Evidence theory of exponential possibility distributions

Abstract

This paper studies a certain form of evidence theory using exponential possibility distributions. Because possibility distributions are obtained from an expert knowledge or can be identified from given data, a possibility distribution is regarded as a representation of evidence in this paper. A rule of combination of evidence is given similar to Dempster's rule. Also, the measures of ignorance and fuzziness of evidence are defined by a normality factor and the area of a possibility distribution, respectively. These definitions are similar to those given by G. Shafer and A. Kaufman et al., respectively. Next, marginal and conditional possibilities are discussed from a joint possibility distribution, and it is shown that these three definitions are well matched to each other. Thus, the posterior possibility is derived from the prior possibility in the same form as Bayes' formula. This fact shows the possibility that an information-decision theory can be reconstructed from the viewpoint of possibility distributions. Furthermore, linear systems whose variables are defined by possibility distributions are discussed. Operations of fuzzy vectors defined by multidimensional possibility distributions are well formulated, using the extension principle of L. A. Zadeh.