Decision Making Model and Method Based on Distance Measure Between Interval Numbers in Railway Location
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摘要: 为了研究铁路选线方案决策中定量指标与定性指标难以综合评价的系统量化问题，引入区间数理论，建立了基于区间数距离的铁路线路方案决策优化模型. 首先将选线方案中的定量和定性指标转化为区间数，得到区间数决策矩阵；然后对决策矩阵进行规范化处理得到规范化区间数决策矩阵；接着利用区间数距离法计算评价指标的权重，构造加权规范化决策矩阵；再基于加权规范化决策矩阵，利用区间数距离对决策方案排序择优，得出综合比选结果；最后结合工程比选实例验证了模型的作业程式. 结果研究表明：该模型在将含有不确定性信息的定性指标进行量化时，比传统的AHP方法可减少主观原因对决策结果的影响，尤其是指标权重的计算结果更可靠；在进行决策方案排序择优时比利用传统的投影法计算更为简便.Abstract: In order to solve the problem that quantitative and qualitative indexes are difficult to be unified into comprehensive fuzzy assessment of railway location selection, the theory of interval numbers is introduced to build a fuzzy optimal selection model based on distance measure between interval numbers. First, the quantitative and qualitative indexes in railway location schemes are transformed into interval numbers to obtain an interval number decision matrix, which is then normalized into a normalized interval number decision matrix. Second, weights of evaluation indexes are calculated by the distance measure between interval numbers and a weighted normalization decision matrix is obtained. On the basis of the weighted normalization decision matrix, the railway location schemes are ranked by the distance measure between interval numbers and the optimal scheme is selected. Finally, an engineering example of railway location selection was used to illustrate the operation procedure. The results prove that compared with the traditional analytic hierarchy process (AHP) method, this model can reduce the influence of subjective reasons on decision results in quantifying qualitative indexes with uncertainty; especially, the calculation results of index weights are more reliable. In addition, the proposed method is more convenient than the traditional projection method for priority ranking of alternative solutions.
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表 1 语言标度与区间数的转换
Table 1. Transformation between linguistic scale and interval number
语言标度 区间数 语言标度 区间数 极差或极小 [0，1.0] 较好或较大 (5.5，7.0] 很差或很小 (1.0，2.0] 好或大 (7.0，8.0] 差或小 (2.0，3.0] 很好或很大 (8.0，9.0] 较差或较小 (3.0，4.5] 极好或极大 (9.0，10.0] 一般 (4.5，5.5] 
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表 2 铁路选线方案评价指标体系
Table 2. Evaluation index system of railway route selection
宏观指标 微观指标 指标特点 指标作用 技术可行性 线路长度 定量指标 成本型指标 拆迁建筑物数量 征地量 土石方工程量 桥隧总长 经济合理性 土建工程总投资费 定量指标 成本型指标 与列车有关的运营费 施工及环境影响 对沿线生态环境影响 定性指标 成本型指标 对沿线历史名胜影响 交通设施对施工影响 不良地质条件对工程影响 社会政治经济意义 吸引客货流能力 定性指标 效益型指标 对城市规划布局影响 改善铁路网布局意义 满足地方需求能力
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表 3 线路方案及其评价指标取值
Table 3. Index values of alternative routes
评价指标 沿雅鲁藏布
江方案D1沿尼洋河
方案D2线路长度/km 426.94 398.8 桥隧总长/km 277.166 270.289 征地量/m2 10 797 306.5 16 279 工程总投资/亿元 316.39 302.65 交通设施对施工影响 较大 较小 不良地质条件对工程影响 一般 较大 改善铁路网布局意义 较大 一般 满足地方需求能力 较好 一般
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