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.

Automated summary

This paper discusses the importance of formal contexts in formal concept analysis, proposes the concept of 3-valued formal contexts, and uses 3-way concept analysis to define 3-valued operators and construct 3-valued concept lattices, providing a new cognitive model.