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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: The main purpose of this paper is to solve the functional equation , for and a pair of a t-norm T and a t-conorm S. This equation arises when we consider a convex linear combination of a t-norm and a t-conorm, and set out the problem of finding the intersection of the segments determined by the pairs and . [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]

Abstract: Fuzzy interpolation enhances the robustness of fuzzy systems and helps to reduce systems complexity. Although a number of important fuzzy rule interpolation approaches have been proposed in the literature, most of these approaches cannot be expressed in a closed form. This is usually caused by the effort to avoid possible invalid interpolated results. This paper proposes a different fuzzy rule interpolation approach. It not only can be represented in a closed form but also guarantees that the interpolated results are valid fuzzy sets. This approach is based on a direct use of the extension principle which has been widely utilised for the development of a variety of fuzzy systems. The mathematical properties of the proposed approach are analysed by taking the advantage of the closed form representation. This approach has been applied to a practical problem of predicting diarrhoeal disease rates in remote villages. The results demonstrate the potential of the proposed work in enhancing the robustness of fuzzy interpolation. [Copyright &y& Elsevier]