Generalizations of the Well-Known Chebyshev Type Inequalities for Pseudo-Integrals

In this paper, generalizations of the well-known Chebyshev type integralinequalities for pseudo-integrals are proved. Two cases are considered of the real semiring with pseudo-operations: One, when pseudo-operations are defined by monotone and continuous function g (then the pseudo-integrals reduces gintegral), and the second with a semiring ([a, b], max, ⊙), where the pseudomultiplication ⊙ is generated.