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In this paper we continue our study on the migrative property of triangular norms. First we interpret this property as a particular form of the generalized associativity functional equation. This makes it easy to extend the original property, and also to characterize it with the help of a very simple equation. Then we turn back to the original notion and show two representation (construction) theorems...
In this paper we completely describe all continuous migrative triangular norms. Since the migrative property excludes both idempotent and nilpotent classes, the characterization and construction is carried out by solving a functional equation for additive generators of strict t-norms. We also study cases when the construction results in a smooth generator.
AbstractUninorms are an important generalization of t-norms and t-conorms, having a neutral element lying anywhere in the unit interval. A uninorm shows a typical block structure and is built from a t-norm, a t-conorm and a mean operator. Two important classes of uninorms are characterized, corresponding to the use of the minimum operator (the class Umin) and maximum operator (the class Umax) as mean...
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