An evidential reasoning approach based on criterion reliability and solution reliability. (February 2019) - Fu, Chao; Chang, Wenjun; Xu, Dongling; Yang, Shanlin
Highlights: An approach based on criterion reliability and solution reliability is proposed. Criterion reliabilities are estimated by following a regression idea. The monotonicity of solution reliability with respect to its parameter is proven. Superior intensity is maximized to compare alternatives with the same best ranking. A problem of evaluating environmental protection ways is analyzed. Abstract: In multiple criteria decision making (MCDM), the degree to which the individual assessment of alternative course of action on a criterion correctly portrays the overall assessment is rarely considered, which is understood as the reliability of the criterion. Meanwhile, the large superior intensity of each alternative in a solution is preferred by a decision maker, which is understood as the reliability of the solution. This paper proposes a new evidential reasoning approach for multiple criteria decision making that can consider criterion reliability and also provide high solution reliability. The reliability of each criterion is generated using a decision matrix on the assumption that criterion weights are allowed to be perturbed to help minimize the maximum difference between the true value of criterion reliability and its estimate. Under this assumption, the post-optimal solution space of weight and reliability variables of criteria is found, within which the maximum solution reliability is determined. Under the conditions where the maximum solution reliability within the post-optimal solution space is ensured, a comparison between alternatives is made using their best rankings and superior intensity successively to generate solutions to MCDM problems. A problem of evaluating environmental protection ways for a company located in Tongling of Anhui Province of China is investigated using the proposed approach to demonstrate its validity and applicability. These are highlighted by the comparison of the proposed approach with two other commonly used methods.