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Multi-granulation hesitant fuzzy rough sets and corresponding applications

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Abstract

This paper develops a single-granulation hesitant fuzzy rough set (SGHFRS) model from the perspective of granular computing. In the multi-granulation framework, we propose two types of multi-granulation rough sets model called the optimistic multi-granulation hesitant fuzzy rough sets (OMGHFRSs) and pessimistic multi-granulation hesitant fuzzy rough sets (PMGHFRSs). In the models, the multi-granulation hesitant fuzzy lower and upper approximations are defined based on multiple hesitant fuzzy tolerance relations. The relationships among the SGHFRSs, OMGHFRSs and PMGHFRSs are also established. In order to further measure the uncertainty of multi-granulation hesitant fuzzy rough sets (MGHFRSs), the concepts of rough measure and rough measure about the parameters \(\alpha \) and \(\beta \) are presented and some of their interesting properties are examined. Finally, we give a decision-making method based on the MGHFRSs, and the validity of this approach is illustrated by two practical applications. Compared with the existing results, we also expound its advantages.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions. This study was funded by the National Natural Science Foundation of China (Nos. 11461025; 11561023), the Natural Science Foundation of Gansu Province (No. 17JR5RA284), the Research Project Funds for Higher Education Institutions of Gansu Province (No. 2016B-005), the Fundamental Research Funds for the Central Universities of Northwest MinZu University (Nos. 31920170010, 31920180116) and the first-class discipline program of Northwest Minzu University.

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Authors and Affiliations

  1. School of Mathematics and Computer Science, Northwest MinZu University, LanZhou, 730030, Gansu, China

    Haidong Zhang

  2. Department of Mathematics, Hubei Minzu University, Enshi, 445000, Hubei, China

    Jianming Zhan

  3. School of Electrical Engineering, Northwest MinZu University, LanZhou, 730030, Gansu, China

    Yanping He

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  1. Haidong Zhang
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  2. Jianming Zhan
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  3. Yanping He
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Correspondence to Haidong Zhang.

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Zhang, H., Zhan, J. & He, Y. Multi-granulation hesitant fuzzy rough sets and corresponding applications. Soft Comput 23, 13085–13103 (2019). https://doi.org/10.1007/s00500-019-03853-3

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