Grey relational analysis algorithm on weights in multi-attribute group decision-making

The method which combines objective weights model with subjective weights model is usually used to weigh the factors to overcome the impacts of decision-makers in the multi-attribute group decision making. Due to the incomplete decision-making information, the weights given by each expert are regarded as the uncertain grey value according to the grey system theory and a combined weights algorithm based on grey relational analysis is proposed. According to the experts´ comparison judgment matrix, the weight decision matrix is gained, and the positive and the negative ideal reference sequences are constructed. Then the grey relational grade between the positive ideal reference sequence and the weight sequence of each expert and that between the negative ideal reference sequence and the weight sequence of each expert are calculated. Subsequently, the expert weights are acquired through an optimal function that maximizes the subjective decision preference of each expert. And the weights that have subjective and objective information are acquired by integrating the expert weights with the weight decision matrix. Finally, with the help of simulation example, the rationality and feasibility of the proposed method are proved.