Study of decision implications based on formal concept analysis

In this paper, the notions of decision table and decision rule in Rough Set Theory are introduced naturally into Formal Concept Analysis as decision context and decision implication. Since extracting decision implications directly from decision context takes time, we present an inference rule called a-decision inference rule to eliminate the superfluous decision implications. Moreover, based on the inference rule we introduce the notion of a-maximal decision implication and prove that the set of all a-maximal decision implications is complete (cl-complete) and non-redundant (a-non-redundant). Finally, we present a method to generate the set.