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Symmetry 2016, 8(12), 153; doi:10.3390/sym8120153

A Modification on the Hesitant Fuzzy Set Lexicographical Ranking Method

1
School of Mathematics and Physics, Anhui University of Technology, Ma’anshan 243002, Anhui, China
2
School of Government, Nanjing University, Nanjing 210023, Jiangsu, China
3
Researching Center of Social Security, Wuhan University, Wuhan 430072, Hubei, China
*
Author to whom correspondence should be addressed.
Academic Editor: Angel Garrido
Received: 10 November 2016 / Revised: 27 November 2016 / Accepted: 5 December 2016 / Published: 14 December 2016
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Abstract

Recently, a novel hesitant fuzzy set (HFS) ranking technique based on the idea of lexicographical ordering is proposed and an example is presented to demonstrate that the proposed ranking method is invariant with multiple occurrences of any element of a hesitant fuzzy element (HFE). In this paper, we show by examples that the HFS lexicographical ordering method is sometimes invalid, and a modified ranking method is presented. In comparison with the HFS lexicographical ordering method, the modified ranking method is more reasonable in more general cases. View Full-Text
Keywords: hesitant fuzzy set; lexicographical ordering; ranking method hesitant fuzzy set; lexicographical ordering; ranking method
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Liu, X.; Wang, Z.; Zhang, S. A Modification on the Hesitant Fuzzy Set Lexicographical Ranking Method. Symmetry 2016, 8, 153.

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