Premium
A vector and geometry interpretation of basic probability assignment in Dempster‐Shafer theory
Author(s) -
Luo Ziyuan,
Deng Yong
Publication year - 2020
Publication title -
international journal of intelligent systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.291
H-Index - 87
eISSN - 1098-111X
pISSN - 0884-8173
DOI - 10.1002/int.22231
Subject(s) - dimension (graph theory) , mathematics , discernment , vector space , interpretation (philosophy) , entropy (arrow of time) , point (geometry) , probability distribution , cartesian coordinate system , space (punctuation) , unit vector , algorithm , calculus (dental) , computer science , geometry , pure mathematics , statistics , medicine , philosophy , physics , dentistry , epistemology , quantum mechanics , programming language , operating system
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.