Handling of Dependence in Dempster–Shafer Theory

Dempster's rule of combination can only be used when the bodies of evidence are assumed to be independent. However, such an assumption is often unrealistic. This paper proposes a systematic approach to handle dependence in evidence theory. It includes both the representation of dependence among information sources and the aggregation of the dependent evidence. For the representation of the dependence, the proposed methodology is able to capture both inner dependence (i.e., dependence among features of a system) and outer dependence (i.e., dependence among the evidence sources during the information propagating and evaluating process). We suggest dealing with the inner dependence by applying the analytic network process model, and modeling the outer dependence based on the intersection situations of the identified influencing factors. Then for the combination of dependent evidence, the strategy is to use discounting aggregation where the discounting coefficients are related to the degree of both outer and inner dependence. The discounting operator helps reduce the duplicate calculations in the fusion of dependent evidence and relax the assumption of independence when using Dempster's rule. A case study of transportation project evaluation is used to illustrate the proposed methodology.