A matroidal structure for formal context and its applications on epidemiological study

The spread of an epidemic attracts extensive attention in epidemiological study and is one of instances of data mining. The matroid is an important mathematical structure with high applicability and an efficiency tool for designing optimization algorithms in attribute reduction. Therefore, analyzing the spread of an epidemic by the matroid is highly efficient In this paper, we build a matroid induced by the formal context and discuss whether an epidemic spreads easily or not by this matroid. Firstly, we define a family of sets which are proved to satisfy the circuit axiom of matroids. Therefore, a matroidal structure of the formal context can be built Secondly, in order to study E-spread information systems deeply by the matroid, a graphical representation of matroids is explored. Finally, three necessary and sufficient conditions for an epidemic to spread easily are investigated from the viewpoint of connectivity of matroid induced by the formal context, connectivity of a relevant graph, and matroid approximation operators. Investigation of the spread of an epidemic will benefit to staving off major outbreaks of communicable diseases.