Basic frame of generalized evidence theory

The basic assumption of classical Dempster-Shafer theory of evidence is that the frame of discernment is complete. However, the frame of discernment is often incomplete in real data fusion application systems. A generalized evidence theory (GET) is proposed to solve this problem in this paper. The generalized basic probability assignment (GBPA) is defined. The value assigned to the empty set shows the support degree to incomplete frame of discernment. A new combination rule, called generalized combination rule (GCR), is proposed to handle evidence combination. It is shown that the proposed combination rule satisfies both commutative law and associative law. Another desirable property of the proposed GET is that it will be reduced as the classical evidence theory when the GBPA to empty set is zero. Some numerical examples are used to show the efficiency of the proposed GET.