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(DSm T),a derivative of DST.In DSm T,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 DSm T.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 nonexclusive 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.