ON THE STOLARSKY-TYPE INEQUALITY FOR THE CHQOUET INTEGRAL AND THE GENERATED CHOQUET INTEGRAL

摘要

Roman-Fores (2008) have studied Stolarsky-type inequality for the fuzzy-integral with respect to a fuzzy measure. Recently, Daraby(2012) proved the Stolarsky-type inequality for the pseudo-integral with respect to the Lebesgue measure and gave an open problem: "Does Stolarsky's inequality hold for the Choquet integral?" In this paper, we prove the Stolarsky-type inequality for the Choquet integral with respect to a fuzzy measure. Furthermore, we investigate the Stolarsky-type inequality for the generated Choquet integral with respect to a fuzzy measure.