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A modified belief entropy in Dempster-Shafer framework
Deyun Zhou1, Yongchuan Tang1, Wen Jiang1
1School of Electronics and Information, Northwestern Polytechnical University, Xi'an, Shaanxi, China.
Plos One
|May 9, 2017
Summary
Quantifying uncertainty in Dempster-Shafer evidence theory is improved by a new belief entropy. This method considers the frame of discernment (FOD) scale, enhancing uncertainty quantification efficiency.
Area of Science:
- Artificial Intelligence
- Information Theory
- Decision Support Systems
Background:
- Quantifying uncertainty within Dempster-Shafer evidence theory remains a challenge.
- Existing uncertainty measures often overlook the scale of the frame of discernment (FOD).
- This oversight limits the efficiency of current methods by not fully utilizing available evidence.
Purpose of the Study:
- To propose a novel belief entropy measure for Dempster-Shafer evidence theory.
- To incorporate the scale of the frame of discernment (FOD) and relative focal element scale into uncertainty quantification.
- To develop a more efficient and informative uncertainty measure.
Main Methods:
- A modified belief entropy is proposed, considering the FOD scale and relative scale of focal elements.
- The new measure is inspired by Deng entropy, ensuring consistency with Shannon entropy for probability.
- Numerical examples and a case study are used for validation.
Main Results:
- The proposed belief entropy effectively quantifies uncertain information by including FOD scale.
- The new measure demonstrates consistency with Shannon entropy, aligning with probabilistic interpretations.
- It shows reduced information loss compared to other existing uncertainty measures.
Conclusions:
- The novel belief entropy offers a superior method for quantifying uncertainty in Dempster-Shafer theory.
- By considering FOD scale, the method enhances efficiency and reduces information loss.
- This approach provides a more comprehensive understanding of uncertain information in evidence theory.
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