Sensitivity analysis of TOPSIS method in water quality assessment II: sensitivity to the index input data

This is the second part of the study on sensitivity analysis of the technique for order preference by similarity to ideal solution (TOPSIS) method in water quality assessment. In the present study, the sensitivity of the TOPSIS method to the index input data was investigated. The sensitivity was first theoretically analyzed under two major assumptions. One assumption was that one index or more of the samples were perturbed with the same ratio while other indices kept unchanged. The other one was that all indices of a given sample were changed simultaneously with the same ratio, while the indices of other samples were unchanged. Furthermore, a case study under assumption 2 was also carried out in this paper. When the same indices of different water samples are changed simultaneously with the same variation ratio, the final water quality assessment results will not be influenced at all. When the input data of all indices of a given sample are perturbed with the same variation ratio, the assessment values of all samples will be influenced theoretically. However, the case study shows that only the perturbed sample is sensitive to the variation, and a simple linear equation representing the relation between the closeness coefficient (CC) values of the perturbed sample and variation ratios can be derived under the assumption 2. This linear equation can be used for determining the sample orders under various variation ratios.