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
Abstract
:1. Introduction
2. Materials and Methodology
2.1. Study Area
2.2. Methodology
2.2.1. Fuzzy Comprehensive Assessment Method
- (1)
- Defining the factor set, i.e., U = {u1, u2, …, ui, …, um}, which is a set consisting of m kinds of evaluation factors, and ui is the ith evaluation factor.
- (2)
- Establishing the evaluation set V = {v1, v2, …, vj, …, vn}, which is a discrete set made up of n levels of evaluation results, and vj is the jth evaluation result.
- (3)
- Building the original matrix X,
- (4)
- Determining the weight matrix A = {a1, a2, …, am}, which is a set composed of m kinds of index weights which indicate the importance of various evaluation indexes.
- (5)
- Constructing the single factor evaluation matrix Q by membership function, where Q is a fuzzy relationship matrix that consists of the membership degrees of ui to vj. The matrix is:
- (6)
- Obtaining the comprehensive evaluation set B, which is a set made up of n kinds of evaluation results by fuzzy operating of the single factor evaluation matrix and weight matrix.
2.2.2. Improved Fuzzy Comprehensive Assessment Method
- (1)
- Standardizing the indexes and building the standardization matrix Y = (yij)m × yr (m is the number of indexes, yr is the year for evaluation), which will be explained specifically in Section 2.2.3. Then, the proportion of each index (pik) is determined as follows:
- (2)
- Calculating the information entropy (ei) by
- (3)
- Obtaining the weights of indexes by
2.2.3. Standardization
- (1)
- Building the original matrix X
- (2)
- For a benefit index, the standardized xik, i.e., yik is calculated as
- (3)
- As for a cost index, the standardization equation is
3. Results and Discussion
3.1. Water Environmental Safety Evaluation Index System
3.2. Water Environmental Safety Evaluation of the Heshangshan Drinking Water Source Area
3.2.1. Construction of Factor Set U and Evaluation Set V
3.2.2. Weight Determination
3.2.3. Comprehensive Evaluation
4. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
References
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Destination Layer | Criterion Layer | Index Layer | Subindex Layer |
---|---|---|---|
Water environmental safety of the Heshangshan drinking water sources area | Pressure (P) | Water resources P1 | Per capita water resources D1; |
Per capita domestic water consumption D2; | |||
Annual irrigation water consumption per hectare D3 | |||
Pollution source and its discharge P2 | COD discharge amount D4; | ||
Ammonia nitrogen discharge amount D5; | |||
The number of industrial enterprises beyond designed scale D6 | |||
State (S) | Social economy S1 | Natural population growth rate D7; | |
Population density D8; | |||
Per capita GDP D9 | |||
Water quantity S2 | Daily water supply amount of a project D10; | ||
Annual rainfall D11; | |||
Water consumption per 10,000 yuan of value-added by industry D12 | |||
Water quality S3 | Standard-meeting rate of drinking water for drinking water source area D13; | ||
Wastewater discharge of per unit GDP D14; | |||
Ratio of wastewater and runoff D15; | |||
Eutrophication section percentage of influents in Three Gorges reservoir area D16 | |||
Response (R) | Environmental protection R1 | Wastewater treatment rate of sewage plant D17; | |
Vegetation cover rate D18; | |||
Governance rate of soil and water loss D19 | |||
Industrial structure R2 | Investment rate of environmental protection D20; | ||
Proportion of tertiary industry D21 |
Subindex | Unit | 2010 | 2011 | 2012 | 2013 | 2014 | Type |
---|---|---|---|---|---|---|---|
D1 | M3/person | 1405.50 | 1545.37 | 1425.07 | 1412.39 | 1903.82 | ↑ |
D2 | M3/person | 47.51 | 49.45 | 50.72 | 52.63 | 48.18 | ↓ |
D3 | M3 | 251.00 | 291.00 | 287.00 | 270.00 | 307.00 | ↓ |
D4 | mg/L | 183.04 | 435.53 | 304.23 | 274.95 | 265.02 | ↓ |
D5 | mg/L | 19.51 | 57.47 | 40.33 | 36.63 | 35.19 | ↓ |
D6 | _ | 896.00 | 527.00 | 575.00 | 650.00 | 734.00 | ↓ |
D7 | % | 7.25 | 6.54 | 3.88 | 4.64 | 5.10 | ↓ |
D8 | person/km2 | 400.89 | 404.09 | 406.11 | 407.57 | 409.60 | ↓ |
D9 | 104 yuan | 2.76 | 3.45 | 3.89 | 4.32 | 4.79 | ↑ |
D10 | 104 m3 | 652.66 | 815.42 | 833.24 | 813.34 | 833.34 | ↑ |
D11 | 108 m3 | 872.07 | 899.67 | 890.45 | 876.43 | 1046.52 | ↑ |
D12 | M3 | 128.00 | 92.00 | 76.00 | 77.00 | 71.00 | ↓ |
D13 | % | 100.00 | 100.00 | 100.00 | 100.00 | 100.00 | ↑ |
D14 | M3/104 yuan | 16.16 | 9.56 | 11.60 | 11.15 | 10.22 | ↓ |
D15 | % | 2.76 | 1.86 | 2.78 | 3.00 | 2.27 | ↓ |
D16 | % | 42.20 | 38.90 | 25.00 | 36.10 | 44.40 | ↓ |
D17 | % | 88.86 | 92.21 | 89.77 | 93.20 | 92.25 | ↑ |
D18 | % | 6.05 | 8.45 | 5.34 | 4.87 | 5.21 | ↑ |
D19 | % | 37.00 | 39.00 | 42.10 | 42.10 | 43.10 | ↑ |
D20 | % | 2.93 | 2.72 | 2.10 | 2.02 | 2.06 | ↑ |
D21 | % | 36.40 | 36.20 | 39.40 | 46.70 | 46.80 | ↑ |
Subindexes | Units | Excellent | Good | Substantially Good | Poor | Very Poor |
---|---|---|---|---|---|---|
D1 | M3/person | [3000,∞) | [2000,3000) | [1000,2000) | [500,1000) | (0,500) |
D2 | m3/person | [0,30] | (30,45] | (45,55] | (55,80] | (80,∞) |
D3 | m3 | [0,200] | (200,300] | (300,360] | (380,500] | (500,∞) |
D4 | mg/L | [0,100] | (100,300] | (300,700] | (700,1000] | (1000,∞) |
D5 | mg/L | [0,15] | (15,30] | (30,60] | (60,100] | (100,∞) |
D6 | _ | [0,400] | (400,800] | (800,1400] | (1400,2000] | (2000,∞) |
D7 | % | [0,0.7] | (0.7,1.2] | (1.2,3.5] | (3.5,5] | (5,∞) |
D8 | person/km2 | [0,300] | (300,400] | (400,500] | (500,2000] | (2000,∞) |
D9 | 104 yuan | [5,15) | [3,5) | [1.5,3) | [1,1.5) | (0.5,1) |
D10 | 104 m3 | [1200,∞) | [900,1200) | [600,900) | [300,600) | (0,300) |
D11 | 108 m3 | [1100,∞) | [800,1100) | [650,800) | [400,650) | (0,400) |
D12 | m3 | [0,20] | (20,40] | (40,65] | (65,130] | (130,∞) |
D13 | % | [98,100) | [96,98) | [90,96) | [70,90) | (0,70) |
D14 | m3/104 yuan | [0,20] | (20,50] | (50.100] | (100,150] | (150,∞) |
D15 | % | [0,3] | (3,5.5] | (5.5,7.7] | (7.7,10] | (10,100) |
D16 | % | [0,5] | (5,10] | (10,15] | (15,45] | (45,∞) |
D17 | % | [98,100) | [90,98) | [80,90) | [70,80) | (0,70) |
D18 | % | [90,100) | [50,90) | [10,50) | [4,10) | (4,0) |
D19 | % | (50,100) | [35,50) | [20,35) | [10,20) | [0,10) |
D20 | % | [2.2,100) | [1.7,2.2) | [1.2,1.7) | [0.7,1.2) | (0,0.7) |
D21 | % | [70,100) | [50,70) | [30,50) | [20,30) | (0,20) |
Destination Layer | Criterion Layer | Index Layer | Subindex Layer | Weight |
---|---|---|---|---|
A 1.000 | P 0.278 | P1 0.182 | D1 | 0.111 |
D2 | 0.029 | |||
D3 | 0.041 | |||
P2 0.096 | D4 | 0.031 | ||
D5 | 0.033 | |||
D6 | 0.032 | |||
S 0.420 | S1 0.119 | D7 | 0.041 | |
D8 | 0.043 | |||
D9 | 0.036 | |||
S2 0.162 | D10 | 0.027 | ||
D11 | 0.106 | |||
D12 | 0.029 | |||
S3 0.139 | D13 | 0.000 | ||
D14 | 0.028 | |||
D15 | 0.053 | |||
D16 | 0.058 | |||
R 0.302 | R1 0.150 | D17 | 0.040 | |
D18 | 0.075 | |||
D19 | 0.035 | |||
R2 0.152 | D20 | 0.082 | ||
D21 | 0.070 |
Subindexes | Evaluation Set | ||||
---|---|---|---|---|---|
v1 | v2 | v3 | v4 | v5 | |
Levels of Water Environmental Safety | |||||
I | II | III | IV | V | |
D1 | 0.000 | 0.372 | 0.412 | 0.216 | 0.000 |
D2 | 0.047 | 0.518 | 0.434 | 0.000 | 0.000 |
D3 | 0.136 | 0.475 | 0.389 | 0.000 | 0.000 |
D4 | 0.221 | 0.490 | 0.289 | 0.000 | 0.000 |
D5 | 0.275 | 0.464 | 0.261 | 0.000 | 0.000 |
D6 | 0.090 | 0.546 | 0.364 | 0.000 | 0.000 |
D7 | 0.000 | 0.000 | 0.000 | 0.063 | 0.937 |
D8 | 0.000 | 0.032 | 0.532 | 0.436 | 0.000 |
D9 | 0.378 | 0.423 | 0.199 | 0.000 | 0.000 |
D10 | 0.190 | 0.429 | 0.381 | 0.000 | 0.000 |
D11 | 0.327 | 0.398 | 0.276 | 0.000 | 0.000 |
D12 | 0.000 | 0.000 | 0.370 | 0.407 | 0.222 |
D13 | 0.505 | 0.495 | 0.000 | 0.000 | 0.000 |
D14 | 0.662 | 0.338 | 0.000 | 0.000 | 0.000 |
D15 | 0.569 | 0.431 | 0.000 | 0.000 | 0.000 |
D16 | 0.000 | 0.000 | 0.015 | 0.496 | 0.489 |
D17 | 0.126 | 0.448 | 0.426 | 0.000 | 0.000 |
D18 | 0.000 | 0.000 | 0.103 | 0.508 | 0.390 |
D19 | 0.248 | 0.459 | 0.293 | 0.000 | 0.000 |
D20 | 0.000 | 0.057 | 0.478 | 0.464 | 0.000 |
D21 | 0.000 | 0.339 | 0.403 | 0.258 | 0.000 |
Layer | Evaluation set | |||||
---|---|---|---|---|---|---|
v1 | v2 | v3 | v4 | v5 | ||
Levels of Water Environmental Safety | ||||||
I | II | III | IV | V | ||
Index layer | P1 | 0.036 | 0.429 | 0.425 | 0.110 | 0.000 |
P2 | 0.201 | 0.498 | 0.302 | 0.000 | 0.000 | |
S1 | 0.170 | 0.204 | 0.318 | 0.089 | 0.218 | |
S2 | 0.248 | 0.333 | 0.309 | 0.072 | 0.039 | |
S3 | 0.321 | 0.215 | 0.007 | 0.230 | 0.227 | |
R1 | 0.097 | 0.240 | 0.241 | 0.239 | 0.183 | |
R2 | 0.000 | 0.216 | 0.478 | 0.305 | 0.000 | |
Criterion layer | P | 0.093 | 0.453 | 0.382 | 0.072 | 0.000 |
S | 0.250 | 0.257 | 0.212 | 0.129 | 0.152 | |
R | 0.048 | 0.228 | 0.361 | 0.272 | 0.091 |
Indicator | Level | ||||
---|---|---|---|---|---|
Water environmental safety level | I | II | III | IV | V |
Evaluation set V | v1 | v2 | v3 | v4 | v5 |
Membership degree of destination layer | 0.145 | 0.303 | 0.304 | 0.156 | 0.092 |
Evaluation result of water environmental safety level | — | — | √ | — | — |
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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. https://doi.org/10.3390/w9050329
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(5):329. https://doi.org/10.3390/w9050329
Chicago/Turabian StyleDing, Xiaowen, Xiao Chong, Zhengfeng Bao, Ying Xue, and Shanghong Zhang. 2017. "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 9, no. 5: 329. https://doi.org/10.3390/w9050329