基于强“奖优罚劣”算子的多指标灰靶决策模型

对多指标灰靶决策模型进行了研究。提出了对三种类型指标进行标准化处理的强“奖优罚劣”算子，相较于原有的线性的“奖优罚劣”算子，这种非线性算子进一步加大标准化后同指标各方案的数据的区分度，从而可以提高决策质量。以各方案靶心距平方和最小为目标建立了优化模型，并使用拉格朗日函数求解来得到各指标权重，并以此为基础构建了灰靶决策模型。最后，以实例说明了基于强“奖优罚劣”算子灰靶决策模型的合理性及算法的有效性。

Multi-attribute decision model of grey target based on majorant operator of “rewarding good and punishing bad”

The multi-attribute decision model of grey targets is studied, a new model of grey target decision making is proposed. First the majorant operator of “rewarding good and punishing bad” is presented, this operator is nonlinear and can increase the difference between the data of the same index and different decision schemes. Then a single-object optimal model is established, which is solved by making the square sum of the off-target distance minimum, and the weight of each index is confirmed by constructing the Lagrangian function. Finally, the feasibleness and effectiveness of the method are proved through an example.