Application of improved extension evaluation method to water quality evaluation

•This paper gives a new method-improved extension evaluation method applied to water quality evaluation.•It overcomes the drawback of negative values in the correlative degree.•It settles the evaluation problem of interval water quality standards.•The assessment results of this paper are basically the same as the official water quality.•The concept of non-integral assessment grade we introduce is reasonable.

SummaryThe extension evaluation method (EEM) has been developed and applied to evaluate water quality. There are, however, negative values in the correlative degree (water quality grades from EEM) after the calculation. This is not natural as the correlative degree is essentially an index based on grades (rankings) of water quality by different methods, which are positive. To overcome this negativity issue, the interval clustering approach (ICA) was introduced, which is based on the grey clustering approach (GCA) and interval-valued fuzzy sets. However, the computing process and formulas of ICA are rather complex. This paper provides a novel method, i.e., improved extension evaluation method, so as to avoid negative values in the correlative degree. To demonstrate our proposed approach, the improved EEM is applied to evaluate the water quality of three different cross-sections of the Fen River, the second major branch river of the Yellow River in China and the Han Jiang River, one of the major branch rivers of the Yangtse River in China. The results of the improved evaluation method are basically the same as the official water quality. The proposed method possesses also the same merit as the EEM and ICA method, which can be applied to assess water quality when the levels of attributes are defined in terms of intervals in the water quality criteria. Existing methods are mostly applicable to data in the form of single numeric values.