A Simple Proportional Conflict Redistribution Rule
  One proposes a first alternative rule of combination to WAO (Weighted Average
Operator) proposed recently by Josang, Daniel and Vannoorenberghe, called
Proportional Conflict Redistribution rule (denoted PCR1). PCR1 and WAO are
particular cases of WO (the Weighted Operator) because the conflicting mass is
redistributed with respect to some weighting factors. In this first PCR rule,
the proportionalization is done for each non-empty set with respect to the
non-zero sum of its corresponding mass matrix - instead of its mass column
average as in WAO, but the results are the same as Ph. Smets has pointed out.
Also, we extend WAO (which herein gives no solution) for the degenerate case
when all column sums of all non-empty sets are zero, and then the conflicting
mass is transferred to the non-empty disjunctive form of all non-empty sets
together; but if this disjunctive form happens to be empty, then one considers
an open world (i.e. the frame of discernment might contain new hypotheses) and
thus all conflicting mass is transferred to the empty set. In addition to WAO,
we propose a general formula for PCR1 (WAO for non-degenerate cases).
