A novel method for generating a canonical basis for decision implications based on object-induced three-way operators

Three-way concept analysis can express not only the information that the objects of study have in common but also the information that they do not have in common, which is an extension of classical formal concept analysis. The decision implication is a special representation of the implication in the decision formal context, which reveals the dependency between conditional attributes and decision attributes. This paper is devoted to the study of a novel method for generating a canonical basis for decision implications based on object-induced operators (OE operators). First, the decision implication logic based on OE operators is described from the two aspects of semantics and syntax, which is applied to the decision formal context. Then, a method of obtaining the canonical basis for decision implications based on decision the premise of the OE operators is given, and the completeness, the nonredundancy and the optimality of the canonical basis are proven. Finally, a method of generating true premises based on OE operators is proposed by means of an incremental method, and the canonical basis for decision implications is then generated by the true premises based on OE operators.

Automated summary

This article focuses on a novel method for generating a canonical basis for decision implications based on object-induced operators (OE operators). The logic of decision implication based on OE operators is described, and a method for obtaining the canonical basis for decision implications is given. The completeness, nonredundancy, and optimality of the canonical basis are proven. Additionally, a method for generating true premises based on OE operators is proposed.