Rule acquisition and complexity reduction in formal decision contexts

In this paper, we introduce the notion of formal decision context as an extension of formal contexts by employing the notion of decision information table. We use formal concept analysis to formulate an approach to extract “if–then” rule from formal decision contexts. We also construct a knowledge-lossless method for complexity reduction in formal decision contexts so that the maximum rules extracted from the reduced formal decision contexts are identical to that extracted from the initial decision formal contexts. More specifically, we develop the discernibility matrix and the discernibility function in formal decision contexts to compute all of the attribute reductions without loss of knowledge.

• We employed formal concept analysis to extract “if … then” rule from formal decision contexts.
• We formulated an approach to attribute reduction in formal decision contexts without loss any knowledge.
• We constructed appropriate discernibility functions and corresponding reduction algorithm for decision formal contexts.