Representing attribute reduction and concepts in concept lattice using graphs

Concept lattice is an area of research which is based on a set-theoretical model for concepts and conceptual hierarchies. It is better for the studying of concept lattice to minimize the input data before revealing the construction of a concept lattice. Actually, this duty can be done by attribute reduction for a context. Graph is useful in data analysis since it gives us a visual trend on the behavior of our data points and allows us to test some laws in data analysis. This paper is a preliminary attempt to study how directed graph can be used on attribute reduction and conceptual construction in concept lattices. We investigate all the reducible attributes and concepts in a context with the aid of graph theory. For a context, we define a relevant graph on the set of attributes and, further, define a pre-weighted relevant graph. Afterward, using relevant graphs and pre-weighted relevant graphs with the method of deleting vertices in a directed graph, we find all the reducible attributes in a context. After that, we seek out all of concepts and the concept lattice for a given context. All these results may be not only used to improve the visibility and readability of attribute reduction in a context and the construction of concept lattice, but also broaden the applied range of directed graph such as in the field of attribute reduction.