| Summary: | Three-way concepts analysis, an effective tool for knowledge discovery, is a combination of three-way decision and formal concept analysis. Based on the connections between three-way concepts and formal concepts, the method of obtaining three-way concepts and the method of how to judge attribute characteristics are studied respectively from the perspective of pictorial diagrams. Inspired by the pictorial-diagrams-based acquisition methods of concepts (formal concept, object-oriented concept and property-oriented concept), and combining the connections between three kinds of concepts in combinatorial contexts and four kinds of three-way concepts, the definitions of combinatorial-property (combinatorial-object) pictorial diagram and property pair induced (object pair induced) three-way pictorial diagram are proposed. Then, the acquisition approaches to four kinds of three-way concepts are investigated by using the novel proposed pictorial diagrams. In addition, from the perspective of preserving the structure of the lattice, the general definitions of the reduction and attribute characteristics are given, attribute characteristics of an object induced three-way concept lattice are analyzed by discernibility matrix, and the judg-ment theorems of attribute characteristics are given based on property pair induced pictorial diagrams.
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