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Negation of Belief Function Based on the Total Uncertainty Measure
1School of Computer and Information Science, Southwest University, No. 2 Tiansheng Road, BeiBei District, Chongqing 400715, China.
Entropy (Basel, Switzerland)
|December 3, 2020
Summary
This study introduces a novel negation method for basic probability assignment (BPA), addressing open issues in information representation. The new method reassigns BPA based on total uncertainty, offering a more robust approach than traditional probability negation.
Area of Science:
- Information Theory
- Decision Making
- Mathematical Foundations
Background:
- The negation of probability offers novel information representation methods.
- Negating basic probability assignment (BPA) remains an unresolved challenge in the field.
- Existing methods for negating probability distributions do not directly apply to BPAs.
Purpose of the Study:
- To propose a novel method for negating basic probability assignments (BPAs).
- To develop a negation technique for BPAs grounded in the concept of total uncertainty.
- To provide a mathematically sound method for BPA negation that accounts for non-singleton elements.
Main Methods:
- A new negation method for basic probability assignment (BPA) is proposed.
- The method is based on a total uncertainty measure.
- It considers the uncertainty of non-singleton elements within the power set.
- BPA reassignment is weighted by the cardinality of the intersection between elements.
Main Results:
- The proposed negation method for BPA is mathematically proven to be based on maximum uncertainty.
- This novel BPA negation method reduces to the negation of a probability distribution when the BPA simplifies to classical probability.
- The method effectively handles the negation of uncertain information within the BPA framework.
Conclusions:
- The developed negation method provides a robust solution for negating basic probability assignments.
- This approach enhances information representation by addressing the negation of uncertain information.
- The method's mathematical foundation in maximum uncertainty ensures its validity and applicability.
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