Construction of k-Lipschitz triangular norms and conorms from empirical data

This paper examines the practical construction of <i>k</i>-Lipschitz triangular norms and conorms from empirical data. We apply a characterization of such functions based on <i>k</i>-convex additive generators and translate <i>k</i>-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 <i>k</i>-Lipschitz property of the resulting triangular norms and conorms.<br />