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On additive generators of overlap functions. (English) Zbl 1392.68407

Summary: In this paper, we introduce the notion of additive generator pair for overlap functions. We also study how some of the properties that can be demanded to an overlap function can be expressed in terms of its generator pair. In particular, given a continuous and positive t-norm \(T\), we analyze the overlap functions which are obtained by the distortion of \(T\) by a pseudo-automorphism, showing that the additive generator pair of such overlap function may be given in terms of the considered pseudo-automorphism and the additive generator of \(T\). Finally, we also consider the influence of the migrativity, homogeneity and idempotency properties for the overlap functions obtained by such distortion in terms of their respective additive generator pairs.

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
91B06 Decision theory
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