Variable precision rough set model based on general relations
Degang Chen · Journal of Lanzhou University · 2005
To make up for the drawbacks of general relations of rough set model, a majority inclusion relation is defined. A variable precision rough set model based on general relations is given by means of the error parameter α(0≤α1/2) proposed in this paper. In our model, if α=0, then it is the basic rough set model based on general relations, which was first introduced by Z. Pawlak. Meanwhile, if |Rs(x)|·α= k (where |Rs(x)| stands for the cardinal-number of successor neighbor of element x and k a non-negative integer), it is the graded rough set model. It follows that the model presented in this paper is an extension of the classical basic rough set based on general relations and the graded rough set model. After introducing the error parameter α(0≤α 1/2), more useful information and data are collected and mined. Thus, the drawbacks, which cause the loss of more useful information for demanding the inclusion of absolute precision in the classical basic rough set model, are overcome and some properties of the model presented are discussed. Finally, the relative discernibility, approximation dependency and attribute reduction of the rough set in a generalized approximation space are discussed.