This paper deals with the Lipschitzianity of triangular subnorms. Unlike the case of t-norms, for these operators the problem is widely open and presents an extremely interesting variety of situations. The key point seems to be a weakening of the notion of convexity, called alpha-convexity. The alpha-convex real functions presents characteristics quite different from the usual convex real mappings. We will discuss the link between such kind of functions and the generators of continuous Archimedean triangular subnorms.
Lipschitz triangular subnorms
GHISELLI RICCI, Roberto;
2006
Abstract
This paper deals with the Lipschitzianity of triangular subnorms. Unlike the case of t-norms, for these operators the problem is widely open and presents an extremely interesting variety of situations. The key point seems to be a weakening of the notion of convexity, called alpha-convexity. The alpha-convex real functions presents characteristics quite different from the usual convex real mappings. We will discuss the link between such kind of functions and the generators of continuous Archimedean triangular subnorms.File in questo prodotto:
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