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.
2006
284254112X
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11392/1402492
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