Comparison of specificity and information for fuzzy domains

This paper demonstrates how an integrated theory can be built on the foundation of possibility theory. Information and uncertainty were considered in 'fuzzy' literature since 1982. Our departing point is the model proposed by Klir for the discrete case. It was elaborated axiomatically by Ramer, who also introduced the continuous model. Specificity as a numerical function was considered mostly within Dempster-Shafer evidence theory. An explicity definition was given first by Yager, who has also introduced it in the context of possibility theory. Axiomatic approach and the continuous model have been developed very recently by Ramer and Yager. They also establish a close analytical correspondence between specificity and information. In literature to date, specificity and uncertainty are defined only for the discrete finite domains, with a sole exception. Our presentation removes these limitations. We define specificity measures for arbitrary measurable domains

Decision-Making with Belief Functions: a Review

Approaches to decision-making under uncertainty in the belief function framework are reviewed. Most methods are shown to blend criteria for decision under ignorance with the maximum expected utility principle of Bayesian decision theory. A distinction is made between methods that construct a complete preference relation among acts, and those that allow incomparability of some acts due to lack of information. Methods developed in the imprecise probability framework are applicable in the Dempster-Shafer context and are also reviewed. Shafer's constructive decision theory, which substitutes the notion of goal for that of utility, is described and contrasted with other approaches. The paper ends by pointing out the need to carry out deeper investigation of fundamental issues related to decision-making with belief functions and to assess the descriptive, normative and prescriptive values of the different approaches