One version of the Prékopa-Leindler type inequality for the Sugeno integral

Abstract In this paper, we showed that by an example the classical Prekopa-Leindler type inequality is not valid for the Sugeno integral. We proved one version of the Prekopa-Leindler type inequality by adding concave fuzzy measure and quasi-concave fuzzy measure assumptions for the Sugeno integral with different proofs. In the continue, we obtained a derivation version of the Prekopa-Leindler inequality and illustrated all of the main results by examples.