粗集理论中知识的粗糙性研究

粗集理论是处理知识不精确和不完善的一种归纳学习方法,其基本思想是在保持分类能力不变的前提下,通过知识约简,导出概念的分类规则。熵作为对不确定性的一种度量,可用于描述近似空间(U,R)中对象的分类情况。在文中,知识的粗糙性定义为近似空间中的粗糙熵,近似空间上基于等价关系的划分过程是其粗糙熵不断减小的过程。同时讨论了信息系统中的若干粗糙熵性质。

Research on Roughness of Knowledge in Rough Sets Theory

Rough set is one kind of inductive learning methods for knowledge imprecise and incomplete information system.Its basic theory is to derive classification rules of conception by knowledge reduction under the precondition of keeping the ability of classification.Entropy,as a measure of uncertainty,can be used to describe the classification on approximation space(U,R).In this paper,the roughness of knowledge is defined as rough entropy of approximation space,and the process of classification based on equivalence on approximation space is that one of rough-entropy-de-creasing of the approximation space.Some properties of rough entropy of information system are also discussed in this paper.