Deriving coordinated experts’ weights based on sequential quadratic programming algorithm for multi-attribute group decision making

When evaluating the closeness between the decision matrix given by each expert and the overall decision matrix, we should pay more attention to the consistency of the ranking of candidates rather than the deviation degree of the scoring size. Therefore, in this paper, the modified cosine distance measure, instead of the Euclidean distance measure, is used to calculate the proximity between each expert decision matrix and the overall decision matrix. Furthermore, in order to receive more reasonable weights of experts, a new definition of coordinated expert weights in an optimization way is proposed. And then, the sequential quadratic programming (SQP) algorithm is used to derive the coordinated weights of experts, which is not affected by the selection of the initial value of expert weights and can objectively reflect the scoring level of each expert. Since different sorting methods would have inconsistent sorting results, a combined method based on SQP algorithm to derive the coordinated weights of different sorting methods is proposed to promote the ability of ranking the alternatives. Finally, numerical experiments are used to demonstrate the effectiveness of the SQP algorithm to derive coordinated expert weights with the modified cosine distance measure and the superiority of the combined method to rank alternatives.