Generalization of the Jensen inequality for pseudo-integral

Generalizations of the Jensen integral inequality for the pseudo-integral are proven. There are considered two cases of the real semiring with pseudo-operations: one, when pseudo-operations are defined by monotone and continuous function g (then the pseudo-integral reduces on g  -integral), and the second semiring ([a,b],max,⊙)([a,b],max,⊙), where the pseudo-multiplication ⊙ is generated.