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
Unique-IP document downloads: 9 times
Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.
Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.