Extended Dempster-Shafer combination rules based on random set theory

The Dempster combination rule has been widely discussed and used 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 some of its counterintuitive behavior and restrictive requirements, such as independence of the confidence degrees from disparate sources. To clarify the theoretical foundation of the Dempster combination rule and provide a direction as how to solve these problems, the Dempster combination rule is formulated based on the 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. The optimal Bayes combination rule is given finally.