Abstract
As a generalization of fuzzy set, hesitant fuzzy set (HFS) permits the membership of an element to a set having a set of possible values. Distance is one of important tools in measuring the relationship between two HFSs. Based on the cardinality theory, some novel distances which take the cardinal numbers of HFSs into account have been introduced using the concept of “multi-sets.” The main advantage of the distance measures is that they can more objectively and universally measure the relationship between HFSs than the existing methods. Finally, the performance of the proposed distance measures is illustrated through two pattern recognition examples in port enterprise management and transportation infrastructure construction.
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Acknowledgments
The authors are thankful to the editor Dr. Aniello Castiglione and the anonymous reviewers for their insightful and constructive suggestions and helpful comments in improving this paper. The authors are thankful to Dr. Lihua Luo, Dr. Zhijun Gao, and Associate Prof. Jihong Chen, College of Transport and Communications, Shanghai Maritime University. They have provided useful guidance for this paper in its revised process.
Funding The work of the first author is partially supported in part by the National Natural Science Foundation of China (51508319, 51409157), the research program of the National Special Authorized Social Science Fund of China (07@ZH005) and the Nature and Science Fund from Zhejiang Province Ministry of Education (Y201327642). The second author is partially supported by National Natural Science Foundation of China (61374195). The third author is partially supported by the Humanities and Social Fund of Ministry of Education in China (12YJC910004), the National Natural Science Foundation of China (11201190,11571148) and “Qinglan Project” in Jiangsu Province.
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Communicated by V. Loia.
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Zhang, F., Chen, S., Li, J. et al. New distance measures on hesitant fuzzy sets based on the cardinality theory and their application in pattern recognition. Soft Comput 22, 1237–1245 (2018). https://doi.org/10.1007/s00500-016-2411-8
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DOI: https://doi.org/10.1007/s00500-016-2411-8