Abstract: For comprehensive determining indexes’ weight of the multi-attribute decision-making, the article proposes a method considering prior subjective information and objective information into constraints from the angle of the association to estimate the indexes’ synthesis weight. Based on solving the objective weight using the grey correlation deep coefficient on the actual decision problem, this paper focuses on building the subjective constraint condition constructed with the potential ratio of index weight confirmed by specialist which confirm that the subjective and objective factors can be reflected simultaneously in the constraint conditions of the optimization model. The maximum entropy optimization model is built to ensure the credibility of the weight judgment, thus establishing the maximum entropy optimization model for synthesis weights. This method overcomes the uncertainty of weight because of the subjective and objective parameter selection when the subjective and objective conditions are directly grouped through the linear objective function. Finally, comparison with another methods based on a numerical example shows a better effectiveness and practicability of this method.

Key words: grey correlation analysis, synthesis weight, maximum entropy, particle swarm optimization