# A New Comprehensive Evaluation Method for Water Quality: Improved Fuzzy Support Vector Machine

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. FSVM Methodology

#### 2.1. Data Preprocessing

#### 2.1.1. Data Imbalance

#### 2.1.2. Data Normalization

#### 2.2. Basic Model Selection

_{i}to $\mathrm{U}{}^{\prime}=\left\{\left({x}_{i},{y}_{i},{S}_{i}\right),\text{}i=1,2,\dots ,n\right\}$, where ${x}_{i}\in {R}^{m}$, ${y}_{i}\in \left\{+1,-1\right\}$, ${S}_{i}\in \left(0,1\right)$. Thus, the previous SVM model is changed into Equation (3).

#### 2.3. Parameter Optimization

#### 2.4. Cross-Validation

- (1)
- K-cv: The data is divided into k groups, then each time one of them is selected for testing, and the remaining (k − 1) groups are used to train the model. This process will be repeated k times. Finally, the evaluation result is generated by taking the average of all the results.
- (2)
- Loo-cv: Suppose there are n samples, each time (n − 1) samples are used for training, and the remaining one is used as a test set. The above process is repeated n times, and the final result is the average of all values. Since almost every sample is used for training each time, this method leaves almost no information and the results are more reliable. However, because it is repeated too many times, the method is time consuming.

#### 2.5. Multi-Classification Model

## 3. Improved Membership Function

#### 3.1. Membership Function

- (1)
- Trigonometric membership function$$\mu \left(x\right)=\{\begin{array}{cc}0& \hfill x\le a\\ \frac{x-a}{b-a}& \hfill a<x\le b\\ \frac{c-x}{c-b}& \hfill b<x\le c\\ 0& \hfill x>c\end{array}$$
- (2)
- Trapezoidal membership function$$\mu \left(x\right)=\{\begin{array}{ll}0& \hfill x\le a\\ \frac{x-a}{b-a}& \hfill a<x\le b\\ 1& \hfill b<x\le c\\ \frac{c-x}{c-b}& \hfill c<x\le d\\ 0& \hfill x>d\end{array}$$
- (3)
- Distance-based membership function in FSVM$$\mu \left(x\right)=\{\begin{array}{l}1-\frac{{d}_{i+}}{{r}_{+}+\delta},{y}_{i}=+1\\ 1-\frac{{d}_{i-}}{{r}_{-}+\delta},{y}_{i}=-1\end{array}$$
_{+}= max ${d}_{i+}$, r_{−}= max ${d}_{i-}$, ${x}_{+}$ and ${x}_{-}$ are the centers of the positive and negative samples, respectively.

#### 3.2. Basic Form of Membership Function

#### 3.3. Design of the Improved Membership Function

#### 3.3.1. Problems with Existing Membership Functions

#### 3.3.2. Improvement Ideas

- (1)
- When all of the p sample points are not in the class of ${x}_{i}$, ${x}_{i}$ is noise, and has no effect on the classification plane formation, so the value of ${c}_{i}$ is $\delta $.
- (2)
- When all the p sample points are of the same class as ${x}_{i}$, the function is designed according to the degree of compactness of the points around ${x}_{i}$, so the value of ${c}_{i}$ is ${\sum}_{j=1}^{p}\frac{1}{{d}_{ij}}.$
- (3)
- When only q samples of the p points belong to the same class of ${x}_{i}$, ${c}_{i}$ takes the value $\delta $ or ${\sum}_{j=1}^{q}\frac{1}{{d}_{ij}}$, according to the class of its nearest neighbor.

#### 3.3.3. Improved Membership Function

- (1)
- When all the p sample points are not in the same class as ${x}_{i}$, ${x}_{i}$ is judged as noise and it has no effect on the classification plane formation, namely,$$\text{}{c}_{i}=\delta $$
- (2)
- Reselect p sample points around the sample point ${x}_{i}$ that are closest to it and do not contain the points of the above case (1). This can effectively avoid the interference of a single noise point in some cases (1) to the judgment of surrounding sample points.
- When all of the p sample points at this time are not in the same class as ${x}_{i}$, ${x}_{i}$ is judged as noise and it has no effect on the classification plane formation, namely,$${c}_{i}=\delta $$
- When all of the p sample points are of the same class as ${x}_{i}$, the function is designed according to the compactness of the sample points around ${x}_{i}$, that is, the tighter the sample point, the larger the ${c}_{i}$:$${c}_{i}={\displaystyle \sum}_{j=1}^{p}\frac{1}{{d}_{ij}}$$
- When q points in p sample points belong to the same class of ${x}_{i}$, the remaining ones do not belong to this class, the value of ${c}_{i}$ is as follows:$${c}_{i}=\{\begin{array}{ll}\delta ,\hfill & \hfill q-\frac{p}{2}<0\\ {\displaystyle {\displaystyle \sum}_{j=1}^{q}}\frac{1}{{d}_{ij}},\hfill & \hfill q-\frac{p}{2}>0\end{array}$$

- (1)
- For the case of Figure 4, it is clear that this problem has been solved by using the method of intra-class hyperplane instead of hypersphere. The value of ${S}_{i1}$ of the new function is the same for A and B in Figure 4, but, depending on the situation of the surrounding points of A and B, different ${S}_{i2}$ may be given. Finally, the result is the combination of ${S}_{i1}$ and ${S}_{i2}.$
- (2)
- For the case of Figure 5, the new function judges the sample point based on the number of same-class and different-class points around it, rather than the distance to the intra-class hyperplane.
- (3)

#### 3.4. Data Verification

#### 3.4.1. Experiment Based on Artificial Data

^{−6}, which are all the noise points that are placed previously. Another point (0.36, 0.14) can be seen as an isolated point from the figure below, so its ${S}_{i2}$ value is only 0.0630. Therefore, it can be seen that the improved FSVM handles these 11 points that are not useful for classification very well. In the same way, the results of the other several experiments are also the same.

#### 3.4.2. Experiment Based on UCI Dataset

## 4. Results and Discussion

#### 4.1. Selection of Dataset and Evaluation Indicators

_{3}-N). The distribution of the dataset is very unbalanced as shown in Table 6, and there are many minority classes at the same time, that is, there are several classes at the same time whose number of samples is much smaller than that of the class with the most samples. Therefore, the undersampling method is performed first. The data is then put into the FSVM model based on the improved membership function of this paper.

#### 4.2. Analysis and Comparison of Evaluation Results

#### 4.3. Analysis and Comparison of Model Performance

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Galaitsi, S.E.; Russell, R.; Bishara, A.; Durant, J.L.; Bogle, J.; Huber-Lee, A. Intermittent Domestic Water Supply: A Critical Review and Analysis of Causal-Consequential Pathways. Water
**2016**, 8, 274. [Google Scholar] [CrossRef] - Kou, L.; Li, X.; Lin, J.; Kang, J. Simulation of Urban Water Resources in Xiamen Based on a WEAP Model. Water
**2018**, 10, 732. [Google Scholar] [CrossRef] - Huang, X.; Chen, X.; Huang, P. Research on Fuzzy Cooperative Game Model of Allocation of Pollution Discharge Rights. Water
**2018**, 10, 662. [Google Scholar] [CrossRef] - Liu, Y.; Zhang, J.; Zhao, Y. The Risk Assessment of River Water Pollution Based on a Modified Non-Linear Model. Water
**2018**, 10, 362. [Google Scholar] [CrossRef] - Liyanage, C.P.; Yamada, K. Impact of population growth on the water quality of natural water bodies. Sustainability
**2017**, 9, 1405. [Google Scholar] [CrossRef] - Guo, J.S.; Wang, H.; Long, T.Y. Analysis and Development of Water Quality Evaluation Method. Chongqing Environ. Sci.
**1999**, 21, 1–3. [Google Scholar] - Tao, T.; Sun, S.; Jiang, D.; Fang, H. Fuzzy Comprehensive Evaluation Apply in Water Quality Assessment of Chaohu Lake. Environ. Sci. Manag.
**2010**, 35, 177–180. [Google Scholar] - Gao, J. Application of Fuzzy Comprehensive Evalution to Water Quality of Binhe Park. J. Taiyuan Normal Univ.
**2011**, 3, 106–109. [Google Scholar] - Ding, X.; Chong, X.; Bao, Z.; Xue, Y.; Zhang, S. Fuzzy Comprehensive Assessment Method Based on the Entropy Weight Method and Its Application in the Water Environmental Safety Evaluation of the Heshangshan Drinking Water Source Area, Three Gorges Reservoir Area, China. Water
**2017**, 9, 329. [Google Scholar] [CrossRef] - Wang, H.M.; Lu, W.X.; Xin, G.; Wang, H.X. Application of Grey Clustering Method for Surface Water Quality Evaluation. Water Sav. Irrig.
**2007**, 5, 20–22. [Google Scholar] - Deng, X.; Chen, Q.; Zhang, J. Application of Grey Clustering Method to Water Quality Evaluation in Jinjiang River of Fujian Province. Environ. Sci. Manag.
**2010**, 35, 187–191. [Google Scholar] - Yun, Y.; Zou, Z. An improved synthetic evaluation method on water quality evaluation in city sections of the Three Gorges reservoir area. In Proceedings of the IEEE International Conference on Grey Systems and Intelligent Services, Nanjing, China, 18–20 November 2008; IEEE: Piscataway, NJ, USA, 2008; pp. 289–293. [Google Scholar]
- Li, Y.; Zhou, J.; Wang, X.; Zhou, X. Water Quality Evaluation of Nearshore Area Using Artificial Neural Network Model. In Proceedings of the International Conference on Bioinformatics and Biomedical Engineering, Beijing, China, 11–13 June 2009; IEEE: Piscataway, NJ, USA, 2009; pp. 1–4. [Google Scholar]
- Li, S.; Zhao, N.; Shi, Z.; Tang, F. Application of artificial neural network on water quality evaluation of Fuyang River in Handan city. In Proceedings of the International Conference on Mechanic Automation and Control Engineering, Wuhan, China, 26–28 June 2010; IEEE: Piscataway, NJ, USA, 2010; pp. 1829–1832. [Google Scholar]
- Hua, Z.L.; Qian, W.; Li, G.U. Application of improved LM-BP neural network in water quality evaluation. Water Resour. Prot.
**2008**, 24, 22–25. [Google Scholar] - Liu, K. Fuzzy Probabilistic Neural Network Water Quality Evaluation Model and Its Application. J. China Hydrol.
**2007**, 1, 31, 42–45. [Google Scholar] - Yang, Z.M. Uncertainty Support Vector Machine; Science Press: Beijing, China, 2012. [Google Scholar]
- Deng, N.; Tian, Y.; Zhang, C. Support Vector Machines: Optimization Based Theory, Algorithms, and Extensions; Chapman & Hall/CRC: Boca Raton, FL, USA, 2012. [Google Scholar]
- Samadzadegan, F.; Hasani, H.; Schenk, T. Simultaneous feature selection and SVM parameter determination in classification of hyperspectral imagery using Ant Colony Optimization. Can. J. Remote Sens.
**2012**, 38, 139–156. [Google Scholar] [CrossRef] - Syarif, I.; Prugel-Bennett, A.; Wills, G. SVM Parameter Optimization using Grid Search and Genetic Algorithm to Improve Classification Performance. Telkomnika
**2016**, 14, 1502–1509. [Google Scholar] [CrossRef] [Green Version] - Huang, C.L.; Dun, J.F. A distributed PSO–SVM hybrid system with feature selection and parameter optimization. Appl. Soft Comput. J.
**2008**, 8, 1381–1391. [Google Scholar] [CrossRef] - Fei, B.; Liu, J. Binary tree of SVM: A new fast multiclass training and classification algorithm. IEEE Trans. Neural Netw.
**2006**, 17, 696–704. [Google Scholar] [CrossRef] [PubMed] - Liu, C.; Wang, W.; Wang, M.; Lv, F.; Konan, M. An efficient instance selection algorithm to reconstruct training set for support vector machine. Knowl.-Based Syst.
**2016**, 116, 58–73. [Google Scholar] [CrossRef] - Li, X.; Wang, L.; Sung, E. AdaBoost with SVM-based component classifiers. Eng. Appl. Artif. Intell.
**2008**, 21, 785–795. [Google Scholar] [CrossRef] [Green Version] - Suykens, J.A.K.; Vandewalle, J. Least Squares Support Vector Machine Classifiers; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1999. [Google Scholar]
- Zhou, Z.Y.; Wang, X.L. Water quality evaluation based on Support Vector Machine with parameters optimized by genetic algorithm. Comput. Eng. Appl.
**2008**, 44, 190–193. [Google Scholar] - Chen, L.; Liu, J.M.; Liu, X.X. Application of Support Vector Machine in the groundwater quality evaluation. J. Northwest A F Univ.
**2010**, 38, 221–226. [Google Scholar] - Dai, H.L. Forecasting and evaluating water quality of Changjiang River based on composite least square SVM with intelligent genetic algorithms. Appl. Res. Comput.
**2009**, 26, 79–81. [Google Scholar] - Lin, C.F.; Wang, S.D. Fuzzy support vector machines. IEEE Trans. Neural Netw.
**2002**, 13, 464–471. [Google Scholar] [PubMed] - Ren, Y.F. Some Studies of SVM Model Improvement. Master’s Thesis, Nanjing University of Posts and Telecommunications, Nanjing, China, 2013. [Google Scholar]
- Wu, M. Some Researches on the Algorithm of Support Vector Machine Classification. Master’s Thesis, Nanjing University of Posts and Telecommunications, Nanjing, China, 2014. [Google Scholar]
- Xu, C.Y. Research of Fuzzy Support Vector Machine and its Application of Gene Classification. Master’s Thesis, Nanjing Forestry University, Nanjing, China, 2013. [Google Scholar]
- Chawla, N.V.; Bowyer, K.W.; Hall, L.O.; Kegelmeyer, W.P. SMOTE: Synthetic minority over-sampling technique. J. Artif. Intell. Res.
**2002**, 16, 321–357. [Google Scholar] [CrossRef] - Hu, S.; Liang, Y.; Ma, L.; He, Y. MSMOTE: Improving Classification Performance When Training Data is Imbalanced. In Proceedings of the International Workshop on Computer Science & Engineering, Qingdao, China, 28–30 October 2009; pp. 13–17. [Google Scholar]
- Kohavi, R. A study of cross-validation and bootstrap for accuracy estimation and model selection. In Proceedings of the International Joint Conference on Artificial Intelligence, Montreal, QC, Canada, 20–25 August 1995; Morgan Kaufmann Publishers Inc.: Burlington, MA, USA, 1995; pp. 1137–1143. [Google Scholar]
- Hsu, C.W.; Lin, C.J. A comparison of methods for multiclass support vector machines. IEEE Trans. Neural Netw.
**2002**, 13, 415–425. [Google Scholar] [PubMed] [Green Version] - Platt, J.C. Sequential Minimal Optimization: A Fast Algorithm for Training Support Vector Machines. In Advances in Kernel Methods-Support Vector Learning; Philomel Books: New York, NY, USA, 1999; pp. 212–223. [Google Scholar]
- Liu, L.; Jiang, T.; Xu, H.; Wang, Y. Potential Threats from Variations of Hydrological Parameters to the Yellow River and Pearl River Basins in China over the Next 30 Years. Water
**2018**, 10, 883. [Google Scholar] [CrossRef] - Xu, Z.X. Single Factor Water Quality Identification Index for Environmental Quality Assessment of Surface Water. J. Tongji Univ.
**2005**, 33, 482–488. [Google Scholar] - Goutte, C.; Gaussier, E. A Probabilistic Interpretation of Precision, Recall and F-Score, with Implication for Evaluation. In Proceedings of the European Conference on Information Retrieval, Santiago de Compostela, Spain, 21–23 March 2015; Springer: Berlin/Heidelberg, Germany, 2005; pp. 345–359. [Google Scholar]

**Figure 7.**A situation of membership function based on compactness. (

**a**,

**b**) Distribution of the sample points for the two cases; (

**c**,

**d**) Identification of neighbors by a circle; (

**e**,

**f**) Distribution of neighbors.

**Figure 8.**Counterexample of the first attempt. The figures (

**a**–

**d**) are four different cases of surrounding neighbors.

**Figure 9.**Counterexample of the second attempt. The figures (

**a**–

**d**) are four different cases of surrounding neighbors.

Category | DO (≥) | CODmn (≤) | NH_{3}-N (≤) |
---|---|---|---|

I | 7.5 | 2 | 0.15 |

II | 6 | 4 | 0.5 |

III | 5 | 6 | 1 |

IV | 3 | 10 | 1.5 |

V | 2 | 15 | 2 |

Inferior V | <2.0 | >15 | >2.00 |

$\mathit{y}$ | ${\mathit{x}}_{1}$ | ${\mathit{x}}_{2}$ | ${\mathit{S}}_{\mathit{i}2}$ | $\mathit{y}$ | ${\mathit{x}}_{1}$ | ${\mathit{x}}_{2}$ | ${\mathit{S}}_{\mathit{i}2}$ |
---|---|---|---|---|---|---|---|

−1 | 0.22 | 0.80 | 0.3287 | −1 | 0.73 | 0.90 | 6.17 × 10^{−6} |

−1 | 0.41 | 0.54 | 0.3761 | −1 | 0.93 | 0.83 | 6.17 × 10^{−6} |

−1 | 0.16 | 0.98 | 0.1909 | 1 | 0.34 | 0.07 | 6.17 × 10^{−6} |

−1 | 0.12 | 0.72 | 0.2546 | 1 | 0.22 | 0.92 | 6.17 × 10^{−6} |

−1 | 0.17 | 0.84 | 0.3883 | 1 | 0.06 | 0.29 | 6.17 × 10^{−6} |

−1 | 0.19 | 0.43 | 0.3100 | 1 | 0.48 | 0.31 | 6.17 × 10^{−6} |

−1 | 0.27 | 0.47 | 0.4214 | 1 | 0.63 | 0.21 | 0.1526 |

−1 | 0.28 | 0.56 | 0.6710 | 1 | 0.95 | 0.65 | 0.3475 |

−1 | 0.20 | 0.27 | 0.1277 | 1 | 0.80 | 0.07 | 0.2154 |

−1 | 0.20 | 0.75 | 0.2858 | 1 | 0.75 | 0.41 | 0.3068 |

−1 | 0.26 | 0.50 | 0.3991 | 1 | 0.81 | 0.67 | 0.3720 |

−1 | 0.33 | 0.65 | 0.1835 | 1 | 0.91 | 0.93 | 0.2784 |

−1 | 0.36 | 0.14 | 0.0630 | 1 | 0.77 | 0.81 | 0.3665 |

−1 | 0.20 | 0.48 | 0.3500 | 1 | 0.60 | 0.48 | 0.3823 |

−1 | 0.42 | 0.36 | 0.0946 | 1 | 0.73 | 0.76 | 0.3186 |

−1 | 0.07 | 0.79 | 0.2842 | 1 | 0.71 | 0.42 | 0.3982 |

−1 | 0.03 | 0.78 | 0.2730 | 1 | 0.98 | 0.97 | 0.1617 |

−1 | 0.04 | 0.67 | 0.4481 | 1 | 0.81 | 0.99 | 0.1910 |

−1 | 0.08 | 0.13 | 0.1211 | 1 | 0.85 | 0.86 | 0.4601 |

−1 | 0.16 | 0.02 | 0.1879 | 1 | 0.86 | 0.39 | 0.4178 |

−1 | 0.15 | 0.56 | 0.3917 | 1 | 0.67 | 0.45 | 0.9910 |

−1 | 0.01 | 0.30 | 0.2041 | 1 | 0.78 | 0.78 | 0.4035 |

−1 | 0.27 | 0.94 | 0.2795 | 1 | 0.78 | 0.91 | 0.2237 |

−1 | 0.05 | 0.98 | 0.1216 | 1 | 0.71 | 0.60 | 0.1552 |

−1 | 0.07 | 0.29 | 0.2036 | 1 | 0.92 | 0.15 | 0.2456 |

−1 | 0.32 | 0.80 | 0.2002 | 1 | 0.87 | 0.90 | 0.6229 |

−1 | 0.43 | 0.90 | 0.4366 | 1 | 0.68 | 0.45 | 1.0000 |

−1 | 0.43 | 0.60 | 0.5239 | 1 | 0.73 | 0.21 | 0.1997 |

−1 | 0.29 | 0.88 | 0.2491 | 1 | 0.69 | 0.90 | 0.1696 |

−1 | 0.50 | 0.94 | 0.2531 | 1 | 0.89 | 0.76 | 0.2117 |

−1 | 0.28 | 0.55 | 0.7064 | 1 | 0.87 | 0.88 | 0.6807 |

−1 | 0.26 | 0.73 | 0.2413 | 1 | 0.72 | 0.28 | 0.2682 |

−1 | 0.17 | 0.58 | 0.3887 | 1 | 0.85 | 0.67 | 0.3610 |

−1 | 0.22 | 0.03 | 0.1858 | 1 | 0.97 | 0.66 | 0.3351 |

−1 | 0.25 | 0.45 | 0.3884 | 1 | 0.89 | 0.12 | 0.2691 |

−1 | 0.04 | 0.65 | 0.4183 | 1 | 0.85 | 0.41 | 0.4281 |

−1 | 0.44 | 0.52 | 0.3003 | 1 | 0.69 | 0.72 | 0.2458 |

−1 | 0.03 | 0.37 | 0.1829 | 1 | 0.80 | 0.28 | 0.2356 |

−1 | 0.22 | 0.94 | 0.2751 | 1 | 0.53 | 0.83 | 0.2377 |

−1 | 0.41 | 0.83 | 0.2080 | 1 | 0.61 | 0.39 | 0.2323 |

−1 | 0.20 | 0.85 | 0.4059 | 1 | 0.92 | 0.50 | 0.1605 |

−1 | 0.31 | 0.37 | 0.1803 | 1 | 0.51 | 0.86 | 0.2558 |

−1 | 0.41 | 0.59 | 0.5391 | 1 | 0.54 | 0.51 | 0.1625 |

−1 | 0.44 | 0.87 | 0.4405 | 1 | 0.83 | 0.57 | 0.1810 |

−1 | 0.47 | 0.93 | 0.3934 | 1 | 0.75 | 0.33 | 0.2900 |

−1 | 0.10 | 0.67 | 0.3253 | 1 | 0.61 | 0.46 | 0.3996 |

−1 | 0.76 | 0.25 | 6.17 × 10^{−6} | 1 | 0.79 | 0.71 | 0.3303 |

−1 | 0.58 | 0.88 | 6.17 × 10^{−6} | 1 | 0.56 | 0.88 | 0.1994 |

−1 | 0.85 | 0.56 | 6.17 × 10^{−6} | 1 | 0.84 | 0.72 | 0.3496 |

−1 | 0.60 | 0.28 | 6.17 × 10^{−6} | 1 | 0.80 | 0.02 | 0.1947 |

SVM | FSVM1 | FSVM2 | FSVM | |
---|---|---|---|---|

Precision | 0.8312 | 0.8312 | 0.8312 | 0.8312 |

Recall | 0.7512 | 0.7512 | 0.7512 | 0.7512 |

F1-score | 0.7892 | 0.7892 | 0.7892 | 0.7892 |

SVM | FSVM1 | FSVM2 | FSVM | |
---|---|---|---|---|

Precision | 0.7934 | 0.8167 | 0.8167 | 0.8167 |

Recall | 0.7619 | 0.7857 | 0.7857 | 0.7857 |

F1-score | 0.7774 | 0.8009 | 0.8009 | 0.8009 |

SVM | FSVM1 | FSVM2 | FSVM | |
---|---|---|---|---|

Precision | 0.6839 | 0.8750 | 0.5692 | 0.8750 |

Recall | 0.5715 | 0.5313 | 0.5882 | 0.5313 |

F1-score | 0.6227 | 0.6611 | 0.5785 | 0.6611 |

Value | Count | Percent |
---|---|---|

I | 605 | 22.98% |

II | 1560 | 59.25% |

III | 189 | 7.18% |

IV | 103 | 3.91% |

V | 95 | 3.61% |

Inferior V | 81 | 3.08% |

No. | pH | DO (mg/L) | CODMn (mg/L) | NH_{3}-N (mg/L) | FSVM | SFE |
---|---|---|---|---|---|---|

1 | 7.76 | 8.16 | 1.8 | 0.22 | 1 | 2 |

2 | 8.11 | 9.52 | 2.3 | 0.1 | 1 | 2 |

3 | 8.13 | 8.92 | 2.6 | 0.15 | 1 | 2 |

4 | 7.92 | 9.56 | 1.5 | 0.2 | 1 | 2 |

5 | 8.18 | 8.52 | 2.1 | 0.13 | 1 | 2 |

6 | 7.75 | 10.7 | 2.4 | 0.36 | 1 | 2 |

7 | 7.95 | 9.65 | 2.2 | 0.2 | 1 | 2 |

8 | 8.11 | 8.59 | 1.6 | 0.17 | 1 | 2 |

9 | 7.86 | 11.1 | 2.1 | 0.35 | 1 | 2 |

10 | 7.61 | 5.82 | 4.2 | 0.14 | 1 | 3 |

11 | 6.55 | 5.14 | 2.8 | 0.11 | 1 | 3 |

SVM | FSVM1 | FSVM2 | FSVM | |
---|---|---|---|---|

Precision | 0.7609 | 0.8345 | 0.5840 | 0.8395 |

Recall | 0.6979 | 0.7083 | 0.6563 | 0.7396 |

F1-score | 0.7280 | 0.7663 | 0.6180 | 0.7864 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Shan, W.; Cai, S.; Liu, C.
A New Comprehensive Evaluation Method for Water Quality: Improved Fuzzy Support Vector Machine. *Water* **2018**, *10*, 1303.
https://doi.org/10.3390/w10101303

**AMA Style**

Shan W, Cai S, Liu C.
A New Comprehensive Evaluation Method for Water Quality: Improved Fuzzy Support Vector Machine. *Water*. 2018; 10(10):1303.
https://doi.org/10.3390/w10101303

**Chicago/Turabian Style**

Shan, Wei, Shensheng Cai, and Chen Liu.
2018. "A New Comprehensive Evaluation Method for Water Quality: Improved Fuzzy Support Vector Machine" *Water* 10, no. 10: 1303.
https://doi.org/10.3390/w10101303