| The Dempster-Shafer (D-S) theory of evidence has attracted much attention in AI community in recent years because it suggests a coherent approach, which is sometimes called evidential reasoning, to aggregate evidence bearing on hypothesis groups in expert systems. However, there are two major difficulties in applications of the theory: (1) The certainty degrees of rules are difficult to represent. (2) The theory can not handle evidence bearing on vague concepts. To overcome these difficulties, I made two extensions to the D-S theory for its application to reasoning in expert systems.; In our first extension, the multivalued mapping in the D-S theory is extended to a probabilistic one to represent rules' certainty degrees. Dempster's rule is then modified to combine belief update rather than absolute belief. The result is consistent with Bayes' theorem and is justified with conditional independence assumptions that are weaker than those of PROSPECTOR and MYCIN.; In the second extension, we formulate the D-S theory as an optimization problem where a basic probability assignment (bpa) constrains the underlying probability distributions. We first define the probabilistic constraints imposed by a fuzzy bpa. Lower and upper probability of a fuzzy set are, then, obtained by maximizing or minimizing probability of the set. The optimization problem is partitioned into subproblems, which are solved using a linear time algorithm.; By implementing a prototype expert system that diagnoses rheumatoid arthritis using the knowledge base of CADIAG-2, we explore the issues related to applications of the extended D-S theory in expert systems. In addition to rules and hypotheses, the system's knowledge base contains frames, which represent frames of discernment in the D-S theory. For a better explanation capabilities, we explicitly stores the roles of rules and the class relationships among hypotheses. With these modifications, the system demonstrates the application of our work to reasoning in expert systems. |
