Generalized evidence theory

Dempster-Shafer evidence theory is an efficient tool in knowledge reasoning and decision-making under uncertain environments. Conflict management is an open issue in Dempster-Shafer evidence theory. In past decades, a large amount of research has been conducted on this issue. In this paper, we propose a new theory called generalized evidence theory (GET). In comparison with classical evidence theory, GET addresses conflict management in an open world, where the frame of discernment is incomplete because of uncertainty and incomplete knowledge. Within the presented GET, we define a novel concept called generalized basic probability assignment (GBPA) to model uncertain information, and provide a generalized combination rule (GCR) for the combination of GBPAs, and build a generalized conflict model to measure conflict among evidences. Conflicting evidence can be effectively handled using the GET framework. We present many numerical examples that demonstrate that the proposed GET can explain and deal with conflicting evidence more reasonably than existing methods.