论文部分内容阅读
Abstract ［Objectives］This study was conducted to evaluate the air quality of Shijiazhuang City, in order to facilitate the government to correctly formulate measures to prevent and control air pollution and protect Shijiazhuangs ambient air quality.
［Methods］ With the air quality data of Shijiazhuang City from February to March in 2019 as the research object, the gray correlation analysis method was used to determine weight A of each pollutant factor first, and then a single factor evaluation matrix R was constructed. The weight A and the single factor evaluation matrix R were synthesized using the M (·, +) fuzzy composite operator, obtaining a fuzzy matrix B between the factor set and the evaluation level.
［Results］ The eigenvalue of air quality was calculated according to matrix B: H =2.259 5.
［Conclusions］ The air quality in Shijiazhuang City from February to March was between grade 2 and grade 3, closer to grade 2, indicating that the air quality was good.
Key words Fuzzy comprehensive evaluation; Grey correlation; Air quality; Shijiazhuang
Received: February 26, 2020Accepted: April 21, 2020
Supported by Research Project of Science and Technology Youth Fund of Universities in Hebei Province (QN2016243); Research and Development Fund Project of Agricultural University of Hebei (JY2018046).
Zhuhong YUAN (1998-), female, P. R. China, devoted to research about applied mathematics. E-mail:171362958@qq.com.
*Corresponding author. E-mail: jdg109@sina.com.
With the rapid development of the social economy, the air pollution situation is becoming more and more serious, which not only affects peoples normal life order, but also seriously harms peoples health. Energy saving and emission reduction have become the theme of todays social development, and solving environmental pollution problems is urgent. Constructing mathematical models to evaluate and analyze air quality can provide a scientific basis for efficiently controlling air pollution and improving the living environment of residents.
Data Standardization
First, the air quality data of Shijiazhuang City from February to March in 2019 was collected as the research object, and a pollutant set, {PM2.5 , PM10 , SO2, NO2, CO, O3}, was established as the factor set. Then, data transformation and processing was carried out on the collected original data to eliminate the influence of dimension. In this paper, the Min-max standardization method was used to linearly transform the original data［1］, making the result fall on the interval［0, 1］. The original data yi was transformed as below: z = yi -max{ yi }max{ yi }-max{ yi }
Determining Weights Based on Grey Correlation Analysis
Calculation methods
First, we determined a reference sequence T 0=［ T 0(1), T 0(2) , …, T 0(m)］ and a comparison sequence T1, T2, …, Tk. T0(1) is the value at time 1, and T0(m) is the value at time m. Then, the grey correlation coefficient between the reference sequence and comparison sequence was calculated according to following formula:
ζi(k) =min s min t ｜ T0(t)-Ts(t) ｜+ ρ max s max t ｜ T0(t)-Ts(t) ｜｜ T0(k)-Ti(k) ｜+ ρ max s max t ｜ T0(t)-Ts(t) ｜
Wherein a smaller resolution coefficient suggests a smaller resolution, and is often taken to be 0.5. Finally, the correlation between each comparison sequence and reference sequence was calculated according to ri=1n∑n k=1ζi(k) . If the correlation between the comparison sequence and the reference sequence is large, it can be considered that their relative changes are basically consistent［3］.
Calculation results
The weight coefficient was determined by the gray correlation analysis method, and the results were normalized［4］, as shown in Table 1 below.
Fuzzy Comprehensive Evaluation and Analysis
Establishing factor set and evaluation set
According to the national published standards for ambient air quality, the main factors affecting air quality are PM2.5 , PM10 , SO2, NO2, CO and O3. Therefore, we gave a set of factors as below:
U={u1, u2, …u6} ={PM2.5 , PM10 , SO2, CO, NO2, O3},
The ambient air quality was evaluated as excellent, good, light pollution, moderate pollution, heavy pollution and severe pollution. Therefore, the evaluation set was:
V={v1, v2, …,v6} ={excellent, good, light pollution, moderate pollution, heavy pollution, severe pollution}.
Constructing a single factor evaluation matrix
Suppose the total number of monitoring and sampling of factor i is n , and the times of excellent, good, light pollution, moderate pollution, heavy pollution and severe pollution are n1, n2, n3, n4, n5 and n 6, respectively, then the single factor evaluation result is: r1=(ri1 , ri2 , ri3 , ri4 , ri5 , ri6 )=n1n, n2n, n3n, n4n, n5n, n6n.
According to the pollutant concentration limit in Table 2, we acquired the number of days that each indicator belongs to excellent, good, light pollution, moderate pollution, heavy pollution, severe pollution, and then calculated the proportion of days for each indicator in each evaluation,therey constructing a single factor evaluation matrix［5］. The results are shown in Table 3.
We calculated the weight A and the single-factor evaluation matrix R above, and then, using B~=A○R , we acquired the evaluation result as:
B~ =［0.199 0, 0.199 0, 0.169 5, 0.169 5, 0.199 0］
We could not judge the final result, so it was not appropriate to use the fuzzy operator. The weighted average model was used below.
Weighed average model— M (·, +)
The operation formula of the weighted average model was as follows:
bj=∑6i=1airij
Where ai represents the element in the weight and rij represents the element in the single-factor evaluation matrix. We acquired the evaluation result by the matrix composite operation as:
B=［0.457 6, 0.294 2, 0.109 0, 0.039 5, 0.034 2, 0.065 6］
It could be known that excellent accounted for 81.06% of all grades［6］, more than 50%, so the comprehensive evaluation of Shijiazhuangs air quality from February to March was good, of grade 2.
In addition, we also started from another perspective, we introduced an eigenvalue H . If H is closer to K ( K is a positive integer), the air quality can be judged to be of grade K , and the smaller the H value, the better the air quality.
H=∑6k=1k*bk
We calculated the eigenvalue of the air quality grade of Shijiazhuang City: H =2.259 4, which was close to 2, from which we judged the air quality of Shijiazhuang City from February to March as grade 2, good.
In summary, Shijiazhuangs air quality from February to March was judged as grade 2, good.
Conclusions
At present, the problem of atmospheric environmental pollution is becoming more and more prominent, and the haze weather seriously affects peoples social life and physical health. The evaluation of ambient air quality can objectively reflect the environmental situation and provide a theoretical basis for the development of air governance programs. The air quality data of Shijiazhuang City from February to March in 2019 was analyzed and judged to be of grade 2, good. For Shijiazhuang City with severe haze in previous years, the atmospheric environmental governance has achieved significant results, and the government should continue to strengthen supervision of air quality. References
［1］ HE QH, WANG JS, CHEN CM. Fussy comprehensive evaluation of ambient environmental quality in Nantong［J］. Journal of University of South China: Science and Technology, 2009, 23(3): 88-92. (In Chinese)
［2］ LI XC, CHENG RG, LI KZ. Fuzzy comprehensive valuing and grey forecast for air environmental quality［J］. System Engineering Theory and Practice, 2003(4): 124-129. (In Chinese)
［3］ XIE JJ, LIU CP. Fuzzy mathematics method and its application［M］. Wuhan: Huazhong University of Science&Technology Press, 2000. (In Chinese)
［4］ JI SJ, LYU JC. Fuzzy clustering and identification for spring maize varieties based on MATLAB ［J］. Journal of Shandong Agricultural University: Natural Science Edition, 2018,49(6): 965-967. (In Chinese)
［5］ FU HN, CHEN TY. Application of fuzzy comprehensive evaluation in Wuhan air quality evaluation ［J］. Journal of Hubei University: Natural Science Edition, 2007 (3): 298-301. (In Chinese)
［6］ HUANG DM, CHEN XQ, XIAO T. The comprehensive evaluation of the air quality for Baoding City based on principal component analysis and Fuzzy comprehensive evaluation［J］. Journal of Baoding University, 2015, 28(2): 119-126, 136. (In Chinese)
Editor: Yingzhi GUANGProofreader: Xinxiu ZHU
［Methods］ With the air quality data of Shijiazhuang City from February to March in 2019 as the research object, the gray correlation analysis method was used to determine weight A of each pollutant factor first, and then a single factor evaluation matrix R was constructed. The weight A and the single factor evaluation matrix R were synthesized using the M (·, +) fuzzy composite operator, obtaining a fuzzy matrix B between the factor set and the evaluation level.
［Results］ The eigenvalue of air quality was calculated according to matrix B: H =2.259 5.
［Conclusions］ The air quality in Shijiazhuang City from February to March was between grade 2 and grade 3, closer to grade 2, indicating that the air quality was good.
Key words Fuzzy comprehensive evaluation; Grey correlation; Air quality; Shijiazhuang
Received: February 26, 2020Accepted: April 21, 2020
Supported by Research Project of Science and Technology Youth Fund of Universities in Hebei Province (QN2016243); Research and Development Fund Project of Agricultural University of Hebei (JY2018046).
Zhuhong YUAN (1998-), female, P. R. China, devoted to research about applied mathematics. E-mail:171362958@qq.com.
*Corresponding author. E-mail: jdg109@sina.com.
With the rapid development of the social economy, the air pollution situation is becoming more and more serious, which not only affects peoples normal life order, but also seriously harms peoples health. Energy saving and emission reduction have become the theme of todays social development, and solving environmental pollution problems is urgent. Constructing mathematical models to evaluate and analyze air quality can provide a scientific basis for efficiently controlling air pollution and improving the living environment of residents.
Data Standardization
First, the air quality data of Shijiazhuang City from February to March in 2019 was collected as the research object, and a pollutant set, {PM2.5 , PM10 , SO2, NO2, CO, O3}, was established as the factor set. Then, data transformation and processing was carried out on the collected original data to eliminate the influence of dimension. In this paper, the Min-max standardization method was used to linearly transform the original data［1］, making the result fall on the interval［0, 1］. The original data yi was transformed as below: z = yi -max{ yi }max{ yi }-max{ yi }
Determining Weights Based on Grey Correlation Analysis
Calculation methods
First, we determined a reference sequence T 0=［ T 0(1), T 0(2) , …, T 0(m)］ and a comparison sequence T1, T2, …, Tk. T0(1) is the value at time 1, and T0(m) is the value at time m. Then, the grey correlation coefficient between the reference sequence and comparison sequence was calculated according to following formula:
ζi(k) =min s min t ｜ T0(t)-Ts(t) ｜+ ρ max s max t ｜ T0(t)-Ts(t) ｜｜ T0(k)-Ti(k) ｜+ ρ max s max t ｜ T0(t)-Ts(t) ｜
Wherein a smaller resolution coefficient suggests a smaller resolution, and is often taken to be 0.5. Finally, the correlation between each comparison sequence and reference sequence was calculated according to ri=1n∑n k=1ζi(k) . If the correlation between the comparison sequence and the reference sequence is large, it can be considered that their relative changes are basically consistent［3］.
Calculation results
The weight coefficient was determined by the gray correlation analysis method, and the results were normalized［4］, as shown in Table 1 below.
Fuzzy Comprehensive Evaluation and Analysis
Establishing factor set and evaluation set
According to the national published standards for ambient air quality, the main factors affecting air quality are PM2.5 , PM10 , SO2, NO2, CO and O3. Therefore, we gave a set of factors as below:
U={u1, u2, …u6} ={PM2.5 , PM10 , SO2, CO, NO2, O3},
The ambient air quality was evaluated as excellent, good, light pollution, moderate pollution, heavy pollution and severe pollution. Therefore, the evaluation set was:
V={v1, v2, …,v6} ={excellent, good, light pollution, moderate pollution, heavy pollution, severe pollution}.
Constructing a single factor evaluation matrix
Suppose the total number of monitoring and sampling of factor i is n , and the times of excellent, good, light pollution, moderate pollution, heavy pollution and severe pollution are n1, n2, n3, n4, n5 and n 6, respectively, then the single factor evaluation result is: r1=(ri1 , ri2 , ri3 , ri4 , ri5 , ri6 )=n1n, n2n, n3n, n4n, n5n, n6n.
According to the pollutant concentration limit in Table 2, we acquired the number of days that each indicator belongs to excellent, good, light pollution, moderate pollution, heavy pollution, severe pollution, and then calculated the proportion of days for each indicator in each evaluation,therey constructing a single factor evaluation matrix［5］. The results are shown in Table 3.
We calculated the weight A and the single-factor evaluation matrix R above, and then, using B~=A○R , we acquired the evaluation result as:
B~ =［0.199 0, 0.199 0, 0.169 5, 0.169 5, 0.199 0］
We could not judge the final result, so it was not appropriate to use the fuzzy operator. The weighted average model was used below.
Weighed average model— M (·, +)
The operation formula of the weighted average model was as follows:
bj=∑6i=1airij
Where ai represents the element in the weight and rij represents the element in the single-factor evaluation matrix. We acquired the evaluation result by the matrix composite operation as:
B=［0.457 6, 0.294 2, 0.109 0, 0.039 5, 0.034 2, 0.065 6］
It could be known that excellent accounted for 81.06% of all grades［6］, more than 50%, so the comprehensive evaluation of Shijiazhuangs air quality from February to March was good, of grade 2.
In addition, we also started from another perspective, we introduced an eigenvalue H . If H is closer to K ( K is a positive integer), the air quality can be judged to be of grade K , and the smaller the H value, the better the air quality.
H=∑6k=1k*bk
We calculated the eigenvalue of the air quality grade of Shijiazhuang City: H =2.259 4, which was close to 2, from which we judged the air quality of Shijiazhuang City from February to March as grade 2, good.
In summary, Shijiazhuangs air quality from February to March was judged as grade 2, good.
Conclusions
At present, the problem of atmospheric environmental pollution is becoming more and more prominent, and the haze weather seriously affects peoples social life and physical health. The evaluation of ambient air quality can objectively reflect the environmental situation and provide a theoretical basis for the development of air governance programs. The air quality data of Shijiazhuang City from February to March in 2019 was analyzed and judged to be of grade 2, good. For Shijiazhuang City with severe haze in previous years, the atmospheric environmental governance has achieved significant results, and the government should continue to strengthen supervision of air quality. References
［1］ HE QH, WANG JS, CHEN CM. Fussy comprehensive evaluation of ambient environmental quality in Nantong［J］. Journal of University of South China: Science and Technology, 2009, 23(3): 88-92. (In Chinese)
［2］ LI XC, CHENG RG, LI KZ. Fuzzy comprehensive valuing and grey forecast for air environmental quality［J］. System Engineering Theory and Practice, 2003(4): 124-129. (In Chinese)
［3］ XIE JJ, LIU CP. Fuzzy mathematics method and its application［M］. Wuhan: Huazhong University of Science&Technology Press, 2000. (In Chinese)
［4］ JI SJ, LYU JC. Fuzzy clustering and identification for spring maize varieties based on MATLAB ［J］. Journal of Shandong Agricultural University: Natural Science Edition, 2018,49(6): 965-967. (In Chinese)
［5］ FU HN, CHEN TY. Application of fuzzy comprehensive evaluation in Wuhan air quality evaluation ［J］. Journal of Hubei University: Natural Science Edition, 2007 (3): 298-301. (In Chinese)
［6］ HUANG DM, CHEN XQ, XIAO T. The comprehensive evaluation of the air quality for Baoding City based on principal component analysis and Fuzzy comprehensive evaluation［J］. Journal of Baoding University, 2015, 28(2): 119-126, 136. (In Chinese)
Editor: Yingzhi GUANGProofreader: Xinxiu ZHU