Dempster-Shafer Theory and Uncertainty Modeling

Dempster-Shafer theory offers a flexible framework for representing and combining evidence when information is imprecise, incomplete or conflicting. At its core is the frame of discernment, a set of mutually exclusive hypotheses over which basic probability assignments (BPAs) distribute belief mass without requiring full allocation to singletons. Belief and plausibility functions then quantify lower and upper bounds on the probability of each hypothesis, reflecting epistemic uncertainty. Evidence from multiple sources is reconciled via Dempster’s rule of combination, which redistributes conflicting belief and yields a fused BPA. In recent years, scholars have enriched this theory with entropy-based measures—such as Deng entropy—to gauge overall uncertainty and to manage high-conflict scenarios. Extensions address open-world assumptions, dynamic fusion in sensor networks and the dual concept of extropy. Practical applications span fault diagnosis in engineering, decision support in healthcare and environmental monitoring, where robust quantification of uncertainty guides risk-sensitive choices. Global interest has grown in tailoring evidence measures to specific domains, balancing interpretability and computational efficiency in real-time systems.

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Dempster-Shafer Theory and Uncertainty Modeling publication trend

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Technical terms

Frame of discernment: The exhaustive set of hypotheses under consideration in evidence theory.

Basic probability assignment (BPA): A function that allocates belief mass to subsets of the frame of discernment, representing evidence support without requiring precise probabilities.

Belief function: The sum of BPAs of all subsets contained within a hypothesis, indicating the guaranteed support for that hypothesis.

Plausibility function: The sum of BPAs of all subsets that intersect a hypothesis, representing the maximum potential support.

Dempster’s rule of combination: A method for fusing independent BPAs by normalising and reallocating conflicting mass among consistent hypotheses.

Deng entropy: An extension of Shannon entropy for Dempster-Shafer theory that measures uncertainty across the power set of hypotheses based on BPAs.

Negation evidence: Representation of information supporting the complement of a hypothesis, used to quantify and fuse “negative” or counter-evidence.

References

1. A numerical comparative study of uncertainty measures in the Dempster–Shafer evidence theory. Information Sciences (2023).
2. Measuring Uncertainty in the Negation Evidence for Multi-Source Information Fusion. Entropy (2022).
3. A Method to Determine Generalized Basic Probability Assignment in the Open World. Mathematical Problems in Engineering (2016).
4. A Dual Measure of Uncertainty: The Deng Extropy. Entropy (2020).
5. The Maximum Deng Entropy. IEEE Access (2019).