Evidence theory of normal possibility and its application

The authors construct a framework of evidence theory by normal possibility distributions defined as exponential functions. A possibility distribution is regarded as an evidence. A rule of combination of evidences is given with the same concept as Dempster´s rule (see A. P. Dempster, 1967). Also, measures of ignorance and fuzziness of an evidence are defined by a normality factor and an area of a possibility distribution, respectively. Marginal and conditional possibilities are defined 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´s formula. Operations of fuzzy vectors defined by multidimensional possibility distributions are well formulated. Comments on an application of possibility distributions are given for discriminant analysis using fuzzy if-then rules