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Soft Computing

, Volume 23, Issue 24, pp 13085–13103 | Cite as

Multi-granulation hesitant fuzzy rough sets and corresponding applications

  • Haidong ZhangEmail author
  • Jianming Zhan
  • Yanping He
Methodologies and Application
  • 100 Downloads

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.

Keywords

Decision-making method Multi-granulation hesitant fuzzy rough set Rough measure Single-granulation hesitant fuzzy rough set 

Notes

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.

Compliance with ethical standards

Conflict of interest

The author declares that there is no conflict of interests.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceNorthwest MinZu UniversityLanZhouChina
  2. 2.Department of MathematicsHubei Minzu UniversityEnshiChina
  3. 3.School of Electrical EngineeringNorthwest MinZu UniversityLanZhouChina

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