\(k\)-\(l_p\)-Lipschitz t-norms. (English) Zbl 1189.03058

Mesiarová, A.

Int. J. Approx. Reasoning 46, No. 3, 596-604 (2007).

Summary: \(k\)-\(l_p\)-Lipschitz t-norms are shown to be ordinal sums of \(k\)-\(l_p\)-Lipschitz Archimedean t-norms. Additive generators of \(k\)-\(l_p\)-Lipschitz t-norms are characterized by means of \(k\)-\(p\)-convexity. Several necessary and sufficient conditions for a function to be a \(k\)-\(p\)-convex additive generator are also given.

MSC:

03E72

Theory of fuzzy sets, etc.

Keywords:

additive generator; \(l_p\) norm; Lipschitz property; triangular norm

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