Jensen-type inequalities for Sugeno integral

In this paper, the classical Jensen inequalities for concave function φ, i.e., φ(∫f(x)dμ)⩾∫φ(f)dμandφ(∑i=1nλixi)⩾∑i=1nλiφ(xi),are adapted for the Sugeno integral using the notion of the supergradient. Moreover, we give some modifications of previous results of Román-Flores et al. concerning Jensen-type inequalities for Sugeno integral. Some examples in the framework of the Lebesgue measure and counting measure to illustrate the results are presented.