Source-linked AI summary
Generalized Evidence Theory
Yong Deng
TL;DR
Conflict management remains an open issue in Dempster-Shafer evidence theory. The paper proposes generalized evidence theory (GET), which handles conflicting evidence under an open-world assumption. GET abandons the strict restriction m(φ) = 0 and is presented as a more reasonable way to explain and deal with conflict.
Problem
Conflict management remains an open issue in Dempster-Shafer evidence theory when evidence conflicts highly.
Method
The paper proposes generalized evidence theory (GET), including generalized evidence, a generalized conflict model, and a generalized combination rule for open-world conflict handling.
Results
GET abandons the strict Dempster-Shafer restriction m(φ) = 0 and handles conflicting evidence under an open-world framework.
Takeaways & Limitations
The paper concludes that GET can explain and deal with conflicting evidence in a more reasonable way.
Takeaways & Limitations
The paper notes that applying the generalized conflict model depends on different conditions, while evidence from different sources must be combined under exclusive conditions.
Abstract
from arXiv · showhide
Conflict management is still an open issue in the application of Dempster Shafer evidence theory. A lot of works have been presented to address this issue. In this paper, a new theory, called as generalized evidence theory (GET), is proposed. Compared with existing methods, GET assumes that the general situation is in open world due to the uncertainty and incomplete knowledge. The conflicting evidence is handled under the framework of GET. It is shown that the new theory can explain and deal with the conflicting evidence in a more reasonable way.
1. Introduction
The introduction frames conflict management as an open issue in Dempster-Shafer evidence theory, arising from unreliable sensors and incomplete open-world knowledge. It motivates generalized evidence theory as a framework for handling such conflicts without the strict closed-world restriction.
- Conflict management remains an open issue when evidence highly conflicts in Dempster-Shafer evidence theory.
- Existing approaches redistribute conflicting mass, average evidence, or replace the conflict coefficient with evidence-distance measures.
- The introduction reports a two-dimensional conflict measure combining the classical conflict coefficient with pignistic betting distance and discusses three adoption cases.
- Evidence conflicts can arise from sensor unreliability caused by disturbances or equipment maintenance conditions.
- Open-world systems create conflict because the available knowledge may be incomplete, such as when an unknown jet-fighter type is absent from the assumed frame.
- The proposed theory develops generalized evidence, generalized evidence distance, a generalized combination rule, and applications under open-world conditions.
2. Preliminaries
The preliminaries define Dempster-Shafer evidence representations, belief and plausibility functions, evidence distances, and conflict measures. They also describe limitations of traditional conflict coefficients and conflict-tolerance thresholds.
- A frame of discernment is a finite nonempty set of mutually exclusive hypotheses, with its power set defining possible focal subsets.
- Mass functions, also called basic probability assignments, map subsets of the frame to values in [0, 1].
- Belief and plausibility functions express lower and upper bounds for the support of a subset.
- Dempster’s combination rule combines two independent BPAs but applies only when their conflict coefficient satisfies K < 1.
- Pignistic probability transformation converts basic probability assignments into probability distributions, enabling pignistic betting distance between BPAs.
- The conflict model combines the classical coefficient K with pignistic betting distance, while the traditional coefficient alone may not efficiently measure disagreement.
- Conflict is identified when both K > ε and difBetP > ε, but ε is subjective because no absolute meaningful threshold satisfies all BPA pairs.
3. The Generalized Theory
GET extends evidence theory to open-world settings by allowing incomplete discernment frames and mass on propositions beyond the known frame. Its generalized combination rule handles conflicting evidence while reducing to established rules in special cases.
- Motivation: GET addresses limitations of Dempster-Shafer theory arising from incomplete discernment frames, high conflict, and computational complexity.The paper motivates a model that represents incomplete frames while keeping complexity no larger than traditional Dempster-Shafer theory.
- Open-world assumption: In GET, the general setting is open world, so the frame may omit unknown targets or other propositions beyond its listed elements.The paper illustrates this with a possible undeclared target d absent from the frame {a, b, c}.
- Basic concepts: GET represents propositions outside the discernment frame through φ, which is not the ordinary empty set and may receive nonzero mass.The generalized mass function can assign probability to focal elements beyond the given frame.
- Basic concepts: Generalized belief and plausibility functions extend their traditional counterparts, while reducing to them when m(φ)=0.The examples show matching generalized and traditional values when no mass is assigned to φ, and explicit φ mass when the frame is incomplete.
- Generalized combination rule: When m(φ)=0, GCR degenerates to Dempster’s rule; with singleton assignments it matches Bayesian combination, while remaining commutative and associative.These properties make the combination result independent of the order in which evidence is combined.
- Application of GCR: The application examples argue that highly conflicting, mutually unsupported GBPAs indicate an incomplete discernment frame rather than requiring traditional Dempster combination.The paper reports m(φ)=0.56+0.44=1 in one such situation and states that traditional Dempster’s rule is unsuitable.
4. Application and Discussion
GET extends Dempster-Shafer evidence theory to open-world settings by permitting m(φ) ≠ 0 and introduces conflict measures that distinguish incomplete from complete frames of discernment. Numerical examples show when generalized conflict coefficients or generalized evidence distance should primarily measure conflict.
- 4.1. The m(φ) in Dempster-Shafer evidence and GET: GET permits m(φ) ≠ 0 during generalized basic probability assignment generation, representing propositions beyond the fixed frame and the frame’s open-world degree.This contrasts with the restriction m(φ) = 0 in traditional Dempster-Shafer evidence theory.
- 4.1. The m(φ) in Dempster-Shafer evidence and GET: GET extends classic Dempster-Shafer theory to express and handle more uncertain information in an open world rather than a close world.
- 4.2. Modified Liu’s conflict model: Liu’s model can classify evidence with K = 0 and difBetP = 0 as non-conflicting even when the two BPAs provide different information and one is more definite.
- 4.2. Modified Liu’s conflict model: The modified conflict model combines the classic conflict coefficient with an evidence-distance measure because pignistic betting distance cannot distinguish equal probabilities from total ignorance.The paper proposes a modified evidence conflict model based on Jousselme’s evidence distance.
- 4.3. Conflict model of GET: In numerical examples, increasing m(φ) or decreasing support for a proposition gradually increases generalized conflict, while m(φ) = 1 in either GBPA makes the coefficient equal 1.When both GBPAs fully support {a} and m(φ) = 0, the generalized conflict coefficient is smallest.
- 4.3. Conflict model of GET: For complete frames, generalized evidence distance changes with the altered subset while the classic coefficient remains 0.6, so evidence distance measures conflict more effectively in that case.
5. Conclusions
The paper proposes generalized evidence theory (GET) to extend Dempster-Shafer theory from closed-world to open-world reasoning. GET retains the existing framework while introducing generalized combination and conflict models for incomplete discernment frames and conflicting evidence.
- 5. Conclusions: GET abandons the strict restriction m(φ) = 0 and thereby extends Dempster-Shafer theory from closed-world to open-world applications.When the discernment frame is complete and m(φ) = 0, GET degenerates to Dempster-Shafer theory.
- 5. Conclusions: GET treats φ as an unknown element rather than merely an empty set, allowing uncertain information to be represented in an open world.The paper states that φ has the properties of other elements within GET.
- 5. Conclusions: The generalized combination rule (GCR) is provided within GET, with a distinction from the Dempster combination rule.
- 5. Conclusions: GET supplies a generalized conflict model that is applied differently according to whether the discernment frame is incomplete or complete.For incomplete frames, generalized conflict coefficients are emphasized; for complete frames, evidence distance is emphasized.
- 5. Conclusions: The paper identifies mutual exclusivity as an additional limitation of classical evidence theory and relates GET and D numbers theory to more flexible uncertainty handling.D numbers theory focuses on mutual exclusion, while both approaches generalize evidence theory for real-world uncertainty.