A vector and geometry interpretation of basic probability assignment in Dempster-Shafer theory

Because of the superiority in dealing with uncertainty expression, Dempster-Shafer theory (D-S theory) is widely used in decision theory. In D-S theory, the basic probability assignment (BPA) is the basis and core. Recently, some researchers represent BPA on a N-dimension frame of discernment (FOD) as 2 N-dimension vector in Descartes coordinate system. This representation treats a BPA as a point in the 2 N-dimensional space. A new vector and geometry interpretation of BPA is proposed in this paper. The BPA on a N-dimension FOD is represented as N-dimension vector with parameters in this method. Then BPA is expressed as subset of N-dimension Cartesian space rather than a point. The proposed method is a new way to represent BPA with vector and geometry. The essence of this method is to convert BPA to probability distribution with parameters. The applications of this representation method in D-S theory have been studied. Based on this method, problems in D-S theory can be solved, which include the fusion of BPAs, the distance between BPAs, the correspondence between BPA and probability, and the entropy of BPAs.