Construction of k-Lipschitz Triangular Norms and Conorms From Empirical Data

This paper examines the practical construction of k -Lipschitz triangular norms and conorms from empirical data. We apply a characterization of such functions based on k -convex additive generators and translate k -convexity of piecewise linear strictly decreasing functions into a simple set of linear inequalities on their coefficients. This is the basis of a simple linear spline-fitting algorithm, which guarantees k -Lipschitz property of the resulting triangular norms and conorms.