On the normalization of fuzzy belief structures

AbstractThe issue of normalization in the fuzzy Dempster-Shafer theory of evidence is investigated. We suggest a normalization procedure called smooth normalization. It is shown that this procedure is a generalization of the usual Dempster normalization procedure. We also show that the usual process of normalizing an individual subnormal fuzzy subset by proportionally increasing the membership grades until the maximum membership grade is one is a special case of this smooth normalization process and in turn closely related to the Dempster normalization process. We look an alternative normalization process in the fuzzy Dempster-Shafer environment based on adding to the membership grade of subnormal focal elements the amount by which the fuzzy subset is subnormal