Approximation of k-Lipschitz t-norms by strict and nilpotent k-Lipschitz t-norms

Abstract

Some topological properties of k-Lipschitz triangular norms are investigated, generalizing the results known for the case . For any fixed the class of all k-Lipschitz t-norms is shown to be compact. Moreover, it is shown that the set of all k-Lipschitz t-norms is the closure of both the set of all strict k-Lipschitz t-norms and the set of all nilpotent k-Lipschitz t-norms.

Keywords:

• Additive generator
• k-Lipschitz property
• Triangular norm

Acknowledgements

This work was supported by grants APVT 20-046402, APVT 51-032002 and VEGA 2/3163/23.