Inequalities for integrals based on nonadditive measures

There are considered generalizations of the classical integral inequalities as Hölder, Minkowski, Chebishev, Berwald to fuzzy integrals, e.g., Choquet and Sugeno integrals. For the universal integral, as generalization of Choquet and Sugeno integral, there are given a general inequality which cover Hölder and Minkowski type inequalities. There are given generalizations of the Hölder, Minkowski and Chebyshev's inequalities for two important cases of the pseudo-integral.