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.