Admissibility of Possibility Functions and Other Non-Probability Functions inLindley's Extension of the Definetti-Savage Uncertainty Game

摘要

One of the key problems remaining in the design of an expert system--as well asin Artificial Intelligence models in general--is what uncertainty function or measure is most appropriate to use. Should one choose a Dempster-Shafer, fuzzy set, or classical probability approach, among a myriad number of possibilities. The purpose of this paper is twofold: First, to clarify Lindley's extension of the dutch book argument for probability and related functions over the choice of other possible uncertainty functions. Second, to show that Lindley's conclusions concerning the inadmissibility of possibility functions and Dempster-Shafer functions were patently incorrect in general. All of this is accomplished by, one and for all, placing the problem within a rigorous game theoretic setting.