Evaluation of lake eutrophication status based on set pair analysis and confidence intervals

Because traditional assessing methods usually yield extreme results and are of poor resolution, a set pair analysis based on triangular fuzzy number is established. Set pair analysis method is an uncertainty analysis method of the system whose formula structure analysis of connection degree is established by the identity degree, discrepancy degree and contrary degree to deal with all kinds of uncertainty and fuzzy problems. The measured value and the lake quality criteria are two interrelated sets put together to compose a set pair with respect to the problem of determination of the magnitude of lake eutrophication. The basic expression of the degree of couplet is extended at different levels and at the same level to form a multi-element connection number, in order to set up a five-element connection number in relation to I-V grades evaluation standard commonly used in lake assessment. The discrepancy degree is expanded into partial identity in discrepancy, entirety discrepancy and partial contrary in discrepancy, this forms a multivariate connection number of identity, partial identity in discrepancy, entirety discrepancy, partial contrary in discrepancy and contrary. By introducing triangular fuzzy number the number of links to get the evaluation grade for a confidence interval was obtained, weight value calculated by weighted average method and finally got the evaluation grade as a confidence interval based on confidence level. The case study shows that the method presents the evaluating grade as a confidence interval which has advantages of high resolution and information utilization.