Information-Based Evaluation of Approximation Methods in Dempster-Shafer Theory

Abstract

Complexity of computations, particularly due to large number of focal elements (FEs), in Dempster-Shafer theory (DST) motivates the development of approximation algorithms. Existing approximation methods include efficient algorithm for special hypothesis space, Monte Carlo based techniques, and simplification procedures. In this paper, the quality of the simplification-based approximation algorithms is evaluated using a new information-based comparison methodology. To this end, three structured testbeds are introduced. Each testbed is designed with an eye on a particular form of uncertainty associated with a body of evidence (BoE) in DST, i.e., conflict and non-specificity. Three proposed testbeds along with the classic testbed are utilized to evaluate the accuracy and complexity of existing algorithms. In light of the proposed evaluation methodology, a new approximation method is presented as well. The proposed algorithm has the ability to choose the most informative FEs without being forced to select the FEs with the largest mass function. Comparison of overall qualitative performance of approximation algorithms provides accuracy versus computational time tradeoff to choose an appropriate approximation method in different applications. Moreover, experiments with testbeds indicate that our proposed algorithm enhances the accuracy and computational tractability simultaneously.