysis of hesitant fuzzy sets on information fusion in decision making. Towards high quality progress. Inf Fus. 2016;29:89–97.
Shang X G, Jiang W S. A note on fuzzy information measures. Pattern Recogn Lett. 1997;18:425–32.
Torra V. Hesitant fuzzy sets. Int J Intell Syst 2010;25:529–539.
Wei C, Yan F, Rodriguez RM. Entropy measures for hesitant fuzzy sets and their application in multi-criteria decision-making. J Intell Fuzzy Syst 2016;31:673–685.
Xia M, Xu Z S. Hesitant fuzzy information aggregation in decision making. Int J Approx Reas. 2011;52: 395–407.
Xu Z S, Xia M. Distance and similarity measures for hesitant fuzzy sets. Inform Sci. 2011;181:2128–38.
Xu ZS, Xia M. Hesitant fuzzy entropy and cross-entropy and their use in multiattribute decision-making. Int J Intell Syst 2012;27:799–822.
Zhao N, Xu Z, Liu F. Uncertainty measures for hesitant fuzzy information. Int J Intell Syst 2015;30: 818–36.
Zhao N, Xu Z, Liu F. Group decision making with dual hesitant fuzzy preference relations. Cogn Comput. 2016;8:1119– 43.
Zhu B, Xu Z, Xia M. Hesitant fuzzy geometric Bonferroni means. Inform Sci. 2012;205:72–85.
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The author declares that he has no conflict of interest.
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Farhadinia, B. A Multiple Criteria Decision Making Model with Entropy Weight in an Interval-Transformed Hesitant Fuzzy Environment. Cogn Comput 9, 513–525 (2017). https://doi.org/10.1007/s12559-017-9480-6
- Hesitant fuzzy set
- Interval-transformed hesitant fuzzy set
- Multiple attribute decision making
- Entropy measure