全覆盖粒计算模型的公理化及其知识约简*

部分覆盖是粒计算理论框架下的第二种粒计算模型,全覆盖粒计算是部分覆盖的一种特例。为实现全覆盖粒计算模型中粒的计算,探究了全覆盖粒计算模型中所提逼近算子的公理化系统,提出了粒的中心、全覆盖粒度熵及全覆盖粒族熵的概念,探讨了基本粒和全覆盖粒重要性度量的方法,并提出了相应的约简与核的判定定理。基于所提定义、定理设计了全覆盖粒的约简算法和全覆盖粒族的约简算法,并从理论上分析了两个算法的复杂度。最后以客户根据专家意见购房为例,验证了所提算法的有效性。

Axiomatization and knowledge reduction of the full covering GrC model

Full covering is a special case of the partial covering which is the second GrC model under the framework of the GrC theory. In order to realize the computing of granule in full covering GrC model, firstly, this paper explored the axiomatic systems for the interior and closure operators of the full covering GrC model, and defined the center of the granule which was used to define the granularity entropy of a full covering and a family of full coverings. Secondly, this paper presented the significance measurement of basic granule and full covering granule based on the granularity entropy, and also discussed the theorems for the reduction of the information system which was modeled as a full covering and a family of full coverings; then designed and analyzed the according knowledge reduction algorithms based on the full covering GrC model and their complexity, namely, the reduction of granules in the full covering (RGFC) and the reduction of a covering in a family of full coverings (RCFFC). Finally, the example of experts assessing house for customers showed that the proposed algorithms were effective.