Sugeno integral based on absolutely monotone real set functions

The class of all absolutely monotone and sign stable set functions with m(∅)=0, denoted by AMSS, is introduced. Necessary and sufficient conditions are obtained for a set function m, m(∅)=0, to be a member of AMSS. A Sugeno type integral of an A- measurable real-valued function is defined with respect to an absolutely monotone and sign stable set function and some of its properties are shown. A representation of a comonotone–cosigned functional by Sugeno integral based on m∈AMSS is obtained.