Synthetic Correlation Coefficient Between Hesitant Fuzzy Sets with Applications
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Hesitant fuzzy sets (HFSs) are becoming more and more popular in the fuzzy domain and attract great attentions. As an important research orientation of HFSs, the correlation coefficient measurement between HFSs is a hot topic. Although some correlation coefficients have been proposed in the previous paper, we have to claim that the existing correlation coefficients are more or less counter-intuitive under some circumstances. On one hand, they consider only one feature of the HFSs and ignore some other important features contributing to the correlation coefficient. On the other hand, they require the lengths of the memberships of each hesitant fuzzy element (HFE) in the HFSs to be same. Therefore, we point out the shortcomings of the existing correlation coefficients in this paper and propose the synthetic correlation coefficient between the HFSs considering the integrality, the distribution and the length of the membership. Firstly, we define such basic concepts as the mean, the variance and the length rate of the HFEs and HFSs to represent the integrality, the distribution and the length. Secondly, based on these basic concepts, we define the mean, the variance and the length correlation coefficients. Furthermore, we construct the synthetic correlation coefficient by weighting these three basic correlation coefficients. In addition, to cope with the practical issues, we extend the synthetic correlation coefficient to the weighted form. Finally, we apply the synthetic correlation coefficient to such information fusion problems as data association, pattern recognition, medical diagnosis, decision making and cluster analysis. Along with some practical examples, the superiority of the proposed synthetic correlation coefficient in validation, discrimination, accuracy, intuitiveness and efficiency is illustrated in detail.
KeywordsSynthetic Correlation coefficient Hesitant fuzzy sets (HFSs) HFSs features Information fusion
The authors are very grateful to the anonymous reviewers and the editor for their valuable 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), the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91538201), the National Natural Science Foundation of China (Grant Nos. 61671463, 61571454), and the Natural Science Foundation of Shandong Province (Grant No. ZR2017BG014).
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