Incomplete decision contexts: Approximate concept construction, rule acquisition and knowledge reduction

Incomplete decision contexts are a kind of decision formal contexts in which information about the relationship between some objects and attributes is not available or is lost. Knowledge discovery in incomplete decision contexts is of interest because such databases are frequently encountered in the real world. This paper mainly focuses on the issues of approximate concept construction, rule acquisition and knowledge reduction in incomplete decision contexts. We propose a novel method for building the approximate concept lattice of an incomplete context. Then, we present the notion of an approximate decision rule and an approach for extracting non-redundant approximate decision rules from an incomplete decision context. Furthermore, in order to make the rule acquisition easier and the extracted approximate decision rules more compact, a knowledge reduction framework with a reduction procedure for incomplete decision contexts is formulated by constructing a discernibility matrix and its associated Boolean function. Finally, some numerical experiments are conducted to assess the efficiency of the proposed method.

► We propose a method to build approximate concept lattice of an incomplete context.
► We present an approach to approximate reasoning for approximate decision rules.
► An approach for mining non-redundant approximate decision rules is developed.
► We put forward a knowledge reduction method for incomplete decision contexts.
► Numerical experiments show that the proposed algorithms perform satisfactorily.