Inequalities of Hlder and Minkowski type for pseudo-integrals with respect to interval-valued ?-measures
In the present paper, the Hlder and Minkowski type of inequality for the pseudo-integral of a real-valued function with respect to the interval-valued pseudo-additive measure is proven. Two cases of semirings are considered. In the first case, pseudo-operations (pseudo-addition and pseudo-multiplication) are set by a strictly monotone continuous function. In the second case, the pseudo-addition is the idempotent operation sup, and pseudo-multiplication is specified by a strictly monotone continuous function, as in the first case. Trivial and nontrivial examples of interval-valued pseudo-additive measures are provided, as well as Hlder and Minkowski type of inequalities with respect to those measures.
pseudo-integral pseudo-operations interval-valued measure hlder type inequality minkowski type inequality