The f-index of inclusion as optimal adjoint pair for fuzzy modus ponens

Abstract

We continue studying the properties of the f-index of inclusion and show that, given a fixed pair of fuzzy sets, their f-index of inclusion can be linked to a fuzzy conjunction which is part of an adjoint pair. We also show that, when this pair is used as the underlying structure to provide a fuzzy interpretation of the modus ponens inference rule, it provides the maximum possible truth-value in the conclusion among all those values obtained by fuzzy modus ponens using any other possible adjoint pair.