Uncertainty modeling using fuzzy measures

We consider the representation of information about the value of an uncertain variable using a monotonic set measure, fuzzy measure. We introduce a number of notable measures that are useful for the representation of this kind of information. We look at the formulation of the concept of entropy in this framework. The Choquet integral is introduced as a tool to help obtain expected value like formulations in the case of measure type uncertainty. It is shown how this can be used in decision making with alternatives having uncertain payoffs. A formulation for the variance associated with measure based uncertain information is provided. The issue of the fusion of multiple pieces of measure-represented information is investigated.