Bi-aggregated contrapositivisation: A new contrapositivisation technique for fuzzy implications

We introduce a new contrapositivisation technique for fuzzy implications constructed from a pair of bivariate aggregation functions and a fuzzy negation, which we call bi-aggregated contrapositivisation. We show that the bi-aggregated contrapositivisation generalizes the upper, lower, medium and aggregated contrapositivisations. We characterize this new technique according to some of the main properties commonly associated with fuzzy implications. We study briefly the N -compatibility of the operators bi-aggregated contrapositivisators and we investigate how an automorphism acts under such operators. We also studied some properties that are satisfied by the bi-aggregated contrapositivisator of the main classes of fuzzy implications. Finally, we present three new methods of generating bivariate aggregation functions from bi-aggregated contrapositivisators and fuzzy negations.