Inequalities for integrals based on nonadditive measures

Abstract

There are considered generalizations of the classical integral inequalities as Holder, 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 Holder and Minkowski type inequalities. There are given generalizations of the Holder, Minkowski and Chebyshev's inequalities for two important cases of the pseudo-integral.