伽罗瓦连接在构造拟阵中的应用

Application of Galois connection in constructing matroids

如何将处理数据的有效方法应用到构建拟阵结构的研究中,使拟阵论的成果以更多方式应用到数据处理的研究中,是目前拟阵论研究需要解决的问题之一。为此,将处理数据的有效工具形式概念分析理论中的基本运算—伽罗瓦连接作为桥梁,给出伽罗瓦背景的定义,得到由1个拟阵建立伽罗瓦背景的方法。进而得到,在拟阵同构和伽罗瓦同构意义下:在拟阵族与伽罗瓦背景族之间存在着一一映射;在拟阵族和伽罗瓦连接族之间存在着一一对应,从而发现拟阵与伽罗瓦连接之间的关系。用此关系得到伽罗瓦连接构造拟阵的2种方法。通过与已知的一些相关方法比较,发现该方法的优势。此外,用生物实例说明这2种方法在生物信息数据处理中的作用。

How to apply the effective methods of processing data to the research of constructing the matroid structure,so that the results of matroid theory can be applied to the research of data processing in more ways,is one of the problems that need to be solved in the research of matroid theory.Therefore,Galois connection,which is the basic operation in the theory of formal concept analysis that is an effective way in dealing data,is used as a bridge to give the definition of Galois context and obtain a method to establish a Galois context with a matroid.Furthermore,it finds that,under the matroid isomorphism and Galois isomorphism,there is a bijection between the family of matroids and the family of Galois contexts,and a bijection between the family of matroids and the family of Galois connections.Moreover,the relationship between matroids and Galois connections is found.This relationship is used to obtain the two methods for constructing matroids with Galois connections.Comparison with some relative known methods shows the advantages of the two methods.In addition,the biology examples show the role of the two methods in dealing the data of biological information.