一般关系下的变精度粗糙集模型

Variable precision rough set model based on general relations

通过分析一般关系下基本粗糙集模型的不足,定义了一般关系下的多数包含关系,借助引入的 误差参数α(0≤α<1/2),给出了一般关系下的变精度粗糙集模型．在该模型中,当α=0时,退化为一般关 系下的基本粗糙集模型(Z．Pawlak模型);当|Rs(x)|·α=k时(|Rs(x)|表示元素x后继邻域Rs(x)之基 数,k为非负整数),退化为常见的程度粗糙集模型．通过它与一般关系下基本粗糙集模型(Z．Pawlak模 型)的比较,可以看出,在引入误差参数α后,能够使尽可能多的有用信息被提取、挖掘．从而克服了基 本粗糙集模型中由于要求绝对精确的包含关系而使大量有用信息丢失的现象,并讨论了所给模型的一 些性质．最后,在所给模型基础上讨论了一种广义近似空间中集合的相对可辨性、近似依赖和属性约 简．

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≤α 〈 1/2） 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.