Approximate concept construction with three-way decisions and attribute reduction in incomplete contexts

Incomplete contexts are a kind of formal contexts in which the relationship between some objects and some attributes is unavailable or lost. Knowledge discovery in incomplete contexts is of interest because such databases are frequently encountered in the real world. This paper mainly focuses on two issues: approximate concept construction with three-way decisions and attribute reduction in incomplete contexts. The theory of three-way decisions is formulated based on the notions of acceptance, rejection and non-commitment. It is an extension of the commonly used binary-decision model with an added third option. Based on three-way decisions, we propose two models to construct approximate concepts in incomplete contexts, and the equivalence of the two is revealed. To simplify the representation of the approximate concept lattices, we further present the attribute reduction approaches.