Comparative study of variable precision rough set model and graded rough set model

Abstract

The variable precision rough set model and graded rough set model are 2 important extended rough set models. This paper aims to make a comparative study of the 2 models. Rough set regions, primitive notions, are proposed first for the 2 models, which classify the universe more precisely. Then, both of their logical meanings related to quantitative indexes and their basic structure are investigated, and their precise descriptions are obtained as well. Furthermore, in the graded rough set model, macroscopic and microscopic algorithms are proposed and analyzed to calculate rough set regions; then, the conclusion is drawn that macroscopic and microscopic algorithms have advantages in time and space complexities, respectively, and a medical example is provided to illustrate the rough set regions and the 2 algorithms. In addition, 3 new properties of the 2 models are investigated, which are the results of extending the classical rough set model, i.e. the relationships between approximations and the basic set, the power actions of approximation operators, and the modifications of approximation operator actions on set operations. Finally, the classical rough set model is used to obtain many corresponding results, and moreover, the relationship and transformation between the 2 models is investigated. The study results of this paper have extended and enriched rough set theory from both operator-oriented and set-oriented points of view.