On some properties of threshold generated implications

In this paper, the recently introduced construction method of a fuzzy implication from two given ones, called threshold generation method, is studied. This method preserves several of the most usual properties of fuzzy implications from the initial ones to the threshold generated implication. In particular, the preservation of the exchange principle, the law of importation and the distributivities with t-norms and t-conorms, stating the minimal necessary conditions to ensure this fact is studied. From these results, some properties of h-implications, as a particular case of threshold generated implications, are pointed out.