A comparative study of decision implication, concept rule and granular rule.

Decision implication is a basic form of knowledge representation of formal concept analysis in the setting of decision-making. Concept rules are decision implications that reveal the dependencies between condition concepts and decision concepts. Granular rules are concept rules that reveal the dependencies between condition object concepts and decision object concepts. This paper conducts a comparative study of decision implication, concept rule and granular rule. First, we conclude that both concept rules and granular rules are not complete w.r.t. decision implications, and that granular rules are not complete w.r.t. concept rules, implying that there exists information loss when studying decision implications by using only concept rules or granular rules, or when studying concept rules by using only granular rules. Next, with the help of decision implication logic, we identify accurately the information loss in concept rules and granular rules, and explore the underlying reason behind the information loss in concept rules and granular rules. Finally, by using the obtained results, we revisit some work on concept rule and granular rule, make some insightful remarks on the non-redundancy of concept rules and clarify some seemingly misleading statements on the representation of concept rules by granular rules.