基于集对分析联系数的区间数型多属性决策投影模型及其在基坑支护方案评价中的应用

A Projection Model for Intervals Multi-Attribute Decision Making Based on Connection Number of Set Pair Analysis and Its Application in Evaluation of Supporting Schemes for Foundation Pit

多属性决策时因掌握的信息有限,加之问题本身的复杂性、不确定性以及人类思维的模糊性,其属性的精确值往往难以获取,常用区间数形式表示针对多属性决策中各指标区间数不能直接进行大小比较的问题,提出一种基于集对分析联系数的区间数型多属性决策投影模型.模型用备择方案在理想方案上的投影进行集结,根据区间数的误差分布形式,沟通区间数与联系数的关系,根据a+bi型联系数大小比较法则,综合评价方案优劣.以某大厦基坑支护拟用的4种方案优化选择为例,说明方法的应用与模糊优化理论模型和灰色物元分析优化模型进行了对比,得到的结果一致.

Due to limited information obtained,and its complicacy,uncertainty and the fuzziness of human thinking in multi-attribute decision making,precision values of these attributes which would normally be inaccessible is often represented as interval numbers.With respect to problems in which the intervals for index would be not directly comparable in multi-attribute decision making,a projection model for intervals multi-attribute decision making based on connection number of set pair analysis is proposed.The model mustered the projection of alternative schemes on ideal one,and interval number may be linked with connection number based on the error distribution of interval numbers.According to the principle of comparing connection number a＋bi,scheme was evaluated synthetically.By taking 4 kinds of schemes which would be used in a certain square as an example,application is introduced and the results are in agreement with fuzzy optimal theory model and optimization model of grey matter element analysis.