Lipschitz continuity of triangular subnorms

Authors:
Roberto Ghiselli Ricci;Radko Mesiar;Andrea Mesiarová-Zemánková
Affiliations:
Department of Economia e Management, University of Ferrara, I-44121 Ferrara, Italy;Faculty of Civil Engineering, Department of Mathematics, Slovak University of Technology, 81 368 Bratislava, Slovakia and Institute for Research and Applications of Fuzzy Modelling, University of ...;Mathematical Institute, Slovak Academy of Sciences, Bratislava, Slovakia
Venue:
Fuzzy Sets and Systems
Year:
2014

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Abstract

This paper deals with the Lipschitz property of triangular subnorms. Unlike the case of triangular norms, for these operations the problem is still open and presents an interesting variety of situations. We provide some characterization results by weakening the notion of convexity, introducing two generalized versions of convexity for real functions, called @a-lower convexity and sub-convexity. The @a-lower convex and sub-convex real mappings present characteristics quite different from the usual convex real mappings. We will discuss the link between such kind of functions and the generators, and their pseudo-inverse, of continuous Archimedean triangular subnorms.