An ECR-PCR rule for fusion of evidences defined on a non-exclusive framework of discernment

In the research of uncertain information processing, Dempster-Shafer Theory (DST) provides a framework for dealing with uncertain information, where evidence is defined on a Frame of Discernment (FOD) consisting of mutually exclusive elements. However, the requirement of exclusiveness on FOD sometimes is not satisfied, as shown in Dezert-Smarandache Theory(DSmT), a derivative of DST. In DSmT, the non-exclusiveness is expressed by propositions’ intersection and the fusion of evidence is realized through a Proportional Conflict Redistribution (PCR) rule. In order to handle non-exclusive FODs, a new framework called D Number Theory (DNT) has been proposed recently, which quantifies the non-exclusive degree between propositions different from DSmT. In previous studies, an Exclusive Conflict Redistribution (ECR) rule has been designed in DNT to implement the fusion of evidence defined on a non-exclusive FOD, but there are some deficiencies in the ECR rule. In this paper, a new rule called ECR-PCR rule is proposed by combining the ECR and PCR rules to better implement the fusion of evidence defined on a non-exclusive FOD. Within the proposed rule, the definition of conflict utilizes the idea of ECR's exclusive conflict, and the disposal of conflict is following the idea of PCR's proportional redistribution. Properties of the ECR-PCR rule are presented. The effectiveness of the proposed new rule is verified through numerical examples and applications, in comparison with other fusion methods.