Generalization of the Chebyshev inequality for pseudo-integral

Abstract

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, ⊙), where ⊙ is generated. There are proven generalizations of the Chebyshev's inequality for the both cases of the pseudo-integral.