Interpreting belief functions as probabilities: a new combination rule

Abstract

Dempster and Shafer introduced the belief function to measure someone's degree of beliefs or subjective probabilities. In IFSA'99 and NAFIPS'9, we presented two distinct proofs that a belief function is, in fact, an inner probability using the methods of functional analysis and measure theory respectively. In this paper, we continue the study and derive a new Dempster's rule of combination based on probability theory.