On the comonotonic-★-property for Sugeno integral

摘要

The so-called comonotonic-★-property for Sugeno integral is introduced and investigated, where ★:[0,∞]2→[0,∞] is a binary operation. Under the assumption that limb→∞a★b∈{a,∞} and lima→∞a★b∈{b,∞}, we prove that Sugeno integral possesses comonotonic-★-property if and only if ★ equals to one of the four operators: minimum, maximum, PF (the first projection) and PL (the last projection). We also discuss comonotonic-★-property when this assumption does not hold.