Genetic Algorithm Based on a New Similarity for Probabilistic Transformation of Belief Functions

Abstract

Recent studies of alternative probabilistic transformation (PT) in Dempster–Shafer (DS) theory have mainly focused on investigating various schemes for assigning the mass of compound focal elements to each singleton in order to obtain a Bayesian belief function for decision-making problems. In the process of such a transformation, how to precisely evaluate the closeness between the original basic belief assignments (BBAs) and transformed BBAs is important. In this paper, a new aggregation measure is proposed by comprehensively considering the interval distance between BBAs and also the sequence inside the BBAs. Relying on this new measure, we propose a novel multi-objective evolutionary-based probabilistic transformation (MOEPT) thanks to global optimizing capabilities inspired by a genetic algorithm (GA). From the perspective of mathematical theory, convergence analysis of EPT is employed to prove the rationality of the GA used here. Finally, various scenarios in evidence reasoning are presented to evaluate the robustness of EPT.

Keywords

• probabilistic transformation (PT)
• similarity measure
• convergence analysis
• belief functions (BFs)