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Grey Relational Analysis Algorithm on Weights in Multi-Attribute Group Decision-making

机译：多属性群决策权重的灰色关联分析算法

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摘要

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.
机译：通常采用客观权重模型与主观权重模型相结合的方法来权衡各种因素，以克服决策者在多属性群体决策中的影响。由于决策信息不完整，根据灰色系统理论，将各专家给出的权重作为不确定的灰度值，提出了一种基于灰色关联分析的组合权重算法。根据专家的比较判断矩阵，得到权重决策矩阵，并构造出正负理想参考序列。然后计算每个专家的正理想参考序列与权重序列之间的灰色关联度，以及每个专家的负理想参考序列与权重序列之间的灰色关联度。随后，通过使每个专家的主观决策偏好最大化的最佳函数来获取专家权重。通过将专家权重与权重决策矩阵相集成，可以获取具有主观和客观信息的权重。最后，通过仿真实例，验证了该方法的合理性和可行性。

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