On Carlson’s inequality for Sugeno and Choquet integrals

Abstract

We present a Carlson type inequality for the generalized Sugeno integral and a much wider class of functions than the comonotone functions. We also provide three Carlson type inequalities for the Choquet integral. Our inequalities generalize many known results.

Inequalities of Lyapunov and Stolarsky Type for Choquet-Like Integrals with respect to Nonmonotonic Fuzzy Measures

“…For example, when we think of an integral operator as a predictive tool, then an integral inequality can be very important in measuring and dimensioning such process. Recently, Flores, Agahi, Pap, and Mesiar et al generalized several classical integral inequalities to Sugeno integral and choquet integral, including Chebyshev type inequality [31,32], Jensen type inequality [33,34], Stolarsky type inequality [35,36], Hölder type inequality [37], Minkowski type inequalities [38], Carlson type inequality [39], and Liapunov type inequality [40]. Pseudo-analysis would be an interesting topic to generalize an inequality from the frame work of the classical analysis to that of some integrals which contain the classical analysis as special cases.…”