On Non-additive Probabilistic Inequalities of Hölder-type

Abstract

Non-additive measure is a generalization of additive probability measure. Integral inequalities play important roles in classical probability and measure theory. Some well-known inequalities such as the Minkowski inequality and the Holder inequality play important roles not only in the theoretical area but also in application. Non-additive integrals are useful tools in several theoretical and applied statistics which have been built on non-additive measure. For instance, in decision theory and applied statistics, the use of the non-additive integrals can be envisaged from two points of view: decision under uncertainty and multi-criteria decision-making. In fact, the non-additive integrals provide useful tools in many problems in engineering and social choice where the aggregation of data is required. In this paper, Holder and Minkowski type inequalities for semi(co)normed non-additive integrals are discussed. The main results of this paper generalize some previous results obtained by the authors.