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arXiv · 2307.11059

Coherence and avoidance of sure loss for standardized functions and semicopulas

Erich Peter Klement·Damjana Kokol Bukovšek·Blaž Mojškerc·Matjaž Omladič·Susanne Saminger-Platz·Nik Stopar
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Abstract

We discuss avoidance of sure loss and coherence results for semicopulas and standardized functions, i.e., for grounded, 1-increasing functions with value $1$ at $(1,1,\ldots, 1)$. We characterize the existence of a $k$-increasing $n$-variate function $C$ fulfilling $A\leq C\leq B$ for standardized $n$-variate functions $A,B$ and discuss the method for constructing this function. Our proofs also include procedures for extending functions on some countably infinite mesh to functions on the unit box. We provide a characterization when $A$ respectively $B$ coincides with the pointwise infimum respectively supremum of the set of all $k$-increasing $n$-variate functions $C$ fulfilling $A\leq C\leq B$.

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Erich Peter Klement, Damjana Kokol Bukovšek, Blaž Mojškerc, Matjaž Omladič, Susanne Saminger-Platz, Nik Stopar. 2023-07-20. Coherence and avoidance of sure loss for standardized functions and semicopulas. https://doi.org/10.1016/j.ijar.2023.109089

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