On measuring uncertainty and uncertainty-based information: Recent developments

It is shown in this paper how the emergence of fuzzy set theory and the theory of monotone measures considerably expanded the framework for formalizing uncertainty and suggested many new types of uncertainty theories. The paper focuses on issues regarding the measurement of the amount of relevant uncertainty (predictive, prescriptive, diagnostic, etc.) in nondeterministic systems formalized in terms of the various uncertainty theories. It is explained how information produced by an action can be measured by the reduction of uncertainty produced by the action. Results regarding measures of uncertainty band uncertainty-based information) in possibility theory, Dempster-Shafer theory, and the various theories of imprecise probabilities are surveyed. The significance of these results in developing sound methodological principles of uncertainty and uncertainty-based information is discussed.