基于集对投影寻踪的轨道交通线路决策模型
Decision model of rail transit line based on coupling set pair analysis and projection pursuit

轨道交通线路方案择优指标多为定性指标，且具有多重性、多样性及模糊不确定性与转换不确定性，故轨道交通线路方案优选是一个复杂的多属性决策问题。针对以上特点，探讨联系数理论与投影寻踪理论耦合决策模型，该模型首先基于方案优选指标值，应用联系数概念将方案指标进行同一度处理，以定量描述待选样本与最优方案指标间的关系，进而通过投影寻踪模型综合计算待选方案与理想方案的投影值，以对方案进行优选，最后结合实例验证，并与其他方法进行对比分析。结果表明该方法用于轨道交通线路方案优选是有效可行的，取得了较好结果，且计算过程简单，有效避免了多指标高维数据处理的复杂性，也为类似不确定性问题决策提供了新的参考。
Evaluation indicators for selection of rail transit line scheme index are mostly qualitative indicators with multiple and diversified characteristics, fuzzy and conversion uncertainties, so the rail transit line scheme optimization is a complex multi-attribute decision-making problem. Considering the above characteristics, the decision model coupling connection number theory with the projection pursuit theory was discussed. In this model, based on the index values, the identical degree of the connection number was firstly used to quantitatively describe the relationship between the evaluation scheme and the optimal scheme. And then through the projection pursuit model to calculate the projective value in order to select optimal scheme. Finally a case study and comparison with other methods were conducted to confirm the model proposed. The results show that the selection of optimal rail transit lines scheme based on the model is effective and feasible, and its processing procedure is simple. It can avoid the complexity of multiple index and high-dimensional data processing, and also provides a new reference for the similar uncertainty decision-making problems