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Improvements on Correlation Coefficients of Hesitant Fuzzy Sets and Their Applications

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Abstract

Hesitant fuzzy set (HFS) can express the hesitancy and uncertainty according to human’s cognitions and knowledge. The decision making with HFSs can be regarded as a cognitive computation process. Decision making based on information measures is a hot topic, among which correlation coefficient is an important direction. Although many correlation coefficients of HFSs have been proposed in the previous papers, they suffer from different counter-intuitions to a certain extent. Therefore, we mainly focus on improving these counter-intuitions of the existing correlation coefficients of HFSs in this paper. We point out the counter-intuitions of the existing correlation coefficients of HFSs and analyze the reasons of them in the view of the rigorous mathematics and stochastic process rules. We improve these counter-intuitions and develop the correct versions. Moreover, we use two examples about medical diagnosis and cluster analysis to compare the improved correlation coefficients with the existing ones. The improved correlation coefficients can handle the examples well. Further, combining with the comparison analysis, the accuracy and discrimination property of the improved correlation coefficients are demonstrated in detail, which shows the advantages of them. The notion of the improved correlation coefficients can benefit other types of fuzzy sets too.

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Acknowledgments

The authors are very grateful to the three anonymous referees for their constructive comments and suggestions in improving this paper. This work is supported by the Excellent Youth Scholar of the National Defense Science and Technology Foundation of China, the Special Fund for the Taishan Scholar Project (Grant no. ts201712072), and the Natural Science Foundation of Shandong Province (Grant no. ZR2017BG014).

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Authors and Affiliations

  1. Naval Aviation University, Yantai, 264001, China

    Guidong Sun, Xin Guan, Xiao Yi & Zheng Zhou

  2. Institute of Systems Engineering, Academy of Military Sciences, Beijing, China

    Guidong Sun

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  1. Guidong Sun
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  2. Xin Guan
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  3. Xiao Yi
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  4. Zheng Zhou
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Correspondence to Guidong Sun or Xin Guan.

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Sun, G., Guan, X., Yi, X. et al. Improvements on Correlation Coefficients of Hesitant Fuzzy Sets and Their Applications. Cogn Comput 11, 529–544 (2019). https://doi.org/10.1007/s12559-019-9623-z

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  • DOI: https://doi.org/10.1007/s12559-019-9623-z

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