Uncertainty Modeling and Evidence Combination: DST and DSmT in Perspective

Abstract

Dempster-Shafer Theory (DST) and Dezert-Smarandache Theory (DSmT) are prominent frameworks within evidence theory for managing uncertainty and fusing information. While both utilize basic belief assignments (BBAs) on sets of hypotheses, they diverge critically in their foundational mathematical assumptions and conflict handling. This article provides a comprehensive comparison, detailing the philosophical and practical shift from DST to its generalized superset, DSmT. DST is built upon the power set 2^Θ of a mutually exclusive frame of discernment, forcing conflict to be resolved via global normalization (Dempster's Rule), which can lead to counter-intuitive results in high-conflict scenarios (e.g., Zadeh's paradox). DSmT, conversely, operates on the hyper-power set D^Θ of an exhaustive but non-exclusive frame, allowing for the representation of vague, paradoxical, or overlapping concepts (e.g., A∩B). Crucially, DSmT employs the Proportional Conflict Redistribution (PCR) family of rules, which resolves disagreement by locally redistributing conflicting mass back only to the propositions that generated it. This mechanism ensures stability and interpretability, even under extreme conflict. We analyze the trade-offs in expressiveness and computational cost, illustrating that the choice between the two theories hinges on two core factors: the expected level of conflict and the degree of conceptual overlap in the problem domain. Ultimately, DSmT is demonstrated to fully encompass DST, functioning as a robust, flexible alternative for modern multi-sensor fusion, intelligence analysis, and decision-making systems characterized by ambiguity and high disagreement.