Sensitivity analysis of TOPSIS method in water quality assessment: I. Sensitivity to the parameter weights

Sensitivity analysis is becoming increasingly widespread in many fields of engineering and sciences and has become a necessary step to verify the feasibility and reliability of a model or a method. The sensitivity of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method in water quality assessment mainly includes sensitivity to the parameter weights and sensitivity to the index input data. In the present study, the sensitivity of TOPSIS to the parameter weights was discussed in detail. The present study assumed the original parameter weights to be equal to each other, and then each weight was changed separately to see how the assessment results would be affected. Fourteen schemes were designed to investigate the sensitivity to the variation of each weight. The variation ranges that keep the assessment results unchangeable were also derived theoretically. The results show that the final assessment results will change when the weights increase or decrease by ±20 to ±50 %. The feedback of different samples to the variation of a given weight is different, and the feedback of a given sample to the variation of different weights is also different. The final assessment results can keep relatively stable when a given weight is disturbed as long as the initial variation ratios meet one of the eight derived requirements.