Analytical generalized combination rule for evidence fusion

The core of evidence theory is the combination algorithm, which can be divided into two categories: the recursive combination algorithm and the analytical combination algorithm. While the former has been extensively developed, its calculation process requires constant iterations, which makes it difficult to use in certain situations, such as problem optimization. The latter can obtain the final fusion result through one-step calculation; however, it has attracted little attention, and there are still some limitations to be overcome, such as its neglects of reliability and poor handling of local ignorance. This study constructs an analytical generalized combination (AGC) rule for evidence. We propose an AGC rule as an analytical form without iteration to directly fuse multiple pieces of evidence with both weight and reliability. A series of theorems and corollaries are established to demonstrate its effectiveness. We analyze the properties of the AGC rule by clarifying its relationship with existing analytical combination algorithms (i.e., the analytical ER rule and general analytical interval ER algorithm), both shown to be specific cases of the AGC rule. Finally, we demonstrate the proposed AGC rule's practicality and effectiveness using an illustrative example and comparative analysis. The AGC rule has the following advantages of both the analytical algorithm and the generalized combination rule: (1) the fusion result is obtained through a single computational step, (2) weight and reliability are both considered in evidence fusion, and (3) various forms of local ignorance can be handled in the evidence fusion.