TOPSIS模型的改进算法及其在河流健康评价中的应用

Improved Algorithm of TOPSIS Model and Its Application in River Health Assessment

针对传统TOPSIS法在河流健康综合评价中存在的指标信息重复、主观赋权不合理、隶属度难以确定以及可能出现与理想解欧式距离近的方案与负理想解的欧式距离也近的不足,提出一种改进的算法。首先建立标准样本与评价对象样本集成的标准决策矩阵,然后采用层次分析和投影寻踪熵耦合的方法对评价指标进行组合赋权,并构建加权矩阵,最后引入卡方距离代替欧式距离计算与理想方案的贴近度,在此基础上求解评价对象与排序临近标准样本序列的趋近度,确定评价对象的等级。改进算法不仅能避免评价结果受主观判断的不确定性和随意性,而且可以避免距理想解近的方案与负理想解也近的问题,从而提高了TOPSIS模型的科学性和合理性。实证研究表明:该改进算法具有较强的可行性和有效性。

In order to overcome the defects in the traditional TOPSIS model of river health assessment,such as correlations between indices,uncertainty in estimating the weights subjectively,difficulty in determining the membership function and possibility of the scheme closed to ideal solution and negative-ideal solution concurrently,an improved algorithm was presented.At first,the decision-making matrix based on standard samples and evaluation objects was built.Then,the weight of every evaluation index was decided by using AHP and PPC method,and the weighting decision matrix was constructed.At last,Euclid distance was replaced with Chi-square distance to calculate the proximity degree of each alternative to ideal solution.On the basis of this,the evaluation object was graded by the approaching degree of the object and the standard stylebook sequence.In this way,the non-determinacy and randomness resulting from the subjective judgments in the assessment,as well as the problem that coinstantaneous scheme may be ideal or not,were avoided,and the scientificity and rationality of TOPSIS Model can be improved.At the end of this paper,the feasibility and validity of this method were testified by the actual problem.