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Some distances, similarity and entropy measures for interval-valued neutrosophic sets and their relationship

  • Jun YeEmail author
  • Shigui Du
Original Article

Abstract

This paper proposes some new distance measures between interval-valued neutrosophic sets (IvNSs) and their similarity measures. Then, some entropy measures of IvNS based on the distances are proposed as the extension of the entropy measures of interval-valued intuitionistic fuzzy sets (IvIFSs). Also, we investigate the relationship between the presented entropy measures and the similarity measures for IvNSs. Finally, the comparison of the new entropy measures with existing entropy measures for IvNSs is given by the numerical and decision-making examples to demonstrate that the proposed new entropy measures for IvNSs are effective and reasonable and more intelligible in representing the degree of fuzziness of IvNSs than the existing ones.

Keywords

Interval-valued neutrosophic set Distance measure Similarity measure Entropy Decision making 

Notes

Acknowledgements

This paper was supported by the National Natural Science Foundation of China (No. 71471172).

Compliance with ethical standards

Conflict of interest

The authors declare no conflict of interest.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Electrical and Information EngineeringShaoxing UniversityShaoxingPeople’s Republic of China
  2. 2.Department of Civil EngineeringShaoxing UniversityShaoxingPeople’s Republic of China

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