A New Evidential Reasoning Rule Considering Interval Uncertainty and Perturbation

The evidential reasoning (ER) rule has been widely applied in the multiple attribute decision making (MADM), which makes the decision-making process transparent and credible by using a belief structure. To improve the ability of the ER rule in dealing with the interval uncertainty, a new interval ER (IER) rule is proposed in this article. The interval uncertainty is described as the interval grade in the new frame of discernment (FoD) to model the local ignorance. It is proved that the IER rule is a generalization of the ER rule. To study the influence of perturbation on the IER rule, the perturbation is first introduced to the belief structure, and the perturbation analysis (PA) is conducted for the IER rule. An optimization model is established to estimate the perturbation threshold, which can measure the effectiveness of the inference result under perturbation. Two numerical examples and a case study are carried out, respectively, to show the implementation process of the proposed IER rule and validate its effectiveness in different decision-making scenarios.