Kybernetika 61 no. 2, 238-263, 2025

New results on additive generator pairs of overlap and grouping functions

Liang Li-zhi and Wang Xue-pingDOI: 10.14736/kyb-2025-2-0238

Abstract:

In this article, we deeply reveal the relationship between functions $\theta$ and $\vartheta$ in an overlap function additively generated by an additive generator pair ($\theta$,$\vartheta$), which is used to characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions $\theta$ and $\vartheta$. We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo) automorphism. Finally, we dually give the related results concerned grouping functions.

Keywords:

triangular norm, distortion, overlap function, grouping function, additive generator pair

Classification:

03B52, 03E72

paper.pdf

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