知识库的相对约简与拓扑约简  

Relative reductions and topological reductions of knowledge bases

作　　者：吴国俊 徐罗山[1] WU Guo-jun;XU Luo-shan(Department of Mathematics,Yangzhou University,Yangzhou 225002,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《高校应用数学学报（A辑）》2022年第3期308-314,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(11671008,61472343);江苏省高校自然科学基金(15KJD110006)。

摘　　要：在基于二元关系的知识库中引入了相对约简与拓扑约简的概念,研究了它们的性质,证明了拓扑约简是特殊的相对约简.利用偏序集的极小元给出了有限知识库相对约简的存在性及其求法.引入了有限知识库的RM-区分矩阵和相应的RM-区分函数,由此获得了相对约简的另一求法.以具体例子对相对约简的求法进行了说明.In this paper,concepts of relative reductions and topological reductions of knowledge bases based on binary relations is introduced.Properties of them are studied.It is proved that topological reductions are special relative reductions.For finite knowledge bases,using the minimal elements of relevant posets,the existence of relative reduction and all the relative reductions is obtained.RMdiscernibility matrix and corresponding RM-discernibility functions are introduced,and thus another method to find relative reductions is given.A concrete example is presented to illustrate the methods to get relative reductions.

关 键 词：知识库 粗糙集 RM-区分矩阵 相对约简 拓扑约简 

分 类 号：O153.1[理学—数学] O189.1[理学—基础数学]