Generalizing the Dempster-Schafer theory to fuzzy sets

A generalization of the Dempster-Schafer (D-S) theory to deal with fuzzy sets is described in which the belief and plausibility functions are treated as lower and upper probabilities. It is shown that computing the degree of belief in a hypothesis in the D-S theory can be formulated as an optimization problem. The extended belief function is thus obtained by generalizing the objective function and the constraints of the optimization problem. To combine bodies of evidence that may contain vague information, Dempster´s rule (1967) is extended by (1) combining generalized compatibility relations based on the possibility theory, and (2) normalizing combination results to account for partially conflicting evidence. The generalization not only extends the application of the D-S theory but also illustrates a way that probability theory and fuzzy set theory can be integrated in a sound manner in order to deal with different kinds of uncertain information in intelligent systems