Soft Computing

, Volume 22, Issue 4, pp 1237–1245 | Cite as

New distance measures on hesitant fuzzy sets based on the cardinality theory and their application in pattern recognition

  • Fangwei Zhang
  • Shuyan Chen
  • Jianbo Li
  • Weiwei Huang
Methodologies and Application

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.

Keywords

Hesitant fuzzy sets Hesitant fuzzy elements Cardinality theory Distance measure Weighted average operator Pattern recognition 

Notes

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.

Compliance with ethical standards

Conflict of interest

All the four authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants performed by any of the authors.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Fangwei Zhang
    • 1
  • Shuyan Chen
    • 2
  • Jianbo Li
    • 3
  • Weiwei Huang
    • 4
  1. 1.College of Transport and CommunicationsShanghai Maritime UniversityShanghaiChina
  2. 2.School of TransportationSoutheast UniversityNanjingChina
  3. 3.School of Mathematics and StatisticsJiangsu Normal UniversityXuzhouChina
  4. 4.College of Teacher EducationZhaoqing UniverstyZhaoqingChina

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