Combining beliefs

• We have the ability to assign M to a set of hypotheses.
• To combine multiple sources of evidence to a single (or multiple) hypothesis do the following:
  • Suppose and are two belief functions.
  • Let X be the set set of subsets of to which assigns a nonzero value and letY be a similar set for
  • Then to get a new belief function from the combination of beliefs in and we do:

    
    
    

    whenever .

    NOTE: We define to be 0 so that the orthogonal sum remains a basic probability assignment.