粗糙集属性约简的图论方法

Graph Method of Rough Set Attribute Reduction

通过研究粗糙集与图论的关系,提出了以集合为权的加权多重完全多部图的概念,定义了加权多重完全多部图的邻接矩阵,得到了加权完全多部图与决策表的映射关系;给出了粗糙集决策表信息系统的图论形式和决策表信息系统属性约简的图论方法,并根据图论理论对算法进行了优化;得到了在决策表信息系统中,属性的集合不可以约简的充分必要条件;并进一步提出了基于属性置信度的计算方法和多决策属性的处理方法。编程实验结果证明该方法能有效地降低时间和空间复杂度。

Through study of rough set and graph theory,this paper put forward the concept of weighted complete multipartite multigraph which used set as weitht,defined the adjacency matrix of weighted complete multipartite multigraph,obtained the mapping relations between weighted complete multipartite multigraph and decision table,gave a gragh model of the rough set decision table information system and a method of attribute reduction in decision table Information systems based on gragh theory,optimized the algorithm,obtained the sufficient and necessary conditions of attribute reduction in decision table information system,further proposed calculation method which is based on attribute reliability and the processing method of multiple decision attributes.Programming experimental results show that this me-thod can effectively reduce the complexity of time and space.