Threshold generation method of construction of a new implication from two given ones

In this paper, a new construction method of a fuzzy implication from two given ones, called threshold generation method, is introduced. It is a generalization of the way of construction of the recently introduced h-implications, which are fully characterized in this work. The threshold generation method allows to control, up to a certain level, the increasingness on the second variable of the fuzzy implication through an adequate scaling on that variable of the two given implications. The natural propagation of the most usual properties of fuzzy implications from the initial ones to the constructed implication is studied and the necessary and sufficient conditions in order to ensure this propagation are presented. In particular, the preservation of the contrapositive symmetry on threshold generated implications needs of another construction method of a fuzzy implication from a given one and a fuzzy negation.