Chebyshev inequality for q-integrals. (English) Zbl 1459.28015
Summary: Let \(f, g\) be two comonotonic functions on the unit interval. The classical Chebyshev inequality states that the product of the integrals of \(f\) and \(g\) is a lower bound of the integral of the product of \(f\) and \(g\). This study proves a Chebyshev inequality on an abstract space \(X\) for q-integral, which was recently introduced by D. Dubois et al. as a generalization of the Sugeno integral as well as the seminormed integral. It also proves a related inequality for q-cointegrals. Our results generalize previous ones obtained in the framework of Sugeno integral as well as seminormed fuzzy integrals.
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