3-Way Concept Analysis Based on 3-Valued Formal Contexts

As the basic form of data presentation, formal contexts play an elementary and important role in formal concept analysis and in 3-way concept analysis. In fact, many data tables are similar in form to formal contexts. Therefore, these data tables can be studied collectively in a similar framework, and such a study can be significant in knowledge discovery. We propose the notion of 3-valued formal contexts after analyzing the shared characteristics of different data forms such as incomplete formal contexts, conflict situations and other similar cases. After close studies of 3-valued formal contexts, this paper adopts 3-way concept analysis to define 3-valued operators and construct 3-valued concept lattices and finally interpret the meaning of 3-valued operators and discuss the relationship between 3-valued lattices and existing approximation concept lattices. The essence of this method is to present, via 3-way concept analysis, potential information and structure. And 3-way concept analysis shows the common properties of the objects, jointly possessed or jointly not possessed, positive or negative, even the uncertain information. So, this paper actually provides a new model for cognition. Apart from the universal applicability, 3-valued contexts can also be fixed into formal concept analysis. That is, many problems can be studied in the framework of formal concept analysis.