Fitting aggregation operators to data

Theoretical advances in modelling aggregation of information produced a wide range of aggregation operators, applicable to almost every practical problem. The most important classes of aggregation operators include triangular norms, uninorms, generalised means and OWA operators.With such a variety, an important practical problem has emerged: how to fit the parameters/ weights of these families of aggregation operators to observed data? How to estimate quantitatively whether a given class of operators is suitable as a model in a given practical setting? Aggregation operators are rather special classes of functions, and thus they require specialised regression techniques, which would enforce important theoretical properties, like commutativity or associativity. My presentation will address this issue in detail, and will discuss various regression methods applicable specifically to t-norms, uninorms and generalised means. I will also demonstrate software implementing these regression techniques, which would allow practitioners to paste their data and obtain optimal parameters of the chosen family of operators.<br /

Lipschitz Continuity of Triangular Subnorms

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 alfa-lower convexity and sub-convexity.The alfa-lower convex and subconvex 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 pseudoinverse, of continuous Archimedean triangular subnorms