How to Improve Dempster's Combination Rule from Point of View of Random Set Framework

The Dempster's combination rule has been widely used recently since it is a convenient and promising method to combine multi-source information with their own confidence degrees/evidences. On the other hand, it has been criticized and debated upon its some counterintuitive behavior and too restrictive requirements. To clarify the theoretical essence of the Dempster's combination rule and provide a direction to solve these problems, the Dempster's combination rule is formulated based on random set theory first. Then, under this framework, all possible combination rules are presented, and these combination rules based on correlated sensor confidence degrees (evidence supports) are proposed. Finally, the optimal Bayes combination rule can be given whenever all necessary priori conditions are available