Soft Computing

, Volume 21, Issue 24, pp 7293–7311 | Cite as

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.


Concept lattice Relevant graph Pre-weighted relevant graph Attribute reduction Concept 



The author sincerely acknowledges the financial support from the Natural Science Foundation of China (61572011) and Natural Science Foundation of Hebei Province (A2013201119).

Compliance with ethical standards

Conflict of interest

The authors declare that there is no conflict of interest regarding the publication of this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Department of MathematicsHebei UniversityBaodingChina

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