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On novel hesitant fuzzy rough sets

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Abstract

This paper presents a novel framework for the study of hesitant fuzzy rough sets by integrating rough sets with hesitant fuzzy sets. Lower and upper approximations of hesitant fuzzy sets with respect to a hesitant fuzzy approximation space are first defined. Properties of hesitant fuzzy approximation operators are examined. Relationships between hesitant fuzzy approximation spaces and hesitant fuzzy topological spaces are then established. It is proved that the set of all lower approximation sets based on a hesitant fuzzy reflexive and transitive approximation space forms a hesitant fuzzy topology. And conversely, for a hesitant fuzzy rough topological space, there exists a hesitant fuzzy reflexive and transitive approximation space such that the topology in the hesitant fuzzy rough topological space is exactly the set of all lower approximation sets in the hesitant fuzzy reflexive and transitive approximation space. That is to say, there exists a one-to-one correspondence between the set of all hesitant fuzzy reflexive and transitive approximation spaces and the set of all hesitant fuzzy rough topological spaces.

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Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions.

Funding

This study is funded by the National Natural Science Foundation of China (Nos. 11461082, 11601474), 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 (No. 31920190055) 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, People’s Republic of China

    Haidong Zhang

  2. School of Mathematical Sciences, University of Electronic Science and Technology of China, Chengdu, 611731, Sichuan, People’s Republic of China

    Lan Shu

  3. School of Mathematics and Computer Science, Yunnan Minzu University, Kunming, 650500, Yunnan, People’s Republic of China

    Lianglin Xiong

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  1. Haidong Zhang
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  2. Lan Shu
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  3. Lianglin Xiong
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Correspondence to Haidong Zhang.

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Communicated by A. Di Nola.

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Zhang, H., Shu, L. & Xiong, L. On novel hesitant fuzzy rough sets. Soft Comput 23, 11357–11371 (2019). https://doi.org/10.1007/s00500-019-04037-9

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