基于博弈论组合赋权的TOPSIS模型在地下水水质评价中的应用

Application of TOPSIS Model Based on Game Theory to Groundwater Quality Evaluation

农村地下水水源地水质评价是保证农村饮水安全的重要基础。考虑到权重值对TOPSIS模型的重要性,通过基于博弈论集合的模型将模糊层次分析法(FAHP)确定的主观权重和熵权法确定的客观权重进行组合赋权优化,同时引用"虚拟负理想点"代替"传统负理想点",避免样点出现与理想点和负理想点欧式距离等距问题。并以德阳市5个典型乡镇农村地下水饮用水源水质监测数据为评价对象,计算相对贴近度确定各水质等级。该模型评价结果与F指法、熵权-TOPSIS和FAHP-TOPSIS模型评价结果的对比分析。结果表明改进的TOPSIS模型评价结果具有合理性、有效性及实用性,并能准确地反映地下水水质等级以及偏离分级标准的程度。

Evaluation of rural groundwater quality is an important basis to ensuring the safety of drinking water in rural areas.On account of the importance of weight value to the TOPSIS(Technique for Order Preference by Similarity to an Ideal Solution)model,combinatorial weighting and optimization on the subjective weight and the objective weight respectively determined by the fuzzy analytic hierarchy process(FAHP)and the entropy weight method are carried out based on the game theory set model.In the meantime,a“virtual negative ideal point”is defined to replace the traditional negative ideal point,hence avoiding the equivalent Euclidean distance from the sample point respectively to the ideal point and to the negative ideal point.With the water quality monitoring data of five typical villages and towns in Deyang city as evaluation object,the water quality grade is determined by calculating the relative closeness degree.The results of the present model are compared with the evaluation results of F method,the Entropy-TOPSIS and the FAHP-TOPSIS model,which proves that the results of the improved TOPSIS evaluation model is objective,effective and practical.Besides,the present model could also accurately reflect the groundwater quality grade and the deviation from grading standard.