Abstract
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.
Highlights
Rough set theory proposed by Pawlak [1,2,3] is an extension of the classical set theory and can be regarded as a soft computing tool to handle imprecision, vagueness, and uncertainty in data analysis
The main objective of this paper is to extend Pawlak’s single-granulation rough set model and Qian’s multigranulation rough set model (MGRS) to two new types of multiple granulation rough set model, where the set approximations are defined by using multiple equivalence relations on the universe
The original rough set model cannot be used to deal with the information systems with complicated context
Summary
Rough set theory proposed by Pawlak [1,2,3] is an extension of the classical set theory and can be regarded as a soft computing tool to handle imprecision, vagueness, and uncertainty in data analysis. To more widely apply the rough set theory in practical applications, Qian et al [60] extended Pawlak’s single-granulation rough set model to a multi granulation rough set model (MGRS), where the set approximations are defined by multiple equivalence relations on the universe. The main objective of this paper is to extend Pawlak’s single-granulation rough set model and Qian’s multigranulation rough set model (MGRS) to two new types of multiple granulation rough set model, where the set approximations are defined by using multiple equivalence relations on the universe.
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