Interval-valued Chebyshev, Hölder and Minkowski inequalities based on g-integrals

A natural generalization of (classical) measures are monotone set valued functions, the so called non-additive measures. Further generalization of measures are interval-valued measures and interval-valued non-additive measures. Since interval-valued ⊕-measures, as a special case of interval-valued non-additive measures, have been extensively applied in the mathematical representation of the various aspects of uncertainty, the present paper offers a generalization of Chebyshev, Hölder and Minkowski types inequalities obtained by g-integrals for non-negative real-valued functions with respect to an interval-valued ⊕-measures.