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. 2019 May 19;16(10):1769.
doi: 10.3390/ijerph16101769.

Comprehensive Eutrophication Assessment Based on Fuzzy Matter Element Model and Monte Carlo-Triangular Fuzzy Numbers Approach

Yumin Wang  1 , Weijian Ran  2
Affiliations

Comprehensive Eutrophication Assessment Based on Fuzzy Matter Element Model and Monte Carlo-Triangular Fuzzy Numbers Approach

Yumin Wang et al. Int J Environ Res Public Health. .

Abstract

Evaluating the eutrophication level of lakes with a single method alone is challenging since uncertain, fuzzy, and complex processes exist in eutrophication evaluations. The parameters selected for assessing eutrophication include chlorophyII-a, chemical oxygen demand, total phosphorus, total nitrogen, and clarity. Firstly, to deal with the uncertainties and fuzziness of data, triangular fuzzy numbers (TFN) were applied to describe the fuzziness of parameters. Secondly, to assess the eutrophication grade of lakes comprehensively, an improved fuzzy matter element (FME) approach was incorporated with TFNs with weights determined by combination of entropy method and analytic hierarchy process (AHP). In addition, the Monte Carlo (MC) approach was applied to easily simulate the arithmetic operations of eutrophication evaluation. The hybrid model of TFN, FME, and MC method is termed as the TFN⁻MC⁻FME model, which can provide more valuable information for decision makers. The developed model was applied to assess the eutrophication levels of 24 typical lakes in China. The evaluation indicators were expressed by TFNs input into the FME model to evaluate eutrophication grade. The results of MC simulation supplied quantitative information of possible intervals, the corresponding probabilities, as well as the comprehensive eutrophication levels. The eutrophication grades obtained for most lakes were identical to the results of the other three methods, which proved the correctness of the model. The presented methodology can be employed to process the data uncertainties and fuzziness by stochastically simulating their distribution characteristics, and obtain a better understanding of eutrophication levels. Moreover, the proposed model can also describe the trend of eutrophication development in lakes, and provide more valuable information for lake management authorities.

Keywords: Monte Carlo approach; eutrophication evaluation; fuzzy matter element model; triangle fuzzy number.

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Conflict of interest statement

The authors declare no conflict of interest.

Figures

Figure 1
Figure 1
Nonlinear regression of the upper boundaries for (a) chlorophyII-a (Chl-a), (b) total phosphorus (TP), (c) total nitrogen (TN), (d) chemical oxygen demand (CODMn), and (e) clarity (SD).
Figure 2
Figure 2
Flowchart of eutrophication assessment.
Figure 3
Figure 3
Locations of 24 typical lakes/reservoirs in China.
Figure 4
Figure 4
Simulation results of Bosten Lake (S3).
See this image and copyright information in PMC

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