连通图上的粒结构  

Granular Structureon Connected Graphs

作　　者：韩光辉[1] 曾诚[2] 

机构地区：[1]武汉商学院信息工程系,湖北武汉430056 [2]湖北大学计算机与信息工程学院,湖北武汉430062

出　　处：《电脑与信息技术》2015年第6期19-21,55,共4页Computer and Information Technology

基　　金：湖北省自然科学基金(项目编号:2014CFB535);湖北省教育厅科学技术研究重点项目(项目编号:D20131005)

摘　　要：现实世界的许多问题可以抽象成图,所以研究图上的粒计算模型是很有必要的。采用基于集合划分的粒化方法和图论方法研究了连通图上的粒结构。首先讨论集合的划分及其加细,证明了划分的加细是偏序,建立了划分的粗化与划分的划分之间的联系。然后,对连通图的点集进行划分同时保持划分块之间的关联,则粒化相当于图的收缩,粒结构既是基于划分的偏序结构同时又是一种图结构。最后给出了粒层的关联矩阵表示和构造粒层的矩阵变换方法。Because many real-world problems can be abstracted into graphs, it is necessary to study model of granular computing on graphs. Based on the partition model, the granular structure on connected graphs is studied by using graph-theoretic method. First, for a preliminary, partition of a set and its refinement are discussed, a conclusion that refinement is a partial ordering is proved, some relationships between coarsening of partition and partition of partition are presented. Then, the granulation, by dividing vertex set of a connected graph into disjoint subsets and to be incident with edges of the graph, is similar to contraction of the graph, so the granular structure is not only partial ordering structure and also graph structure. Finally, the representation of each level of granulations by an incidence matrix and construction method of granulation hierarchy by using matrices transformation are shown.

关 键 词：粒计算 连通图 粒结构 划分 偏序 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]