全覆盖粒计算模型的粒化、知识逼近及其算子性质研究

Granulation,knowledge approximation and properties of operators of the full covering GrC model

粒计算(GrC)作为处理不精确、不确定、不完备信息的重要工具,其基本思想是粒化、粒的运算和粒运算结果的融合.部分覆盖是粒计算理论框架中的一种重要模型,在电脑安全、搜索引擎和客户评估等领域具有潜在应用价值.全覆盖是部分覆盖的一种特例,已有的研究是从粗糙集理论的角度开展的,这是一种一般拓扑观念下的全覆盖.本文在pre-topology理论的框架下,从粒化、知识逼近和算子性质三个方面,首先介绍了邻域系统的相关定义,并在邻域系统基础之上提出了粒、全覆盖、全覆盖近似空间的概念;然后在全覆盖近似空间中利用已定义的粒重新诠释了一般拓扑中的内点和闭包算子,对全覆盖近似空间中的任意对象进行知识逼近,并用算例来说明;最后探究了全覆盖粒计算模型中这对逼近算子满足的基本性质,并证明了所提性质,为以后设计基于全覆盖粒计算模型的特征选择算法提供了理论基础.

Granular computing（GrC）is a powerful tool to handle imprecise,uncertain and incomplete information.Granulation of problems,computing of granules and integration of the results to granulated problems constitute its basic ideas.Partial covering is a global model in GrC,which has the potential application values in the research fields such as computer security,search engine and customer evaluation.As a special case of the partial covering（the global GrC model）,the full covering had been studied from the perspective of the rough sets,which is depicted under the framework of the general topology.This article developed the granulation,knowledge approximation and the properties of approximation operators of the full covering from the perspective of GrC under the framework of pre-topology theory.Firstly,the concepts of the neighborhood system,the granule and the full covering GrC model were presented,and the full covering approximation space was also defined,and then the neighborhood system of the full cover-ing GrC model was regarded as a basic granule.Secondly,followed by the concepts of interior and closure operators in the pre-topology space,the interior and closure operators of the full covering GrC model were defined by those basic granules,which could be used to approximate any object in the full covering approximation space,and some examples were also illustrated.Finally,the fundamental properties of those two operators were explored under the full covering approximation space,such as monotone and duality,and the proofs were also demonstrated for the proposed theorems and corollaries.All the work was the foundation for axiomatic systems of the operators in the full covering approximation space,and the feature selection algorithm based on the full covering GrC model is the next research in the future.