Upper Bounds of Uncertainty for Dempster Combination Rule-Based Evidence Fusion Systems

Quantifying the epistemic uncertainty for static information and dynamic fusion or reasoning processes is still unsolved for various epistemic uncertainty theories. This study focuses on the Dempster-Shafer evidence theory, which is of great ability in representing and fusing uncertain information with imprecision and ignorance on the basis of basic probability assignment (BPA) and Dempster combination rule (DCR). In order to effectively measure and infer the epistemic uncertainty for both static BPAs and dynamic fusion processes, a solution based on plausibility entropy is proposed in this study. At first, four new properties, called grouping, splitting, weighted additivity, and weighted subadditivity, are proved for the first time in this study to strengthen the theoretical foundation of plausibility entropy in measuring the uncertainty associated with a given BPA. Second, the upper bounds of uncertainty are derived for typical BPA-based multisource information fusion systems, including standard DCR, weighted DCR, discounted DCR fusion systems for evidence defined on the same frame of discernment (FOD), and the DCR fusion system for evidence defined on multiple distinct FODs. Several examples are given to illustrate these results.