On the characterization of Yager's implications (Q712693)

Yager introduced \(f\)-generated and \(g\)-generated implications based on \(f\)-generators and \(g\)-generators, which are important tools in approximate reasoning. Many researches were focused on Yager's implications, and the properties of these implications have been studied in detail but they have not been characterized yet. In this paper, characterizations of Yager's \(f\)- and \(g\)-implications are presented. The characterizations given here are based on the law of importation, a functional equation that has been extensively studied. Moreover, particular characterizations of Reichenbach, Yager and Goguen implications are derived from these results. These results allow the authors to fully determine the intersection of Yager's implications with their \(D\)-conjugates and \(\phi\)-conjugates, and some extensions related to Yager's implications.