Coherence and avoidance of sure loss for standardized functions and semicopulasKlement, Erich Peter (Avtor) Kokol-Bukovšek, Damjana (Avtor) Mojškerc, Blaž (Avtor) Omladič, Matjaž (Avtor) Saminger, Susanne (Avtor) Stopar, Nik (Avtor) copulasquasi-copulassemicopulasstandardized functioncoherenceavoidance of sure lossk-increasing functionWe 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 $A \le C \le B$ for standardized $n$-variate functions $A$, $B$ and discuss methods for constructing such functions. 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 $A \le C \le B$.20242024-03-13 14:50:49Neznano18396sl