Attribute reduction based on directed graph in formal fuzzy contexts

An attribute reduction can make the structure of concept lattices more convenient in formal fuzzy contexts. Thereby, it is beneficial to discover the knowledge. Based on the notion of one-side fuzzy concept, we propose a method of attribute reduction combining with the directed graph theory. Employing the proposed approach, a judgment theorem is given for determining concepts and irreducible elements in formal fuzzy contexts. According to the significance of attributes, these attributes are classified three types: core attributes, relatively necessary attributes and unnecessary attributes, which are referred to the attribute characteristics. Applying with the directed graph, We propose the judgment theorems and the corresponding algorithms for computing the three types of attributes sets. On this basis, a corresponding method of attribute reduction is given in a fuzzy-crisp formal context. The feasibility and effectiveness of the algorithm has been proved via an example. The approach presents a mew method for knowledge reducible in formal fuzzy contexts.