Generalized Evidence Theory (1404.4801v1)

Abstract: 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.

• The paper presents GET, a framework that extends Dempster-Shafer theory by allowing mass assignment to unknown hypotheses under open-world assumptions.
• It introduces a Generalized Basic Probability Assignment and combination rule to effectively recalibrate conflicting evidence in uncertain environments.
• Numerical demonstrations validate GET's flexibility, highlighting its potential for improved decision-making in sensor networks and AI systems.

Generalized Evidence Theory: A Comprehensive Overview

The paper "Generalized Evidence Theory" proposes a novel framework to address conflict management in the field of Dempster-Shafer (DS) evidence theory. The paper introduces a Generalized Evidence Theory (GET), which posits that most real-world scenarios operate under open world assumptions due to inherent uncertainty and incomplete knowledge. This approach marks a significant shift in how conflicting evidence is handled, offering a more rational methodology compared to traditional techniques.

The Theoretical Foundation of GET

The DS theory has been a pivotal instrument in managing uncertainty in information fusion processes. Its ability to capture the imprecise nature of data has garnered extensive academic attention. However, the method often faces challenges when dealing with highly conflicting evidence. Traditional DS theory operates under a closed-world assumption, where the set of hypotheses is exhaustive and complete. GET departs from this premise by allowing for an open-world scenario where incomplete frames of discernment lead to the possibility of assigning belief to the unknown—denoted by $m(\phi) \neq 0$.

Structure and Methodology

GET showcases several defining characteristics that expand beyond the limitations of DS theory:

• Generalized Basic Probability Assignment (GBPA): Unlike the Basic Probability Assignment (BPA) in DS theory, GBPA permits non-zero mass allocations to the empty set (denoted $m(\phi)$), reflecting evidence beyond the scope of known hypotheses.
• Generalized Belief and Plausibility Functions: These extended constructs provide lower and upper bounds on belief, analogous to DS theory but adaptable to the dynamic inclusiveness of GET.
• Generalized Combination Rule (GCR): In GET, conflicting evidence is managed through GCR, which recalibrates the fusion process by assigning probabilities acknowledging potentially unknown factors, as opposed to the strict normalization of DS.

Numerical Demonstrations and Implications

The authors offer several numerical examples demonstrating how GET operates under various scenarios of evidence conflict and completeness of the frame of discernment:

• In cases of high evidence conflict with incomplete discernment, GET handles the assignment of mass to the unknown empty set, providing a stable outcome that reflects real-world uncertainty.
• When applied to traditional complete frames, GET reduces to the classical DS framework but shines in more complex scenarios where the standard DS approach might yield paradoxical results.

The primary implications of this paper for AI and information fusion systems are profound. GET allows for greater flexibility in modeling real-world uncertainty, offering a robust mathematical framework for handling unknown elements that traditional methods might overlook. This adaptability could significantly benefit applications in areas such as sensor networks, decision-making systems, and any domain where the boundaries of belief are continuously explored and expanded.

Future Directions and Theoretical Speculation

As GET matures as a theoretical construct, several avenues for further research emerge. Potential research could delve into the integration of GET with machine learning algorithms, allowing models to incorporate a broader spectrum of evidential reasoning under uncertainty. Additionally, exploring computational efficiencies and scalability for large-scale applications in real-time systems could greatly enhance the practical viability of the methodology.

In conclusion, the Generalized Evidence Theory provides a comprehensive and adaptive approach to evidence fusion in open world scenarios. It refines the understanding of handling uncertainty in complex systems, offering both theoretical insights and practical applications that further enrich the field of artificial intelligence.