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 Ndimension frame of discernment (FOD) as 2^N-dimension vector in Descartes coordinate system. However, the concept of orthogonality in this method is confused and inexplicable. A new representation method of BPA is proposed in this paper. The BPA on a N-dimension FOD is represented as Ndimension vector with parameters in this method. Then BPA is expressed as subset of N-dimension Cartesian space. The essence of this method is to convert BPA to probability distribution (PD) with parameters. 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. This representation conforms to the definition of orthogonality, and can get satisfactory computing results.
Comments: 24 Pages.
[v1] 2018-11-29 12:40:00
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