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Abstract: The -migrative triangular subnorms, where T stands for the three prototype triangular norms (namely the product, the Łukasiewicz t-norm and the minimum), are investigated in detail. The paper gives necessary and sufficient conditions under which a triangular subnorm with a continuous additive generator is -migrative with respect to any of the three prototype triangular norms. [Copyright &y& Elsevier]

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]