A general evidential reasoning algorithm for multi-attribute decision analysis under interval uncertainty

Evidential reasoning (ER) is one of the important approaches used to solve multi-attribute decision analysis (MADA) problems under uncertainty, involving both quantitative and qualitative attributes. The ER approach provides a distributed modeling framework fusing several types of uncertain and incomplete information, including ignorance and vagueness, to work out the optimum alternative rationally. In this paper, we review the original ER algorithm and recursive interval evidential reasoning (IER) algorithm and derive a general analytical algorithm for IER, thus enabling an aggregation of attributes' assessments in an explicit manner. Then, a more complicated uncertain occasion is investigated, where it is possible to conduct evaluation assessments, including quantitative data, belief degrees, grades, and weights, in the form of an interval. A pair of nonlinear optimization models based on the new algorithm is established to solve this problem under interval uncertainty, and the maximum and minimum expected utilities of each alternative are calculated and ranked accordingly. Additionally, we prove that the original ER and recursive IER algorithms are special cases of the new algorithm. Finally, a numerical example is used to demonstrate the steps involved in the proposed approach.