Concept reduction in formal concept analysis based on representative concept matrix

Reduction theory is an important topic in formal concept analysis, and the research of reduction theory generally focuses on attribute reduction. Attribute reduction deletes redundant attributes and simplifies formal context. Nevertheless, it may lose part of original information of formal context. As a new direction of knowledge reduction, concept reduction avoids the defects of information loss caused by attribute reduction and enriches reduction theory. Concept reduction not only preserves the binary relation of a formal context, but also reduces the number of formal concepts. Furthermore, the information of formal context can be expressed simply and completely, and the complexity of solving problems with formal concept analysis can be reduced. In this paper, the definition of representative concept matrix is given to visualize the connection between concepts and binary relation. Then, the method for calculating concept reducts by representative concept matrix is obtained, and two simplified representative concept matrices named the clarified representative concept matrix and the minimal representative concept matrix are proposed. In addition, an algorithm for obtaining the minimal representative concept matrix is presented and compared with the previous algorithm. Finally, from the perspective of concept consistent set and minimal representative concept matrix respectively, the characteristics of three types of concepts, i.e., core concepts, relatively necessary concepts and absolutely unnecessary concepts, are discussed.