Study on deduction process and inference methods of decision implications

Abstract

Decision implication is a basic form of knowledge representation of Formal Concept Analysis in the setting of decision-making. Inference rules are generally utilized to infer new decision implications from a given set of decision implications. Three inference rules have been proposed for the deduction process on decision implications, i.e., Augmentation, Combination and Con-Combination. How to apply the inference rules, however, is not discussed in literature. To this end, we studied the properties of the inference rules and found that in the deduction process, Augmentation should be applied only once and that both Combination and Con-Combination need to be applied at most $\lceil \log _{2}m\rceil$ times. Moreover, by analyzing the interchangeabilities of the inference rules, we found that Augmentation and Combination are interchangeable, but Augmentation and Con-Combination are not. Based on these results, three inference methods were then proposed and their efficiencies were verified by experiments. The experimental results show that one of the inference methods, namely, applying Augmentation once and then applying Con-Combination at most $\lceil \log _{2}m\rceil$ times, is the most efficient inference method.