A clustering reduction algorithm for fuzzy concept lattice

Abstract

Formal concept analysis is a powerful tool in analyzing data and extracting rules from the formal context. The main framework of formal concept analysis is concept lattice which essentially describes the relationship between the objects and the attributes. And each node of the concept lattice is a formal concept. When processing the uncertain information, the concept lattice normally contains a plenty of reduplicative and redundant information. Therefore, the reduction of fuzzy concept lattice becomes very important to enhance the effectiveness of the relevant fuzzy concept lattice. At present, many concept lattice reduction methods are proposed for the attribute reduction. In this paper, a new method of fuzzy concept lattice clustering reduction is proposed for the concept reduction. Specifically, this method searches for the supremum and infimum of similar nodes and clusters the nodes between the supremum and infimum into a new node. Such node will be utilized to represent those similar nodes. Moreover, the lattice structure of the concept will be maintained after being hierarchical. Therefore, the proposed method simplifies the structure of the concept lattice which reduces the size of the data and still maintains properties and advantages of lattice. An example is provided to illustrate the effectiveness of this method.