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Abstract: In recent years, some new construction methods of fuzzy implications from other given ones have been proposed. One of them, the so-called threshold generation method, preserves important properties such as the exchange principle or the law of importation under some minimal conditions. This method is based on an adequate scaling on the second variable of the two initial fuzzy implications. In this paper, we propose a new method to generate fuzzy implications from two given ones in the same spirit of the threshold generation method but now through an adequate scaling on the first variable of the given fuzzy implications. The new implications, called vertical threshold generated implications, are deeply studied focusing on the preservation of the most common properties of fuzzy implications from the initial ones to the generated implication. Moreover, they are fully characterized by means of the -vertical section of the implication. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]