Analysis and Extension of the Evidential Reasoning Algorithm for Multiple Attribute Decision Analysis with Uncertainty

In multiple attribute decision analysis (MADA) problems, one often needs to deal with assessment information with uncertainty. The evidential reasoning approach is one of the most effective methods to deal with such MADA problems. As kernel of the evidential reasoning approach, an original evidential reasoning (ER) algorithm was firstly proposed by Yang et al, and later they modified the ER algorithm in order to satisfy the proposed four synthesis axioms with which a rational aggregation process needs to satisfy. However, up to present, the essential difference of the two ER algorithms as well as the rationality of the synthesis axioms are still unclear. In this paper, we analyze the ER algorithms in Dempster-Shafer theory (DST) framework and prove that the original ER algorithm follows the reliability discounting and combination scheme, while the modified one follows the importance discounting and combination scheme. Further we reveal that the four synthesis axioms are not valid criteria to check the rationality of one attribute aggregation algorithm. Based on these new findings, an extended ER algorithm is proposed to take into account both the reliability and importance of different attributes, which provides a more general attribute aggregation scheme for MADA with uncertainty. A motorcycle performance assessment problem is examined to illustrate the proposed algorithm.