Conditions for Choquet integral representation of the comonotonically additive and monotone functional.
In the paper a locally compact space \(X\) is considered. Two real functions \(f\), \(g\) are comonotonic \((f\sim g)\) if \(f(x)< f(x')\) implies \(g(x)\leq g(x')\). A functional \(I\) is comonotonically additive, if \(f\sim g\) implies \(I(f+ g)= I(f)+ I(g)\) and \(f\leq g\) implies \(I(f)\leq I(g)\). There are given some conditions for the possibility to represent a comonotonically additive functional as a Choquet integral. The results are based on the paper by \textit{Y. Narukawa}, \textit{T. Murofushi} and \textit{M. Sugeno} [Fuzzy Sets Syst. 112, No. 2, 177--186 (2000; Zbl 0954.28007)].
scientific article; zbMATH DE number 1956911