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

Authors:
Gleb Beliakov;Tomasa Calvo
Affiliations:
School of Information Technology, Deakin University, Burwood, Vic., Australia;Departamento de Ciencias de la Computación, Universidad de Alcalá, Madrid, Spain
Venue:
IEEE Transactions on Fuzzy Systems
Year:
2009

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Abstract

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.