Soft Computing

, Volume 23, Issue 10, pp 3237–3251 | Cite as

The comparative study of covering rough sets and multi-granulation rough sets

  • Qingzhao KongEmail author
  • Weihua Xu


The covering rough set (CRS) theory and the multi-granulation rough set (MGRS) theory are both the important generalizations of Pawlak rough set theory. Up to now, substantial contributions have been made to the development of CRS and MGRS. In this paper, in order to shed some light on the comparison and combination of CRS theory and MGRS theory, we investigate the relationship between CRS and MGRS based on different aspects. We firstly put forward an effective approach to describe the covering rough sets by means of the multi-granulation rough sets. Then, we, respectively, study the differences and relations of lower and upper operators, reduction, operation properties and algebraic properties between CRS and MGRS.


Rough sets Multi-granulation Covering Reduction Operation property Algebraic property 



This work is partially supported by the National Natural Science Foundation of China (Nos. 61105041, 61472463, 61402064, 61772002), the Macau Science and Technology Development Foundation (No. 081/2015/A3), the National Natural Science Foundation of CQ CSTC (No. cstc2015jcyjA40053), the Science and Technology Research Program of Chongqing Municipal Education Commission (Grant No. KJ1709221), the Natural Science Foundation of Fujian Province (Nos. 2017J01763, 2016J01022) and the Research Startup Foundation of Jimei University (NO. ZQ2017004) and the Foundation of Education Department of Fujian Province, China (No. JAT160369).

Compliance with ethical standards

Conflict of interest

Author Qingzhao Kong declares that he has no conflict of interest. Author Weihua Xu declares that he has no conflict of interest.

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 2018

Authors and Affiliations

  1. 1.School of ScienceJimei UniversityXiamenChina
  2. 2.School of ScienceChongqing University of TechnologyChongqingChina

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