Generalized combination rule for evidential reasoning approach and Dempster–Shafer theory of evidence

• Published in: Information sciences 2021-02, Vol.547, p.1201-1232
• Main Authors: Du, Yuan-Wei, Zhong, Jiao-Jiao
• Format: Article
• Language: English
• Subjects: Decision analysis; Dempster-Shafer theory of evidence; Evidential reasoning; Generalized combination rule; Weight and reliability
• ISSN: 0020-0255; 1872-6291
• DOI: 10.1016/j.ins.2020.07.072

•Infeasibilities of evidential reasoning (ER) with weight and reliability are analyzed.•Generalized discounting method is defined to discount evidence with two parameters.•Generalized combination (GC) rule is established to make combinations for evidence.•A series of theorems and corollaries of the proposed GC rule are proved.•Comparison and discussion are made with ER and Dempster–Shafer theory of evidence. The Dempster–Shafer (DS) theory of evidence can combine evidence with one parameter. The evidential reasoning (ER) approach is an extension of DS theory that can combine evidence with two parameters (weights and reliabilities). However, it has three infeasible aspects: reliability dependence, unreliability effectiveness, and intergeneration inconsistency. This study aimed to establish a generalized combination (GC) rule with both weight and reliability, where ER and DS can be viewed as two particular cases, and the problems of infeasibility of the parameters can be solved. In this paper, the infeasibilities of ER are analyzed, and a generalized discounting method is introduced to reasonably discount the belief distributions of the evidence using both the weight and the reliability. A GC rule is then constructed to combine evidence by means of the orthogonal sum operation, and the corresponding theorems and corollaries are provided. Finally, the superiority of the GC rule is shown through numerical comparisons and discussion, and an illustrative example is provided to demonstrate its applicability.