Information fusion based on new proportional conflict redistribution rules

In this paper we propose anew family of fusion rules for the combination of uncertainty and conflicting information. This family of rules is based on new Proportional Conflict Redistributions (PCR) allowing us to deal with highly conflicting sources for static and dynamic fusion applications. Here five PCR rules (PCR1-PCR5) are presented, analyzed and compared through several numerical examples. From PCR1 up to PCR5 one increases in one hand the complexity of the rules, but in other hand one improves the exactitude of the redistribution of conflicting masses. The basic common principle of PCR rules is to redistribute the conflicting mass, after the conjunctive rule has been applied, proportionally with some functions depending on the masses assigned to their corresponding columns in the mass matrix. Alongside of these new five PCR rules, there are infinitely many ways these redistributions (through the choice of the set of weighting factors) can be chosen. PCR1 is equivalent to the weighted average operator (WAO) on Shafer's model only for static fusion problems but these two operators do not preserve the neutral impact of the vacuous belief assignment (VBA). The PCR2-PCR5 rules presented here, preserve the neutral impact of VBA and turn out to be what we consider as reasonable and can serve as alternatives to the hybrid DSm rule. PCR4 is an improvement of minC and Dempster's rules of combination and PCR5 is what we feel is the most exact PCR fusion rule developed up to now. The hybrid DSm rule manages the transfer of the belief committed to the conflict through a simple and direct way while the transfer used within PCR rules is more subtle and complex. The PCR rules can be used also and naturally as new efficient alternatives to the Dempster's rule and its other alternatives already proposed in the Dempster-Shafer theory (DST) over the last twenty years.