Iterative Approximation of Basic Belief Assignment Based on Distance of Evidence.

Area of Science:

• Artificial Intelligence
• Information Theory
• Decision Theory

Background:

• Approximating basic belief assignments (BBAs) is crucial for managing computational complexity in belief function theory, especially with numerous focal elements.
• Traditional BBA approximation methods often rely on focal element characteristics like mass assignment and cardinality, potentially impacting information accuracy.
• Evaluating BBA approximation involves considering both computational efficiency and the information loss, measured by the distance between original and approximated BBAs.

Purpose of the Study:

• To propose a novel iterative BBA approximation approach that minimizes the distance between successive approximations.
• To enhance the efficiency and rationality of BBA approximation techniques in belief function theory.
• To provide a comprehensive evaluation of the proposed method against traditional approaches.

Main Methods:

• An iterative approximation algorithm is developed, removing one focal element per iteration based on maximizing closeness (minimizing distance) between successive BBAs.
• The iteration continues until a predefined number of focal elements is achieved.
• Performance evaluation employs time-based, closeness-based, and newly proposed metrics to compare approximation methods.

Main Results:

• Experimental results demonstrate the rationality and efficiency of the proposed iterative BBA approximation method.
• The new approach effectively reduces computational cost while minimizing information loss compared to traditional methods.
• Comparative analyses validate the superiority of the proposed closeness-based iterative strategy.

Conclusions:

• The proposed iterative BBA approximation method offers a significant improvement in computational efficiency and information preservation.
• This approach provides a more rational and effective way to handle complex BBAs in belief function applications.
• The findings contribute to advancing approximation techniques within the theory of belief functions.