On k-Lipschitzian (T, N)-Implications.

Implications and k-Lipschitz condition have been recurrent topics of studies in fuzzy theory. Additionally, they play a singular role concerning the robustness of rule-based fuzzy reasoning. Therefore, in this paper, we investigate the properties required for fuzzy negations N, t-norms T and (T, N)-implications satisfying the k-Lipschitz condition for a specific, and arbitrary, k. Besides, we generate new Lipschitzian implications from (T, N)-implications using automorphisms.