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 -additive functional by Sugeno integral based on m ∈ AMSS is obtained.