Jensen’s inequalities for standard and generalized asymmetric Choquet integrals

In a recent paper by the authors, Jensen’s inequality for Choquet integral was given, and a wrong assertion—“Jensen’s inequality does not hold for asymmetric Choquet integral” was made. This paper can be viewed as a continuation of the previous one, Jensen’s inequality for asymmetric Choquet integral is proved, the error is corrected. As its generalization, Jensen’s inequality for generalized asymmetric Choquet integral is obtained.