In this paper,
the classical Jensen inequalities for concave function φ, i.e.,
class="formula" id="ueq0001">
are adapted for
the Sugeno integral using
the notion of
the supergradient. Moreover, we give some modifications of previous results of Rom&a
acute;n-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.