Comonotonic Random Sets and Its Additivity of Choquet Integrals

Abstract

In this paper, we propose a concept of comonotonicity of random sets, which is a set inclusion relation and generalized notion of comonotonicity of real-valued random variables. Then we study some elementary properties of comonotonicity of random sets and comonotonic additivity of real-valued Choquet integral for random set mappings. After this, some other properties of this kind of real-valued Choquet integral for random set mappings are characterized by the comonotonic additivity, for instance, translation invariance, sup-norm continuous, positive homogeneity.