Abstract
In this study, we propose new distance measures for dual hesitant fuzzy sets (DHFSs) in terms of the mean, standard deviation of dual hesitant fuzzy elements (DHFEs), respectively, which overcome some drawbacks of the existing distance measures. Meanwhile, we extend DHFS to its higher order type and refer to it as the higher order dual hesitant fuzzy set (HODHFS). HODHFS is the actual extension of DHFS that enables us to define the membership and non-membership of a given element in terms of several possible generalized type of fuzzy sets (G-Type FSs). The rationale behind HODHFS can be seen in the case that the decision makers are not satisfied by providing exact values for the membership degrees and the non-membership degrees. To indicate HODHFSs have a good performance in decision making, we introduce several distance measures for HODHFSs based on our proposed new distance for dual hesitant fuzzy sets. Finally, we practice our proposed measures for HODHFSs in multi-attribute decision making illustrating their applicability and availability.
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Acknowledgements
The authors thank the editor and the referees for their valuable comments and suggestions. This research has been supported by the National Natural Science Foundation of China (11461043, 11361042) and supported partly by the Provincial Natural Science Foundation of Jiangxi, China (20142BAB201005, 20161BAB201009).
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Communicated by Rosana Sueli da Motta Jafelice.
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Chen, J., Huang, X. & Tang, J. Distance measures for higher order dual hesitant fuzzy sets. Comp. Appl. Math. 37, 1784–1806 (2018). https://doi.org/10.1007/s40314-017-0423-3
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DOI: https://doi.org/10.1007/s40314-017-0423-3