Application of interval clustering approach to water quality evaluation

• This paper gives a new method ICA applied to water quality evaluation.
• It makes up a deficiency of negative values in the correlative degree.
• It settles the evaluation problem of interval criteria and interval samples.
• Interval weights are introduced to deal with the uncertainty of weights.
• The method is not restricted to WQE only.

SummaryThe extension evaluation method (EEM) has been applied to evaluate water quality. However, in real-life applications, sample data may be given as intervals because of errors produced in measurement, poor data brought by poor information, and imprecise data induced by human errors. To deal with data set in the form of a number of intervals, the interval extension evaluation method (IEEM) has been previously introduced. However, the correlative degrees that are obtained from IEEM may yield negative numbers. In evaluating water quality one generally assigns ranks or grades that are non-negative. Then it is expected that correlative degrees must be non-negative. This paper provides a novel method, i.e., the interval clustering approach (ICA), which is based on the grey clustering approach (GCA) and interval-valued fuzzy sets, to overcome this negativity issue. The method also introduces the notion of weightings in the form of intervals, by which interval samples can be analyzed with a view to delineating the important attributes via the interval weights. To demonstrate our proposed approach, the ICA 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. Our proposed method is a useful tool for the analysis of poorly measured data, poorly collected data and imprecise hydrological data which are very commonly encountered in water research. In brief, our method is novel for analyzing interval data. The GCA is a special case of the ICA, as these intervals are degenerated single values.