¹School of Naval Architecture, Ocean and Civil Engineering, Shanghai JiaoTong University, Shanghai, China
²Navy Submarine Academy, Qingdao, Shandong, China

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Abstract—Due to having the explicit evidential reasoning (ER) aggregation function, the analytical ER algorithm has been extensively applied to decision problems under uncertainty. However, there are some different opinions to the validity of the analytical ER algorithm. In this paper, a new method is proposed for proving the equivalence between the recursive and analytical ER algorithms, in such a way that is different from and, it is believed, more rigorous than that of Wang et al (2006). The new method is based directly on Dempster-Shafer’s combination rule and mathematics induction principle. It allows to consider simultaneously the combination and normalization of evidence. In addition, the iterative relationship of the normalization factors between two algorithms is derived. The paper further demonstrates the validity of the analytical ER algorithm theoretically and clarifies the relationship between the recursive and analytical ER algorithms.

Index Terms—Dempster-Shafer theory; combination and normalization of evidence; multiple attribute decision analysis; evidential reasoning approach.

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Cite: Xinning Wang, "Equivalence between Recursive and Analytical Evidential Reasoning Algorithms," Journal of Software vol. 8, no. 3, pp. 754-759, 2013.