A Chebyshev type inequality for fuzzy integrals (Q2383853)

The classical Chebyshev's integral inequality \(\int_0^1 fg \,d\mu \geq(\int_0^1 f \,d\mu )(\int_0^1 g \,d\mu)\) for \(f, g: [0,1] \to [0, \infty )\) of the same monotonicity type is shown for the case, when the Lebesgue integral is replaced by the Sugeno integral. As a corollary an analogous result for finite number of fuctions is included.