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Correlation Coefficients of Hesitant Fuzzy Sets and Their Application Based on Fuzzy Measures

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Abstract

In this paper, several new correlation coefficients of hesitant fuzzy sets are defined, not taking into account the length of hesitant fuzzy elements and the arrangement of their possible values. To address the situations where the elements in a set are correlative, several Shapley weighted correlation coefficients are presented. It is worth noting that the Shapley weighted correlation coefficient can be seen as an extension of the correlation coefficient based on additive measures. When the weight information of attributes is partly known, models for the optimal fuzzy measure on an attribute set are constructed. After that, an approach to clustering analysis and decision making under hesitant fuzzy environment with incomplete weight information and interactive conditions is developed. Meanwhile, corresponding examples are provided to verify the practicality and feasibility of the new approaches.

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Acknowledgments

The authors first gratefully thank the Editor-in-Chief Professor Amir Hussain and three anonymous referees for their valuable and constructive comments which have much improved the paper. This work was supported by the State Key Program of National Natural Science of China (No. 71431006), the Funds for Creative Research Groups of China (No. 71221061), the Projects of Major International Cooperation NSFC (No. 71210003), the National Natural Science Foundation of China (Nos. 71201089, 71201110, 71271217 and 71271029), the National Science Foundation for Post-doctoral Scientists of China (2014M560655), and the Program for New Century Excellent Talents in University of China (No. NCET-12-0541).

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  1. Business School, Central South University, Changsha, 410083, China

    Fanyong Meng & Xiaohong Chen

  2. School of Management, Qingdao Technological University, Qingdao, 266520, China

    Fanyong Meng

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Correspondence to Fanyong Meng.

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Meng, F., Chen, X. Correlation Coefficients of Hesitant Fuzzy Sets and Their Application Based on Fuzzy Measures. Cogn Comput 7, 445–463 (2015). https://doi.org/10.1007/s12559-014-9313-9

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