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New results on additive generator pairs of overlap and grouping functions

Liang Li-zhi; Wang Xue-ping — 2025

Kybernetika

In this article, we deeply reveal the relationship between functions $θ$ and $ϑ$ in an overlap function additively generated by an additive generator pair ( $θ$ , $ϑ$ ), which is used to characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions $θ$ and $ϑ$ . 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....

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