A representation of a comonotone-◯∨-additive and monotone functional by two Sugeno integrals

There is obtained a representation of a comonotone-◯∨-additive, weak ◯∧-homogeneous and monotone functional L (defined on the class of functions on finite set) as a symmetric maximum of two Sugeno integrals. This representation is a generalization of certain previous results, which are useful for cumulative prospect theory. As a consequence of a result on general fuzzy rank and sign-dependent functionals considered on functions defined on the infinitely countable basic set X it is obtained that the symmetric Sugeno integral is comonotone-◯∨-additive functional on the class of functions with finite support.