Spatiotemporal Hybrid Air Pollution Early Warning System of Urban Agglomeration Based on Adaptive Feature Extraction and Hesitant Fuzzy Cognitive Maps
Abstract
:1. Introduction
- (1)
- Although the hybrid model can serve the purpose of the problem well by combining specific methods, there are still some disadvantages. Most of the current hybrid models only focus on extracting data features through the decomposition of time series, which greatly improves the fitting effect of data but ignores the potential risk of information leakage in the decomposition process [28]. Therefore, the data preprocessing method needs to be further improved.
- (2)
- In the past, the study of air pollution was based on the division of administrative regions, and the effects of meteorology and time were analyzed separately. However, air pollution is a cross-regional environmental pollution problem, and the spatial spillover effect between urban agglomerations cannot be ignored [29].
- (3)
- Traditional single models cannot achieve high accuracy requirements, while hybrid models can improve forecasting accuracy.
- (4)
- The study of time series data only focuses on the order of time and ignores the particularities of the air quality data itself, such as the ambiguity and uncertainty of the data.
- Spatial spillover effects are considered the main factors affecting the air quality index (AQI) of different cities. It verifies that the spatiotemporal correlation of the extracted data is necessary to improve the accuracy of air pollution forecasting.
- The Hampel filter algorithm optimized by the squirrel search algorithm is innovatively introduced into the air quality forecasting model to process and correct the data outliers to improve the forecasting accuracy of the hybrid model.
- Hesitant fuzzy cognitive maps are first proposed to forecast air pollution. It can effectively solve the gray information of air quality or fuzzy relationships and uncertainties, thus further improving the accuracy of forecasting.
- The proposed model was comprehensively evaluated with the actual AQI dataset, five model evaluation criteria, and thirteen comparative models collected from the Beijing-Tianjin-Hebei region. The empirical results show that the proposed hybrid method has superior forecasting performance compared with the comparison models and can provide a theoretical basis for air pollution forecasting and early warning.
2. Design of Spatiotemporal Hybrid Air Pollution Early Warning System
2.1. Spatial Correlation Analysis Module
2.1.1. Moran Index
2.1.2. Local Gravitational Clustering
2.2. Data Preprocessing Module
2.2.1. Squirrel Search Algorithm
2.2.2. Hampel Filter
2.3. Fuzzy Information Forecasting Module
2.3.1. The Basic Definition of Hesitant Fuzzy Theory
2.3.2. The FCM Framework
2.3.3. Hesitant Fuzzy Processing Time Series
- Step 1: Define the universe of discourse and divide the interval.
- Step 2: Calculate membership degree.
- Step 3: Build fuzzy relationship matrix.
- Step 4: Defuzzify
Algorithm 1: HFCM | ||||
Objective function: min (MAPE) =$\frac{1}{n}{\displaystyle \sum _{i=1}^{n}\left|\frac{{\widehat{y}}_{i}(x)-{y}_{i}(x)}{{y}_{i}(x)}\right|}\times 100\%$ | ||||
Input: $\left({x}_{1}^{c},{x}_{2}^{c},{x}_{3}^{c},\dots ,{x}_{n}^{c}\right)$—a sequence of sample data. $\left({h}_{1}^{c},{h}_{2}^{c},{h}_{3}^{c}\dots {h}_{n}^{c}\right)$—a sequence of FCM output Output: $\left\{\begin{array}{c}MAPE(r,:)=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}\left|\frac{{\widehat{y}}_{i}(x)-{y}_{i}(x)}{{y}_{i}(x)}\right|}\times 100\%\\ RMSE(r,:)=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^{n}{\left({y}_{i}(x)-{y}_{i}(x)\right)}^{2}}}\\ MAE(r,:)=\frac{1}{n}{\displaystyle \sum _{i=1}^{n}\left|{\widehat{y}}_{i}(x)-{y}_{i}(x)\right|}\end{array}\right.$ | ||||
Parameters: ip: number of the intervals i: i-th sample j: $\left\{\begin{array}{cc}0\hfill & adaptivedivisioninterval\\ 1\hfill & equalfrequencydivisioninterval\end{array}\right.$ $Lo(N)$: the left endpoint of the adaptive division interval $Up\left(N\right)$: the right endpoint of the adaptive division interval ${P}_{LB}\left(N\right)$: the left endpoint of the equal frequency division interval ${P}_{UB}\left(N\right)$: the right endpoint of the equal frequency division interval $mbge\left(i\right)$: the membership degree of the adaptive division interval $mbgu\left(i\right)$: the membership degree of the equal frequency division interval nn: min number of the intervals mm: max number of the intervals | ||||
1: | /* Initialize the data and convert it into growth rate */ | |||
2: | /* Define the universe of discourse */ | |||
3: | FOR ip = nn: mm (number of the intervals); N = ip; | |||
4: | /* Calculate $Lo(N);Up(N)$ by cumulative distribution function. (Equation (26)) */ | |||
5: | /* Calculate ${P}_{LB}\left(N\right);{P}_{UB}(N)$ by fuzzy c-means clustering (Equation (27)) */ | |||
6: | /* Calculate the weights of different intervals */ | |||
7: | $de={P}_{UB}(N)-{P}_{LB}(N),du=Up\left(N\right)-Lo\left(N\right)$; | |||
8: | $we=de/\left(de+du\right),wu=du/\left(de+du\right)$ | |||
9: | /* Calculate $mbge\left(i\right);mbgu(i)$ */ | |||
10: | Calculate: Membership grades $u(i)=1-({(1-mbge(i))}^{we})\times ({(1-mbgu(i))}^{wu})$; | |||
11: | /* Judgment fuzzy sets */${u}_{ki}=max({u}_{1i},{u}_{2i},{u}_{3i}\dots .,{u}_{ji}),1kn$ | |||
12: | IF ${H}_{Ak}$ is fuzzy set corresponding to${u}_{ki}$ | |||
13: | Assign fuzzy set ${H}_{Ak}$ to ${x}_{i}^{c}$ | |||
14: | END | |||
15: | IF${H}_{Ai}$ is fuzzy production of day n, and ${H}_{AK}$ is fuzzy production of day n + 1 | |||
16: | $Fuzzylogicrelationship=\left\{{H}_{A1}-{H}_{A2},\dots ,{H}_{Ai}-{H}_{Aj}\right\}$ | |||
17: | END | |||
18: | /* Determine the fuzzy logic relation group */ | |||
19: | /* Count the frequency of each logical relationship */ | |||
20: | /* Calculate the percentage rate of each occurrence logic */ | |||
21: | /* Calculate the weight matrix and normalize the weight. */ | |||
22: | Calculate: $grade\left(i,j\right)=trimf\left(\left({h}_{1}^{c},{h}_{2}^{c},{h}_{3}^{c}\dots {h}_{n}^{c}\right),\left[Lower\left(j\right),mid\_point\left(j\right),Upper(j)\right]\right)$; | |||
23: | /* The maximum membership principle determines the fuzzy set to which it belongs. */ | |||
24: | Calculate: $combinedmid=\left(we.*mid\_point\left(j\right)+wu.*mid\_point\left(j\right)\right)./\left(we+wu\right)$; | |||
25: | /* Defuzzification to obtain the predicted value */ | |||
26: | /* Turning growth rates into data ${\widehat{y}}_{i}(x)$ */ | |||
27: | END | |||
28: | $\left[r,c\right]=find\left(MAPE==min\left(MAPE\right)\right)$ | |||
29: | Returned: r (The location of the optimal concept) |
2.4. Error Evaluation Module
2.4.1. Error Test
2.4.2. Hypothesis Testing
3. Results
3.1. Study Area and Data Description
3.2. Spatial Feature Extraction Results
3.2.1. Spatial Autocorrelation
3.2.2. Local Gravitational Clustering
3.3. Model Comparison Results
3.3.1. Feature Extraction Strategy
3.3.2. Probabilistic Hesitation Fuzzy Set Strategy
3.3.3. Comparison of Mixed Models in Different Data Preprocessing Environments
4. Discussion
4.1. Robustness of the Proposed Model
4.2. Differences of the Proposed Model
4.3. Application of the Proposed Model
- Air pollution has spatial spillover effects, so the spatial feature analysis module can comprehensively consider the interaction of urban agglomerations. In addition, it also provides theoretical support for the formulation of pollution control policies among urban agglomerations and facilitates coordinated governance among urban agglomerations.
- In fact, air quality is affected by many factors, including information ambiguity and uncertainty. Through the data preprocessing module, it can remove the outliers and noise from the data, making the data features more obvious and achieving better forecasting performance.
- Accurate AQI forecasting results can provide early warning information for actual life and production activities. From the perspective of the public, the forecasting of air quality can let the public understand the air quality, the scope of air quality dete-rioration, the degree of deterioration, and the development trend; secondly, it guides the daily activities and behaviors of residents, protects the physical and mental health of the people, and reduces the incidence of diseases. From the perspective of social economy, it can not only provide the theoretical basis for pollution control measures, such as strict control of motor vehicle pollution, reduction of coal consumption, shut-down of polluting enterprises, control of construction sites and road dust, and super-vision of factories with large pollutant emissions.
5. Conclusions
- First, the spatial feature extraction module is built. The module successfully extracted the spatial overflow features, captured the dynamic transition of air quality, and per-formed cluster analysis with different sizes and weights for irregular data.
- The adaptive Hampel filtering model improved by SSA is the best data processing sub-module for comparison with FCM, DHP-FCM, and HHP-FCM.
- The first proposed HFCM forecasting model plays an irreplaceable role in time series forecasting in the same data preprocessing environment. The model reduced MAPE by 94.1083%, 96.9120%, and 98.2361% for three different urban clusters.
- In the environment of different data preprocessing methods, the model proposed in this paper can still make accurate forecasts for data with large fluctuations and mu-tations. MAPE, RMSE, and MAE reach the minimum values in the three urban ag-glomerations.
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Nomenclature
AR | Auto-regressive model |
ANN | Artificial neural network |
API | Air pollution index |
AQI | Air quality index |
ARMA | Auto-regressive moving average model |
CDF | Cumulative distribution function |
CE | Centrality |
CO | Coordination |
DA | Dragonfly algorithm |
DM | Diebold–Mariano |
FCM | Fuzzy cognitive maps |
FLG | Fuzzy logic group |
FLR | Fuzzy logic relation |
FTS | Fuzzy time series |
HBA | Honey badger algorithm |
HFCM | Hesitant fuzzy cognitive maps |
LGC | Local gravitational clustering |
LRF | Local resultant force |
MA | Moving average model |
MAD | Median absolute difference |
MAE | Mean absolute error |
MAPE | Mean absolute percentage error |
MDM | Modified Diebold–Mariano |
RF | Random foresting |
RMSE | Root mean square error |
RNN | Recurrent neural network |
SSA | Squirrel search algorithm |
SVM | Support vector machine |
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AQI | Level | I | Descriptions | Color |
---|---|---|---|---|
0–50 | I | 0.155 | Good | Green |
51–100 | II | 0.207 | Moderate | Yellow |
101–150 | III | 0.176 | Lightly polluted | Orange |
151–200 | IV | 0.095 | Moderately polluted | Red |
201–300 | V | 0.066 | Heavily polluted | Purple |
>300 | VI | 0.195 | Severely polluted | Maroon |
No. | City Name | Longitude | Latitude | Training | Testing | Max | Min | Mean | Std |
---|---|---|---|---|---|---|---|---|---|
1 | Shijiazhuang | 114.502461 | 38.045474 | 1656 | 413 | 442 | 19 | 97.85 | 57.78 |
2 | Hengshui | 115.665993 | 37.735097 | 1656 | 413 | 377 | 16 | 89.68 | 50.88 |
3 | Baoding | 115.482331 | 38.867657 | 1656 | 413 | 476 | 17 | 92.46 | 56.39 |
4 | Xingtai | 114.508851 | 37.068256 | 1656 | 413 | 463 | 17 | 97.28 | 56.61 |
5 | Handan | 114.490686 | 36.612273 | 1656 | 413 | 389 | 16 | 99.81 | 56.43 |
6 | Beijing | 116.405285 | 39.904989 | 1656 | 413 | 454 | 11 | 72.05 | 47.77 |
7 | Cangzhou | 116.857461 | 38.310582 | 1656 | 413 | 346 | 16 | 81.99 | 45.15 |
8 | Langfang | 116.713873 | 39.529244 | 1656 | 413 | 413 | 13 | 78.05 | 46.25 |
9 | Tianjin | 117.190182 | 39.125596 | 1656 | 413 | 365 | 14 | 78.29 | 42.51 |
10 | Tangshan | 118.175393 | 39.635113 | 1656 | 413 | 399 | 16 | 84.83 | 45.85 |
11 | Chengde | 117.939152 | 40.976204 | 1656 | 413 | 409 | 17 | 59.69 | 31.20 |
12 | Qinhuangdao | 119.586579 | 39.942531 | 1656 | 413 | 364 | 16 | 66.22 | 35.44 |
13 | Zhangjiakou | 114.884091 | 40.811901 | 1656 | 413 | 488 | 19 | 59.34 | 36.17 |
Year | I | E(I) | Sd(I) | z | p-Value * |
---|---|---|---|---|---|
2017 | 0.155 | −0.083 | 0.092 | 2.599 | 0.005 |
2018 | 0.207 | −0.083 | 0.092 | 3.164 | 0.001 |
2019 | 0.176 | −0.083 | 0.09 | 2.873 | 0.002 |
2020 | 0.095 | −0.083 | 0.09 | 1.983 | 0.024 |
2021 | 0.066 | −0.083 | 0.09 | 1.661 | 0.048 |
2022 | 0.195 | −0.083 | 0.091 | 3.064 | 0.001 |
Cities | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 |
---|---|---|---|---|---|---|
1 | LL | LL | LL | LL | LL | LL |
2 | LL | LL | LL | HL | LL | LL |
3 | HH | HH | HH | HH | HH | HH |
4 | HL | HL | HL | HL | HL | HL |
5 | LL | LL | LL | LL | LL | LL |
6 | HH | HH | HH | HH | HH | HH |
7 | HH | HH | HH | HH | HH | HH |
8 | HH | HH | HH | HH | HL | HH |
9 | LH | LH | LH | LH | LH | LH |
10 | LL | LL | LL | LL | LL | LL |
11 | HH | HL | HH | HL | LL | HL |
12 | LL | LL | LL | LL | LL | LL |
13 | HH | HH | HH | HH | HH | HH |
Cities | Method | MAPE | RMSE | MAE |
---|---|---|---|---|
Category I Beijing | FCM | 25.54 | 25.15 | 17.76 |
DHP-FCM | 39.47 | 37.52 | 24.25 | |
SHP-FCM | 25.12 | 26.34 | 17.79 | |
HHP-FCM | 25.40 | 21.94 | 15.91 | |
Category II Shijiazhuang | FCM | 40.51 | 37.73 | 21.18 |
DHP-FCM | 31.96 | 24.38 | 15.43 | |
SHP-FCM | 36.27 | 21.02 | 15.36 | |
HHP-FCM | 36.25 | 21.08 | 15.40 | |
Category III Chengde | FCM | 29.50 | 20.66 | 14.25 |
DHP-FCM | 28.85 | 20.31 | 13.93 | |
SHP-FCM | 27.78 | 19.22 | 13.29 | |
HHP-FCM | 29.56 | 19.62 | 13.87 |
Cities | Method | MAPE (%) | RMSE | MAE |
---|---|---|---|---|
Category I Beijing | SHP-FCM | 25.12 | 26.34 | 17.79 |
SHP-GFCM | 20.66 | 18.45 | 12.85 | |
SHP-HFCM | 1.48 | 1.39 | 1.81 | |
Category II Shijiazhuang | SHP-FCM | 36.27 | 21.02 | 15.36 |
SHP-GFCM | 28.76 | 21.30 | 13.78 | |
SHP-HFCM | 1.12 | 4.33 | 0.69 | |
Category III Chengde | SHP-FCM | 27.78 | 19.22 | 13.29 |
SHP-GFCM | 24.14 | 1.11 | 9.75 | |
SHP-HFCM | 0.49 | 0.62 | 0.23 |
Cities | Method | MAPE (%) | RMSE | MAE |
---|---|---|---|---|
Category I Beijing | DHP-FCM | 39.47 | 37.52 | 24.25 |
DHP-GFCM | 30.21 | 26.19 | 18.98 | |
DHP-HFCM | 21.45 | 21.74 | 13.48 | |
HHP-FCM | 25.40 | 21.94 | 15.91 | |
HHP-GFCM | 27.24 | 23.24 | 16.89 | |
HHP-HFCM | 25.00 | 21.48 | 15.58 | |
SHP-FCM | 25.12 | 26.34 | 17.79 | |
SHP-GFCM | 20.66 | 18.45 | 12.85 | |
SHP-HFCM | 1.48 | 1.39 | 1.81 | |
Category II Shijiazhuang | DHP-FCM | 31.96 | 24.38 | 15.43 |
DHP-GFCM | 32.64 | 19.40 | 13.66 | |
DHP-HFCM | 14.66 | 16.72 | 7.01 | |
HHP-FCM | 36.25 | 21.08 | 15.40 | |
HHP-GFCM | 38.97 | 22.18 | 16.30 | |
HHP-HFCM | 34.24 | 20.64 | 14.83 | |
SHP-FCM | 36.27 | 21.02 | 15.36 | |
SHP-GFCM | 28.76 | 21.30 | 13.78 | |
SHP-HFCM | 1.12 | 4.33 | 0.69 | |
Category III Chengde | DHP-FCM | 28.85 | 20.31 | 13.93 |
DHP-GFCM | 18.67 | 11.87 | 8.38 | |
DHP-HFCM | 0.53 | 0.47 | 0.25 | |
HHP-FCM | 29.56 | 19.62 | 13.87 | |
HHP-GFCM | 29.27 | 19.61 | 13.82 | |
HHP-HFCM | 29.46 | 19.63 | 13.87 | |
SHP-FCM | 27.78 | 19.22 | 13.29 | |
SHP-GFCM | 24.14 | 1.11 | 9.75 | |
SHP-HFCM | 0.49 | 0.62 | 0.23 |
MAPE (%) | RMSE | MAE | |||||||
---|---|---|---|---|---|---|---|---|---|
Random | Proposed | Change | Random | Proposed | Change | Random | Proposed | Change | |
Beijing | |||||||||
FCM | 32.15 | 25.54 | 6.61 | 30.15 | 25.15 | 5.00 | 20.26 | 17.76 | 2.5 |
SHP-FCM | 30.72 | 25.12 | 5.6 | 28.61 | 26.34 | 2.27 | 19.89 | 17.79 | 2.1 |
SHP-HFCM | 1.39 | 1.48 | 0.09 | 1.58 | 1.39 | 0.19 | 1.76 | 1.81 | 0.05 |
Mean | 21.42 | 17.38 | 4.04 | 20.11 | 17.63 | 2.49 | 13.97 | 12.45 | 1.52 |
Std | 17.36 | 13.77 | 3.59 | 16.07 | 14.07 | 1.99 | 10.58 | 9.22 | 1.36 |
Shijiazhuang | |||||||||
FCM | 45.49 | 40.51 | 4.98 | 28.28 | 37.73 | 9.45 | 19.63 | 21.18 | 1.55 |
SHP-FCM | 45.71 | 36.27 | 9.44 | 28.16 | 21.02 | 7.14 | 19.57 | 15.36 | 4.21 |
SHP-HFCM | 0.83 | 1.12 | 0.29 | 4.17 | 4.33 | 0.16 | 0.52 | 0.69 | 0.17 |
Mean | 30.68 | 25.97 | 4.71 | 20.20 | 21.03 | 0.82 | 13.24 | 12.41 | 0.83 |
Std | 25.85 | 21.62 | 4.23 | 13.89 | 16.70 | 2.81 | 11.02 | 10.56 | 0.46 |
Chengde | |||||||||
FCM | 32.26 | 29.50 | 2.76 | 20.34 | 20.66 | 0.32 | 13.81 | 14.25 | 0.44 |
SHP-FCM | 32.04 | 27.78 | 4.26 | 20.55 | 19.22 | 1.33 | 13.98 | 13.29 | 0.69 |
SHP-HFCM | 0.67 | 0.49 | 0.18 | 0.50 | 0.62 | 0.12 | 0.31 | 0.23 | 0.08 |
Mean | 21.66 | 19.26 | 2.40 | 13.80 | 13.50 | 0.30 | 9.37 | 9.26 | 0.11 |
Std | 18.18 | 16.28 | 1.90 | 11.52 | 11.18 | 0.34 | 7.84 | 7.83 | 0.01 |
Category | Method | DM | P | MDM | P |
---|---|---|---|---|---|
Category I Beijing | DHP-FCM | 15.2192 | 8.39 × 10^{−42} | 15.2007 | 1.01 × 10^{−41} |
DHP-GFCM | 9.7186 | 3.11 × 10^{−20} | 9.7068 | 3.42 × 10^{−20} | |
DHP-HFCM | 8.0531 | 3.88 × 10^{−25} | 8.0423 | 2.63 × 10^{−25} | |
HHP-FCM | 13.6566 | 2.83 × 10^{−35} | 13.6401 | 3.31 × 10^{−35} | |
HHP-GFCM | 5.8835 | 8.34 × 10^{−9} | 5.8764 | 8.67 × 10^{−9} | |
HHP-HFCM | 5.1544 | 3.26 × 10^{−7} | 5.1478 | 3.19 × 10^{−7} | |
SHP-FCM | 5.7104 | 2.16 × 10^{−8} | 5.7034 | 2.25 × 10^{−8} | |
SHP-GFCM | 6.4946 | 2.41 × 10^{−10} | 6.4867 | 2.52 × 10^{−10} | |
Category II Shijiazhuang | DHP-FCM | 16.4863 | 3.10 × 10^{−47} | 16.4663 | 3.78 × 10^{−47} |
DHP-GFCM | 10.0901 | 1.55 × 10^{−21} | 10.0778 | 1.71 × 10^{−21} | |
DHP-HFCM | 5.9216 | 8.34 × 10^{−11} | 5.9148 | 8.34 × 10^{−11} | |
HHP-FCM | 15.9536 | 6.12 × 10^{−45} | 15.9342 | 7.42 × 10^{−45} | |
HHP-GFCM | 9.5553 | 1.14 × 10^{−19} | 9.5437 | 1.25 × 10^{−19} | |
HHP-HFCM | 9.1332 | 1.25 × 10^{−13} | 9.1277 | 1.36 × 10^{−13} | |
SHP-FCM | 10.5755 | 2.79 × 10^{−23} | 10.5626 | 3.11 × 10^{−23} | |
SHP-GFCM | 11.6521 | 2.63 × 10^{−27} | 11.6380 | 2.98 × 10^{−27} | |
Category III Chengde | DHP-FCM | 13.0401 | 4.63 × 10^{−41} | 13.0242 | 5.54 × 10^{−41} |
DHP-GFCM | 12.9219 | 8.93 × 10^{−34} | 12.9062 | 1.04 × 10^{−33} | |
DHP-HFCM | 1.4234 | 3.74 × 10^{−51} | 1.4217 | 4.62 × 10^{−51} | |
HHP-FCM | 10.3126 | 4.40 × 10^{−43} | 10.3001 | 5.30 × 10^{−43} | |
HHP-GFCM | 10.2920 | 1.39 × 10^{−39} | 10.2795 | 1.65 × 10^{−39} | |
HHP-HFCM | 10.3339 | 2.25 × 10^{−36} | 10.3214 | 2.64 × 10^{−36} | |
SHP-FCM | 13.4234 | 9.09 × 10^{−33} | 13.4071 | 1.05 × 10^{−32} | |
SHP-GFCM | 13.2622 | 2.72 × 10^{−32} | 13.2461 | 3.14 × 10^{−32} |
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Gu, X.; Li, H.; Fan, H. Spatiotemporal Hybrid Air Pollution Early Warning System of Urban Agglomeration Based on Adaptive Feature Extraction and Hesitant Fuzzy Cognitive Maps. Systems 2023, 11, 286. https://doi.org/10.3390/systems11060286
Gu X, Li H, Fan H. Spatiotemporal Hybrid Air Pollution Early Warning System of Urban Agglomeration Based on Adaptive Feature Extraction and Hesitant Fuzzy Cognitive Maps. Systems. 2023; 11(6):286. https://doi.org/10.3390/systems11060286
Chicago/Turabian StyleGu, Xiaoyang, Hongmin Li, and Henghao Fan. 2023. "Spatiotemporal Hybrid Air Pollution Early Warning System of Urban Agglomeration Based on Adaptive Feature Extraction and Hesitant Fuzzy Cognitive Maps" Systems 11, no. 6: 286. https://doi.org/10.3390/systems11060286