Method for generating decision implication canonical basis based on true premises

Formal concept analysis is able to visualize and represent knowledge using concept lattice and (attribute) implication. Decision implication is a counterpart of implication in the setting of decision-making. Decision implication canonical basis is a complete, non-redundant and optimal set of decision implications. At present, decision implication canonical basis can be generated with the help of minimal generators; however, this method is not efficient because of its exponential complexity. To solve this problem, we propose an algorithm to generate decision implication canonical basis based on true premises and analyze its time complexity. Experimental results verify the efficiency of this algorithm.