Table of Contents
ISRN Applied Mathematics
Volume 2013, Article ID 791356, 16 pages
Research Article

Two New Types of Multiple Granulation Rough Set

1School of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054, China
2School of Management, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China
3School of Science, Xi’an Jiaotong University, Xi’an, Shaanxi 710019, China

Received 6 November 2012; Accepted 22 November 2012

Academic Editors: A. Bellouquid and T. Y. Kam

Copyright © 2013 Weihua Xu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In the paper proposed two new types of the multiple granulation rough set models, where a target concept is approximated from two different kinds of views by using the equivalence classes induced by multiple granulations. A number of important properties of the two types of MGRS are investigated. From the properties, it can be found that Pawlak’s and Qian’s rough set models are special instances of those of our MGRS. Moreover, several important measures are presented in two types of MGRS, such as rough measure and quality of approximation. Furthermore, the relationship and difference are discussed carefully among Pawlak’s rough set, Qian’s MGRS, and two new types of MGRS. In order to illustrate our multiple granulations rough set model, some examples are considered, which are helpful for applying this theory in practical issues. One can get that the paper is meaningful both in the theory and in application for the issue of knowledge reduction in complex information systems.