# Application of TOPSIS Method Combined with Grey Relational Degree in the Selection of Snow-Melting Agent Use Plan

Authors: Haiyan Yang; Mingyang Huang; Guangyu Zhou; Xiaowen Chen; Ruitao Ming
Journal: Journal of Nanomaterials
 (2022)

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## Abstract

With the rapid development of China’s ice and snow industry, the use of snow-melting agents as a nonpoint source pollution source is increasing, and the impact on the environment cannot be ignored. This paper expounds the agent, purpose, mechanism, and current situation of snow-melting agents at home and abroad and analyzes the national standards, industry standards, and technical indicators of various provinces and cities. This paper puts forward the standard of snow-melting agents, standardizes the production management and detection method of snow-melting agents, improves the quality of snow-melting agent products, and solves the adverse effects of environmental pollution of snow-melting agents. In order to select an economical, effective, and environmentally friendly snow-melting agent application plan that is suitable for cold mountainous areas, the article proposes a TOPSIS method evaluation model with the purpose of source control combined with grey correlation. Calcium, magnesium chloride, chloride salt mixed snow-melting agent (1 : 1 : 1 ratio), and calcium and magnesium acetate are used to melt snow in four specific environments (high cold and high sensitivity, high cold and low sensitivity, low cold and high sensitivity, and low cold and low sensitivity). The pros and cons of the dosage regimen are evaluated. The combined weighting method is used to overcome the shortcomings of the individual subjective and objective weighting methods, and it is concluded that calcium and magnesium acetate is the optimal solution in high-cold and high-sensitivity areas, calcium chloride is the optimal solution in high-cold and low-sensitivity areas, and magnesium chloride is the optimal solution in low-cold and high-sensitivity areas. As the optimal solution, calcium chloride with low cold and low sensitivity is the optimal solution.


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## Body

## 1. Introduction

In order to ensure road safety and vehicle mobility in winter, in some cold climate regions such as the north, a large amount of snow-melting agent and sand is applied on the road [1]. The 2022 Winter Olympics will be held in Beijing and Zhangjiakou, which will stimulate the development of my country’s ice and snow industry and will also lead to an increase in the amount of snow-melting agents [2]. The increasing use of snow-melting agents has made people worry about the adverse environmental impact of various snow-melting agents and actively change the snow and ice control strategy model [3]. While the snow-melting agent brings convenience and benefits, its wide use will also damage urban infrastructure such as road surface, pipe network, and metal structure and will have adverse effects on vegetation, soil, water, and other environments [4]. The snow-melting agent is widely used in road snow removal due to its high efficiency of snow melting and ice melting [5], but there are many kinds of snow-melting agents with complex and changeable components. Its main component is inorganic salt, and the price of sodium chloride is relatively cheap, so sodium chloride is widely used as a snow-melting agent [6–9].In addition to the nature of the snowmelt agent itself, the use of the snowmelt agent lacks rationality, and the impact of the binding criteria on the environment is also related. Ski resorts are generally located in the northern mountainous area, with low temperature, high environmental impact, high risk of roads leading to the ski resort, and dense crowds. For these reasons, there is a high demand for snowmelt agents in winter. Therefore, it is necessary to study and provide a decision-making method and provide a scientific basis for the selection of snow-melting agents in cold mountainous areas. For this multiobjective decision-making problem, in order to obtain credible results in a concise and easy-to-use method, the TOPSIS method can be used to evaluate the optimization. In the evaluation, it can comprehensively carry out evaluation optimization, which has great advantages in multiobjective decision-making [10].In winter, snow and dark ice will reduce the skid performance, thus affecting the safety and capacity of the road. Compared with the use of mechanical and heat and other snow and ice removal methods, snow-melting agents have the advantages of low cost and efficiently and effectively destroying the bonding force between ice and the road surface. It is widely used to remove snow and ice in winter but will corrode the structure along the road and its ancillary facilities and poison animals and plants.


## 2. Research Method

### 2.1. Application Plan and Evaluation Index of Snow-Melting Agent in Cold Mountain Area

#### 2.1.1. Application Plan of Snow-Melting Agent in Cold Mountain Area

Snow-melting agents are mainly divided into two categories, namely, chloride-based snow-melting agents and organic-based environmentally friendly snow-melting agents [11]. Chloride-based snow-melting agents include sodium chloride (NaCl), calcium chloride (CaCl2), magnesium chloride (MgCl2), potassium chloride (KCl2), and chloride salt mixed snow-melting agents. Organic environmental protection snow-melting agents include acetic acid, formic acid, urea, and alcohol, among which acetic acid is the most important. Acetic acid snow-melting agents include calcium magnesium acetate (CMA), potassium acetate (KAc), sodium acetate (NAAC), and CMAK (CMA and KAc). According to the difference of the common use of snow-melting agent, sodium chloride, calcium chloride, magnesium chloride, magnesium chloride salt mixed snow-melting agent (1 : 1 : 1 : 1:1 ratio), and magnesium acetate are selected. There are five programs, p1, p2, p3, p4, and p5. Considering the characteristics of cold degree, environmental sensitivity, and economic differences in each ski resort, temperatures below -10°C were defined as high temperatures, and temperatures above -10°C and below 0°C were defined as low temperatures. The optimal use of snowmelt agents was studied using A1, A2, A3, and A4 in four environments, both cold and low-cold low-sensitivity land.


#### 2.1.2. Evaluation Indicators

The evaluation is based on a selection of five snowmelts that vary in price, performance, and degree of environmental impact. The five kinds of snow-melting agents have relatively big differences in price, ranging from several hundred to tens of thousands. In terms of performance, there are also different snow-melting speeds, 30 min deicing rates, and different suitable temperatures. In terms of environmental impact, they have different effects on the soil, water body, vegetation, road, metal, etc. The evaluation indicators are shown in Table1.Table 1
Evaluation index table.
Target
Sodium chloride, calcium chloride, magnesium chloride, chloride mixed type, calcium magnesium acetate
Guidelines
Price
Performance
Environmental impact
Index
Price
Snow-melting speed
Deicing rate
Suitable temperature
Road damage
Metal corrosion
Soil impact
Water impact
Vegetation impact
Indicator meaning
Snow-melting agent price per ton
Snow-melting speed at the same dose
Snow removal amount of the same concentration of snow-melting agent in 30 min
Normal temperature range for snow removal
Corrosion measurement for roads
Corrosiveness to metal measurement
Degree of influence on soil properties
Degree of influence on water properties
Degree of damage to plants
Nature
Cost
Benefit
Benefit
Cost
Cost
Cost
Cost
Cost
Cost


### 2.2. TOPSIS Evaluation Model Combined with Grey Correlation Degree

#### 2.2.1. TOPSIS

The TOPSIS method was proposed by Hwang and Yoon in 1981 who published the monograph “Multi-Attribute Decision Making” [12]. In 2003, Liao proposed the TOPSIS method based on the signal-to-noise ratio-based process capability index. Yanrui studied the index weight determination method and the comprehensive evaluation method, obtained the G1 method based on the index scale to determine the index weight, and improved the TOPSIS method for the service quality evaluation of this paper, to determine the positive and negative ideal values of the index [13]. The TOPSIS method first determines the positive and negative ideal solutions of the problem and compares the distances between the feasible solutions to the positive ideal solution and the negative ideal solution [14]. The traditional TOPSIS method does not consider the similarity in shape, and the TOPSIS method may not obtain correct decision results when the amount of data information is small, but the grey relational analysis method can fully mine the internal information of the data and analyze the reference data. It is similar to the geometric curve of each group of data to determine the pros and cons of the program, and it does not require a large amount of data, which just forms a complementary relationship with the TOPSIS method [15].


### 2.3. The Basic Steps

#### 2.3.1. Create a Matrix

There arem schemes, p1,p2,p3⋯,pm, denoted as p=p1,p2,p3⋯,pm, and the n indicators of each scheme are I1,I2,I3⋯,In, recorded as I=I1,I2,I3⋯,In. Iij refers to the j-th index of the scheme pi. Create an initial evaluation matrix E:
(1)E=Iijm×n.


#### 2.3.2. Cochemotropic Treatment

In the evaluation indexIn, the level of the index value represents the different pros and cons of the plan. In order to facilitate the calculation, the index should be treated with homotaxis, and the indexes in the evaluation matrix should be classified into one category. The conversion methods usually include the reciprocal method and the difference method [10]. The evaluation matrix after homotaxis is E=Iij′m×n, and the transformation method is as follows:
(2)I′ij=1Iij,(3)I′ij=1−IijorI′ij=100−Iij.


#### 2.3.3. Normalization Processing

In order to eliminate the influence of dimension and order of magnitude between the evaluation indicators, the matrix after homotaxis is normalized. After normalization,E=gijm×n; the method is as follows:
(4)gij=Iij′∑i=1nIij′2.


#### 2.3.4. Weighted Processing

Due to the different purposes and requirements of the scheme, the importance of each element of the criterion layer and the index layer will be different, so the matrix should be weighted as follows:(5)E=Zijm×n=gijm×ndiagwjn×n,where ωj represents the weight of the j-th index and satisfies ∑j=1nωj=1.


#### 2.3.5. Positive and Negative Ideal Solution Distances

In the TOPSIS square,pi has n indicators and there are n feasible solutions Zj=Zi1,Zi2,Zi3⋯,Zinj=1,2,3⋯,n; the positive ideal solution assumes Z+, Zj+=Z1+,Z2+,Z3+⋯,Zn+, the distance from the feasible solution Zj to Zj+ is [16]
(6)Si+=∑j−1mZij−Zj+2i=1,2,3⋯,m.In the same way, letZj−=Z1−,Z2−,Z3+⋯,Zn− be the negative ideal solution of the index, and the distance between the feasible solution Zj and the negative ideal solution Zj− is [17]
(7)Si−=∑j=1mZij−Zj−2i=1,2,2⋯,m.


#### 2.3.6. Calculation of Grey Relational Degree

Thei-th sample positive ideal solution is the j-th index grey correlation coefficient:
(8)ξij+=Δmin+ρΔmaxΔij+ρΔmax.In formula (10) ∆ij=Zj+−Zij, Δmin=miniminjΔzij is the minimum difference, Δmax=maximaxjΔzij is the maximum difference, and ρ is the resolution coefficient, generally 0.5.The grey relational degree of the positive ideal solution of thei-th sample is
(9)ξi+=1n∑i=1nξij+.The grey correlation coefficient of thej-th index of the negative ideal solution of the i-th sample is
(10)ξij−=Δmin+ρΔmaxΔij+ρΔmax.The grey relational degree of the negative ideal solution of thei-th sample is
(11)ξi−=1n∑i=1nξij+.


#### 2.3.7. The Pros and Cons of the Plan

Positive and negative ideal solutions and grey relational degree dimensionless processing are(12)Ri∗=RimaxRi1≤i≤m.R
i represents S+, S−, ξj+, and ξj−; Ri∗ represents the parameter values after dimensionless processing and integrates the positive and negative ideal solutions and grey correlation degree after dimensionless processing:
(13)Ti+=fSi−+1−fξi+,(14)Ti−=fSi++1−fξi−.f is the preference coefficient, which can be adjusted according to the preference degree of the decision-maker.C
i represents the relative proximity; the more the relative proximity is equal to 1, the better the solution, and the optimal solution can be obtained by sorting Ci [18]:
(15)Ci=Ti+Ti++Ti−0≤Ci≤1,i=1,2,3⋯,m.


### 2.4. Weight Determination

In order to reduce the limitation of individual weighting, the combined weighting method is adopted in this paper. To reduce the limitations of individual weighting, a combined weighting approach is used. Subjective weights were determined by expert scoring based on the four environmental specificities of low-temperature sensitivity, low-temperature sensitivity, low-temperature sensitivity, and low-temperature sensitivity. Target weights were determined using the entropy weight method. The entropy weight method is the weighting method based on the amount of information in each index. The smaller the entropy of the exponent, the greater the degree of the exponential and the greater the role it plays in the comprehensive evaluation. The weight of this index should also be large [19], and the calculation steps of the entropy weight method are shown in equations (16) and (17). The subjective weight mainly refers to the expert scores on the price, performance, and pollution degree of the snow agent in the research of Yin [20] in 2013. According to the characteristics of cold mountainous areas, the weights of the evaluation schemes for the use of snow-melting agents are shown in Table 2.Table 2
Table of evaluation index weights.
Target
Sodium chloride, calcium chloride, magnesium chloride, chloride mixed type, calcium magnesium acetate
Guidelines
Price
Performance
Environmental impact
Subjective weight
A1
0.050
0.300
0.650
A2
0.300
0.300
0.400
A3
0.150
0.200
0.650
A4
0.350
0.200
0.450
Index
Price
Snow-melting speed
Deicing rate
Suitable temperature
Road damage
Metal corrosion
Soil impact
Water impact
Vegetation impact
Objective weight
0.456
0.069
0.001
0.179
0.066
0.063
0.050
0.066
0.050
Combined weights
A1
0.153
0.070
0.001
0.180
0.134
0.127
0.101
0.133
0.101
A2
0.415
0.063
0.001
0.163
0.080
0.077
0.061
0.080
0.061
A3
0.220
0.045
0.001
0.115
0.139
0.132
0.105
0.138
0.105
A4
0.466
0.040
0.001
0.105
0.087
0.083
0.066
0.087
0.066According to the definition of entropy, the entropy valuebj of the j-th index is
(16)bj=−∑i=1mgijlngij1nmj=1,2,⋯n.In formula (3), 0≤bj≤1, when specifying gij=0, gijlngij=0.
(17)wj=1−bjn−∑j=1mbjj=1,2,⋯n.


## 2.1. Application Plan and Evaluation Index of Snow-Melting Agent in Cold Mountain Area

### 2.1.1. Application Plan of Snow-Melting Agent in Cold Mountain Area

Snow-melting agents are mainly divided into two categories, namely, chloride-based snow-melting agents and organic-based environmentally friendly snow-melting agents [11]. Chloride-based snow-melting agents include sodium chloride (NaCl), calcium chloride (CaCl2), magnesium chloride (MgCl2), potassium chloride (KCl2), and chloride salt mixed snow-melting agents. Organic environmental protection snow-melting agents include acetic acid, formic acid, urea, and alcohol, among which acetic acid is the most important. Acetic acid snow-melting agents include calcium magnesium acetate (CMA), potassium acetate (KAc), sodium acetate (NAAC), and CMAK (CMA and KAc). According to the difference of the common use of snow-melting agent, sodium chloride, calcium chloride, magnesium chloride, magnesium chloride salt mixed snow-melting agent (1 : 1 : 1 : 1:1 ratio), and magnesium acetate are selected. There are five programs, p1, p2, p3, p4, and p5. Considering the characteristics of cold degree, environmental sensitivity, and economic differences in each ski resort, temperatures below -10°C were defined as high temperatures, and temperatures above -10°C and below 0°C were defined as low temperatures. The optimal use of snowmelt agents was studied using A1, A2, A3, and A4 in four environments, both cold and low-cold low-sensitivity land.


### 2.1.2. Evaluation Indicators

The evaluation is based on a selection of five snowmelts that vary in price, performance, and degree of environmental impact. The five kinds of snow-melting agents have relatively big differences in price, ranging from several hundred to tens of thousands. In terms of performance, there are also different snow-melting speeds, 30 min deicing rates, and different suitable temperatures. In terms of environmental impact, they have different effects on the soil, water body, vegetation, road, metal, etc. The evaluation indicators are shown in Table1.Table 1
Evaluation index table.
Target
Sodium chloride, calcium chloride, magnesium chloride, chloride mixed type, calcium magnesium acetate
Guidelines
Price
Performance
Environmental impact
Index
Price
Snow-melting speed
Deicing rate
Suitable temperature
Road damage
Metal corrosion
Soil impact
Water impact
Vegetation impact
Indicator meaning
Snow-melting agent price per ton
Snow-melting speed at the same dose
Snow removal amount of the same concentration of snow-melting agent in 30 min
Normal temperature range for snow removal
Corrosion measurement for roads
Corrosiveness to metal measurement
Degree of influence on soil properties
Degree of influence on water properties
Degree of damage to plants
Nature
Cost
Benefit
Benefit
Cost
Cost
Cost
Cost
Cost
Cost


## 2.1.1. Application Plan of Snow-Melting Agent in Cold Mountain Area

Snow-melting agents are mainly divided into two categories, namely, chloride-based snow-melting agents and organic-based environmentally friendly snow-melting agents [11]. Chloride-based snow-melting agents include sodium chloride (NaCl), calcium chloride (CaCl2), magnesium chloride (MgCl2), potassium chloride (KCl2), and chloride salt mixed snow-melting agents. Organic environmental protection snow-melting agents include acetic acid, formic acid, urea, and alcohol, among which acetic acid is the most important. Acetic acid snow-melting agents include calcium magnesium acetate (CMA), potassium acetate (KAc), sodium acetate (NAAC), and CMAK (CMA and KAc). According to the difference of the common use of snow-melting agent, sodium chloride, calcium chloride, magnesium chloride, magnesium chloride salt mixed snow-melting agent (1 : 1 : 1 : 1:1 ratio), and magnesium acetate are selected. There are five programs, p1, p2, p3, p4, and p5. Considering the characteristics of cold degree, environmental sensitivity, and economic differences in each ski resort, temperatures below -10°C were defined as high temperatures, and temperatures above -10°C and below 0°C were defined as low temperatures. The optimal use of snowmelt agents was studied using A1, A2, A3, and A4 in four environments, both cold and low-cold low-sensitivity land.


## 2.1.2. Evaluation Indicators

The evaluation is based on a selection of five snowmelts that vary in price, performance, and degree of environmental impact. The five kinds of snow-melting agents have relatively big differences in price, ranging from several hundred to tens of thousands. In terms of performance, there are also different snow-melting speeds, 30 min deicing rates, and different suitable temperatures. In terms of environmental impact, they have different effects on the soil, water body, vegetation, road, metal, etc. The evaluation indicators are shown in Table1.Table 1
Evaluation index table.
Target
Sodium chloride, calcium chloride, magnesium chloride, chloride mixed type, calcium magnesium acetate
Guidelines
Price
Performance
Environmental impact
Index
Price
Snow-melting speed
Deicing rate
Suitable temperature
Road damage
Metal corrosion
Soil impact
Water impact
Vegetation impact
Indicator meaning
Snow-melting agent price per ton
Snow-melting speed at the same dose
Snow removal amount of the same concentration of snow-melting agent in 30 min
Normal temperature range for snow removal
Corrosion measurement for roads
Corrosiveness to metal measurement
Degree of influence on soil properties
Degree of influence on water properties
Degree of damage to plants
Nature
Cost
Benefit
Benefit
Cost
Cost
Cost
Cost
Cost
Cost


## 2.2. TOPSIS Evaluation Model Combined with Grey Correlation Degree

### 2.2.1. TOPSIS

The TOPSIS method was proposed by Hwang and Yoon in 1981 who published the monograph “Multi-Attribute Decision Making” [12]. In 2003, Liao proposed the TOPSIS method based on the signal-to-noise ratio-based process capability index. Yanrui studied the index weight determination method and the comprehensive evaluation method, obtained the G1 method based on the index scale to determine the index weight, and improved the TOPSIS method for the service quality evaluation of this paper, to determine the positive and negative ideal values of the index [13]. The TOPSIS method first determines the positive and negative ideal solutions of the problem and compares the distances between the feasible solutions to the positive ideal solution and the negative ideal solution [14]. The traditional TOPSIS method does not consider the similarity in shape, and the TOPSIS method may not obtain correct decision results when the amount of data information is small, but the grey relational analysis method can fully mine the internal information of the data and analyze the reference data. It is similar to the geometric curve of each group of data to determine the pros and cons of the program, and it does not require a large amount of data, which just forms a complementary relationship with the TOPSIS method [15].


## 2.2.1. TOPSIS

The TOPSIS method was proposed by Hwang and Yoon in 1981 who published the monograph “Multi-Attribute Decision Making” [12]. In 2003, Liao proposed the TOPSIS method based on the signal-to-noise ratio-based process capability index. Yanrui studied the index weight determination method and the comprehensive evaluation method, obtained the G1 method based on the index scale to determine the index weight, and improved the TOPSIS method for the service quality evaluation of this paper, to determine the positive and negative ideal values of the index [13]. The TOPSIS method first determines the positive and negative ideal solutions of the problem and compares the distances between the feasible solutions to the positive ideal solution and the negative ideal solution [14]. The traditional TOPSIS method does not consider the similarity in shape, and the TOPSIS method may not obtain correct decision results when the amount of data information is small, but the grey relational analysis method can fully mine the internal information of the data and analyze the reference data. It is similar to the geometric curve of each group of data to determine the pros and cons of the program, and it does not require a large amount of data, which just forms a complementary relationship with the TOPSIS method [15].


## 2.3. The Basic Steps

### 2.3.1. Create a Matrix

There arem schemes, p1,p2,p3⋯,pm, denoted as p=p1,p2,p3⋯,pm, and the n indicators of each scheme are I1,I2,I3⋯,In, recorded as I=I1,I2,I3⋯,In. Iij refers to the j-th index of the scheme pi. Create an initial evaluation matrix E:
(1)E=Iijm×n.


### 2.3.2. Cochemotropic Treatment

In the evaluation indexIn, the level of the index value represents the different pros and cons of the plan. In order to facilitate the calculation, the index should be treated with homotaxis, and the indexes in the evaluation matrix should be classified into one category. The conversion methods usually include the reciprocal method and the difference method [10]. The evaluation matrix after homotaxis is E=Iij′m×n, and the transformation method is as follows:
(2)I′ij=1Iij,(3)I′ij=1−IijorI′ij=100−Iij.


### 2.3.3. Normalization Processing

In order to eliminate the influence of dimension and order of magnitude between the evaluation indicators, the matrix after homotaxis is normalized. After normalization,E=gijm×n; the method is as follows:
(4)gij=Iij′∑i=1nIij′2.


### 2.3.4. Weighted Processing

Due to the different purposes and requirements of the scheme, the importance of each element of the criterion layer and the index layer will be different, so the matrix should be weighted as follows:(5)E=Zijm×n=gijm×ndiagwjn×n,where ωj represents the weight of the j-th index and satisfies ∑j=1nωj=1.


### 2.3.5. Positive and Negative Ideal Solution Distances

In the TOPSIS square,pi has n indicators and there are n feasible solutions Zj=Zi1,Zi2,Zi3⋯,Zinj=1,2,3⋯,n; the positive ideal solution assumes Z+, Zj+=Z1+,Z2+,Z3+⋯,Zn+, the distance from the feasible solution Zj to Zj+ is [16]
(6)Si+=∑j−1mZij−Zj+2i=1,2,3⋯,m.In the same way, letZj−=Z1−,Z2−,Z3+⋯,Zn− be the negative ideal solution of the index, and the distance between the feasible solution Zj and the negative ideal solution Zj− is [17]
(7)Si−=∑j=1mZij−Zj−2i=1,2,2⋯,m.


### 2.3.6. Calculation of Grey Relational Degree

Thei-th sample positive ideal solution is the j-th index grey correlation coefficient:
(8)ξij+=Δmin+ρΔmaxΔij+ρΔmax.In formula (10) ∆ij=Zj+−Zij, Δmin=miniminjΔzij is the minimum difference, Δmax=maximaxjΔzij is the maximum difference, and ρ is the resolution coefficient, generally 0.5.The grey relational degree of the positive ideal solution of thei-th sample is
(9)ξi+=1n∑i=1nξij+.The grey correlation coefficient of thej-th index of the negative ideal solution of the i-th sample is
(10)ξij−=Δmin+ρΔmaxΔij+ρΔmax.The grey relational degree of the negative ideal solution of thei-th sample is
(11)ξi−=1n∑i=1nξij+.


### 2.3.7. The Pros and Cons of the Plan

Positive and negative ideal solutions and grey relational degree dimensionless processing are(12)Ri∗=RimaxRi1≤i≤m.R
i represents S+, S−, ξj+, and ξj−; Ri∗ represents the parameter values after dimensionless processing and integrates the positive and negative ideal solutions and grey correlation degree after dimensionless processing:
(13)Ti+=fSi−+1−fξi+,(14)Ti−=fSi++1−fξi−.f is the preference coefficient, which can be adjusted according to the preference degree of the decision-maker.C
i represents the relative proximity; the more the relative proximity is equal to 1, the better the solution, and the optimal solution can be obtained by sorting Ci [18]:
(15)Ci=Ti+Ti++Ti−0≤Ci≤1,i=1,2,3⋯,m.


## 2.3.1. Create a Matrix

There arem schemes, p1,p2,p3⋯,pm, denoted as p=p1,p2,p3⋯,pm, and the n indicators of each scheme are I1,I2,I3⋯,In, recorded as I=I1,I2,I3⋯,In. Iij refers to the j-th index of the scheme pi. Create an initial evaluation matrix E:
(1)E=Iijm×n.


## 2.3.2. Cochemotropic Treatment

In the evaluation indexIn, the level of the index value represents the different pros and cons of the plan. In order to facilitate the calculation, the index should be treated with homotaxis, and the indexes in the evaluation matrix should be classified into one category. The conversion methods usually include the reciprocal method and the difference method [10]. The evaluation matrix after homotaxis is E=Iij′m×n, and the transformation method is as follows:
(2)I′ij=1Iij,(3)I′ij=1−IijorI′ij=100−Iij.


## 2.3.3. Normalization Processing

In order to eliminate the influence of dimension and order of magnitude between the evaluation indicators, the matrix after homotaxis is normalized. After normalization,E=gijm×n; the method is as follows:
(4)gij=Iij′∑i=1nIij′2.


## 2.3.4. Weighted Processing

Due to the different purposes and requirements of the scheme, the importance of each element of the criterion layer and the index layer will be different, so the matrix should be weighted as follows:(5)E=Zijm×n=gijm×ndiagwjn×n,where ωj represents the weight of the j-th index and satisfies ∑j=1nωj=1.


## 2.3.5. Positive and Negative Ideal Solution Distances

In the TOPSIS square,pi has n indicators and there are n feasible solutions Zj=Zi1,Zi2,Zi3⋯,Zinj=1,2,3⋯,n; the positive ideal solution assumes Z+, Zj+=Z1+,Z2+,Z3+⋯,Zn+, the distance from the feasible solution Zj to Zj+ is [16]
(6)Si+=∑j−1mZij−Zj+2i=1,2,3⋯,m.In the same way, letZj−=Z1−,Z2−,Z3+⋯,Zn− be the negative ideal solution of the index, and the distance between the feasible solution Zj and the negative ideal solution Zj− is [17]
(7)Si−=∑j=1mZij−Zj−2i=1,2,2⋯,m.


## 2.3.6. Calculation of Grey Relational Degree

Thei-th sample positive ideal solution is the j-th index grey correlation coefficient:
(8)ξij+=Δmin+ρΔmaxΔij+ρΔmax.In formula (10) ∆ij=Zj+−Zij, Δmin=miniminjΔzij is the minimum difference, Δmax=maximaxjΔzij is the maximum difference, and ρ is the resolution coefficient, generally 0.5.The grey relational degree of the positive ideal solution of thei-th sample is
(9)ξi+=1n∑i=1nξij+.The grey correlation coefficient of thej-th index of the negative ideal solution of the i-th sample is
(10)ξij−=Δmin+ρΔmaxΔij+ρΔmax.The grey relational degree of the negative ideal solution of thei-th sample is
(11)ξi−=1n∑i=1nξij+.


## 2.3.7. The Pros and Cons of the Plan

Positive and negative ideal solutions and grey relational degree dimensionless processing are(12)Ri∗=RimaxRi1≤i≤m.R
i represents S+, S−, ξj+, and ξj−; Ri∗ represents the parameter values after dimensionless processing and integrates the positive and negative ideal solutions and grey correlation degree after dimensionless processing:
(13)Ti+=fSi−+1−fξi+,(14)Ti−=fSi++1−fξi−.f is the preference coefficient, which can be adjusted according to the preference degree of the decision-maker.C
i represents the relative proximity; the more the relative proximity is equal to 1, the better the solution, and the optimal solution can be obtained by sorting Ci [18]:
(15)Ci=Ti+Ti++Ti−0≤Ci≤1,i=1,2,3⋯,m.


## 2.4. Weight Determination

In order to reduce the limitation of individual weighting, the combined weighting method is adopted in this paper. To reduce the limitations of individual weighting, a combined weighting approach is used. Subjective weights were determined by expert scoring based on the four environmental specificities of low-temperature sensitivity, low-temperature sensitivity, low-temperature sensitivity, and low-temperature sensitivity. Target weights were determined using the entropy weight method. The entropy weight method is the weighting method based on the amount of information in each index. The smaller the entropy of the exponent, the greater the degree of the exponential and the greater the role it plays in the comprehensive evaluation. The weight of this index should also be large [19], and the calculation steps of the entropy weight method are shown in equations (16) and (17). The subjective weight mainly refers to the expert scores on the price, performance, and pollution degree of the snow agent in the research of Yin [20] in 2013. According to the characteristics of cold mountainous areas, the weights of the evaluation schemes for the use of snow-melting agents are shown in Table 2.Table 2
Table of evaluation index weights.
Target
Sodium chloride, calcium chloride, magnesium chloride, chloride mixed type, calcium magnesium acetate
Guidelines
Price
Performance
Environmental impact
Subjective weight
A1
0.050
0.300
0.650
A2
0.300
0.300
0.400
A3
0.150
0.200
0.650
A4
0.350
0.200
0.450
Index
Price
Snow-melting speed
Deicing rate
Suitable temperature
Road damage
Metal corrosion
Soil impact
Water impact
Vegetation impact
Objective weight
0.456
0.069
0.001
0.179
0.066
0.063
0.050
0.066
0.050
Combined weights
A1
0.153
0.070
0.001
0.180
0.134
0.127
0.101
0.133
0.101
A2
0.415
0.063
0.001
0.163
0.080
0.077
0.061
0.080
0.061
A3
0.220
0.045
0.001
0.115
0.139
0.132
0.105
0.138
0.105
A4
0.466
0.040
0.001
0.105
0.087
0.083
0.066
0.087
0.066According to the definition of entropy, the entropy valuebj of the j-th index is
(16)bj=−∑i=1mgijlngij1nmj=1,2,⋯n.In formula (3), 0≤bj≤1, when specifying gij=0, gijlngij=0.
(17)wj=1−bjn−∑j=1mbjj=1,2,⋯n.


## 3. Results and Analysis

### 3.1. Scheme Calculation

#### 3.1.1. Matrix Creation and Calculation

There are a total of 9 indicators for each of the 5 snow-melting agent schemes, and the index evaluation data are shown in Table3.Table 3
Evaluation index data table.
Plan
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Price (yuan/ton)1
400
900
1000
766
14000
Snow-melting speed2
100%
150%
150%
133%
200%
Deicing rate3
100%
102.4%
96.4%
99.6%
95.2%
Suitable working temperature (°C)4
-1~-10
-1~-30
-1~-20
-1~-20
-1~-30
Road damage4
100%
97%
97%
98%
33%
Degree of metal corrosion4
100%
89%
87%
91%
26%
Soil impact5
100%
96%
81%
92.3%
37%
Water impact5
100%
112%
84%
98.6%
40%
Vegetation impact5
100%
96%
81%
92.3%
37%
12010 Beijing area recommended list price of snow-melting agent products. 2Snowmelt velocity defined by NaCl as standard [21]. 3The deicing rate of 18% concentration snow-melting agent in 30 min is based on NaCl [22]. 4Summarized from the experiment of Shi et al. and converted to percentage based on NaCl [23]. 5In 2012, Dai et al. [24] proposed and proved the concept that the effects of different snow-melting agents on soil, water and soil, and plants are significantly different.And the initial evaluation matrixE is established from the above evaluation data and formula (1), using formulas (2) and (3) to carry out the same chemotaxis matrix as shown in Table 4.Table 4
Homozygous matrix.
Plan
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Price (yuan/ton)
14600
14100
14000
14234.
1000
Snow-melting speed
1.000
1.500
1.500
1.330
2.000
Deicing rate
1.000
1.024
0.964
0.996
0.952
Suitable working temperature (°C)
10.000
30.000
20.000
20.000
30.000
Road damage
1.000
1.030
1.030
1.020
1.670
Degree of metal corrosion
1.000
1.110
1.130
1.090
1.740
Soil impact
1.000
1.040
1.190
1.077
1.630
Water impact
1.000
0.880
1.160
1.014
1.600
Vegetation impact
1.000
1.004
1.190
1.077
1.630According to formula (4), the normalization process is performed as shown in Table 5.Table 5
Normalized matrix table.
Plan
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Price (yuan/ton)
0.495
0.491
0.500
0.035
0.512
Snow-melting speed
0.447
0.447
0.396
0.596
0.298
Deicing rate
0.464
0.437
0.451
0.431
0.453
Suitable working temperature (°C)
0.577
0.385
0.385
0.577
0.192
Road damage
0.391
0.391
0.387
0.633
0.379
Degree of metal corrosion
0.399
0.407
0.392
0.626
0.360
Soil impact
0.385
0.440
0.398
0.603
0.370
Water impact
0.386
0.368
0.515
0.515
0.907
Vegetation impact
0.372
0.402
0.513
0.531
0.908The evaluation matrix is weighted according to formula (5), and the distance values are obtained according to formulas (6) and (7): the optimal distance S+ and the worst distance S− are shown in Table 6.Table 6
Positive and negative ideal solution distance table.
Name
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Alpine and highly sensitive
Positive ideal solution distance
0.098
0.066
0.065
0.072
0.073
Negative ideal solution distance
0.073
0.100
0.081
0.080
0.100
Low sensitivity to high and cold
Positive ideal solution distance
0.077
0.041
0.047
0.050
0.198
Negative ideal solution distance
0.198
0.201
0.192
0.195
0.078
Low cold and high sensitivity
Positive ideal solution distance
0.083
0.068
0.061
0.068
0.105
Negative ideal solution distance
0.105
0.111
0.105
0.105
0.085
Hyposensitive
Positive ideal solution distance
0.060
0.044
0.042
0.046
0.222
Negative ideal solution distance
0.223
0.218
0.214
0.218
0.062


### 3.2. Calculation of Grey Relational Degree

According to formulas (8), (9), (10), and (11), the grey correlation degree is calculated for the evaluation matrix, and the resolution coefficient is taken as 0.5, as shown in Table 7.Table 7
Grey correlation table of positive and negative ideal solutions.
Name
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Alpine and highly sensitive
Positive ideal solution distance
0.642
0.727
0.701
0.677
0.926
Negative ideal solution distance
0.910
0.803
0.761
0.807
0.637
Low sensitivity to high and cold
Positive ideal solution distance
0.856
0.901
0.887
0.878
0.926
Negative ideal solution distance
0.922
0.868
0.868
0.882
0.853
Low cold and high sensitivity
Positive ideal solution distance
0.725
0.782
0.774
0.755
0.926
Negative ideal solution distance
0.914
0.844
0.815
0.849
0.720
Hyposensitive
Positive ideal solution distance
0.879
0.908
0.902
0.895
0.926
Negative ideal solution distance
0.922
0.886
0.882
0.894
0.876


### 3.3. Relative Proximity

According to formula (12), the positive and negative ideal solutions and the grey relational degree are dimensionless, and the positive and negative ideal solutions and grey relational degree after comprehensive dimensionlessization using formulas (13) and (14) are shown in Table 8.Table 8
Proximity table of positive and negative ideal solutions.
Name
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Alpine and highly sensitive
Positive ideal solution proximity
0.713
0.890
0.782
0.765
1.000
Negative ideal solution proximity
1.000
0.777
0.749
0.809
0.723
Low sensitivity to high and cold
Positive ideal solution proximity
0.955
0.987
0.957
0.960
0.693
Negative ideal solution proximity
0.693
0.574
0.589
0.605
0.963
Low cold and high sensitivity
Positive ideal solution proximity
0.866
0.922
0.891
0.882
0.885
Negative ideal solution proximity
0.893
0.785
0.734
0.787
0.894
Hyposensitive
Positive ideal solution proximity
0.975
0.980
0.968
0.972
0.638
Negative ideal solution proximity
0.635
0.578
0.573
0.588
0.975The relative proximity calculation formula (15) can obtain the proximity as C, as shown in Table 9.Table 9
Table of relative proximity C values.
Name
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Alpine and highly sensitive
Relative proximity
0.416
0.534
0.511
0.486
0.580
Low sensitivity to high and cold
Relative proximity
0.579
0.632
0.619
0.613
0.418
Low cold and high sensitivity
Relative proximity
0.492
0.540
0.548
0.528
0.497
Hyposensitive
Relative proximity
0.605
0.629
0.628
0.623
0.396


## 3.1. Scheme Calculation

### 3.1.1. Matrix Creation and Calculation

There are a total of 9 indicators for each of the 5 snow-melting agent schemes, and the index evaluation data are shown in Table3.Table 3
Evaluation index data table.
Plan
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Price (yuan/ton)1
400
900
1000
766
14000
Snow-melting speed2
100%
150%
150%
133%
200%
Deicing rate3
100%
102.4%
96.4%
99.6%
95.2%
Suitable working temperature (°C)4
-1~-10
-1~-30
-1~-20
-1~-20
-1~-30
Road damage4
100%
97%
97%
98%
33%
Degree of metal corrosion4
100%
89%
87%
91%
26%
Soil impact5
100%
96%
81%
92.3%
37%
Water impact5
100%
112%
84%
98.6%
40%
Vegetation impact5
100%
96%
81%
92.3%
37%
12010 Beijing area recommended list price of snow-melting agent products. 2Snowmelt velocity defined by NaCl as standard [21]. 3The deicing rate of 18% concentration snow-melting agent in 30 min is based on NaCl [22]. 4Summarized from the experiment of Shi et al. and converted to percentage based on NaCl [23]. 5In 2012, Dai et al. [24] proposed and proved the concept that the effects of different snow-melting agents on soil, water and soil, and plants are significantly different.And the initial evaluation matrixE is established from the above evaluation data and formula (1), using formulas (2) and (3) to carry out the same chemotaxis matrix as shown in Table 4.Table 4
Homozygous matrix.
Plan
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Price (yuan/ton)
14600
14100
14000
14234.
1000
Snow-melting speed
1.000
1.500
1.500
1.330
2.000
Deicing rate
1.000
1.024
0.964
0.996
0.952
Suitable working temperature (°C)
10.000
30.000
20.000
20.000
30.000
Road damage
1.000
1.030
1.030
1.020
1.670
Degree of metal corrosion
1.000
1.110
1.130
1.090
1.740
Soil impact
1.000
1.040
1.190
1.077
1.630
Water impact
1.000
0.880
1.160
1.014
1.600
Vegetation impact
1.000
1.004
1.190
1.077
1.630According to formula (4), the normalization process is performed as shown in Table 5.Table 5
Normalized matrix table.
Plan
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Price (yuan/ton)
0.495
0.491
0.500
0.035
0.512
Snow-melting speed
0.447
0.447
0.396
0.596
0.298
Deicing rate
0.464
0.437
0.451
0.431
0.453
Suitable working temperature (°C)
0.577
0.385
0.385
0.577
0.192
Road damage
0.391
0.391
0.387
0.633
0.379
Degree of metal corrosion
0.399
0.407
0.392
0.626
0.360
Soil impact
0.385
0.440
0.398
0.603
0.370
Water impact
0.386
0.368
0.515
0.515
0.907
Vegetation impact
0.372
0.402
0.513
0.531
0.908The evaluation matrix is weighted according to formula (5), and the distance values are obtained according to formulas (6) and (7): the optimal distance S+ and the worst distance S− are shown in Table 6.Table 6
Positive and negative ideal solution distance table.
Name
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Alpine and highly sensitive
Positive ideal solution distance
0.098
0.066
0.065
0.072
0.073
Negative ideal solution distance
0.073
0.100
0.081
0.080
0.100
Low sensitivity to high and cold
Positive ideal solution distance
0.077
0.041
0.047
0.050
0.198
Negative ideal solution distance
0.198
0.201
0.192
0.195
0.078
Low cold and high sensitivity
Positive ideal solution distance
0.083
0.068
0.061
0.068
0.105
Negative ideal solution distance
0.105
0.111
0.105
0.105
0.085
Hyposensitive
Positive ideal solution distance
0.060
0.044
0.042
0.046
0.222
Negative ideal solution distance
0.223
0.218
0.214
0.218
0.062


## 3.1.1. Matrix Creation and Calculation

There are a total of 9 indicators for each of the 5 snow-melting agent schemes, and the index evaluation data are shown in Table3.Table 3
Evaluation index data table.
Plan
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Price (yuan/ton)1
400
900
1000
766
14000
Snow-melting speed2
100%
150%
150%
133%
200%
Deicing rate3
100%
102.4%
96.4%
99.6%
95.2%
Suitable working temperature (°C)4
-1~-10
-1~-30
-1~-20
-1~-20
-1~-30
Road damage4
100%
97%
97%
98%
33%
Degree of metal corrosion4
100%
89%
87%
91%
26%
Soil impact5
100%
96%
81%
92.3%
37%
Water impact5
100%
112%
84%
98.6%
40%
Vegetation impact5
100%
96%
81%
92.3%
37%
12010 Beijing area recommended list price of snow-melting agent products. 2Snowmelt velocity defined by NaCl as standard [21]. 3The deicing rate of 18% concentration snow-melting agent in 30 min is based on NaCl [22]. 4Summarized from the experiment of Shi et al. and converted to percentage based on NaCl [23]. 5In 2012, Dai et al. [24] proposed and proved the concept that the effects of different snow-melting agents on soil, water and soil, and plants are significantly different.And the initial evaluation matrixE is established from the above evaluation data and formula (1), using formulas (2) and (3) to carry out the same chemotaxis matrix as shown in Table 4.Table 4
Homozygous matrix.
Plan
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Price (yuan/ton)
14600
14100
14000
14234.
1000
Snow-melting speed
1.000
1.500
1.500
1.330
2.000
Deicing rate
1.000
1.024
0.964
0.996
0.952
Suitable working temperature (°C)
10.000
30.000
20.000
20.000
30.000
Road damage
1.000
1.030
1.030
1.020
1.670
Degree of metal corrosion
1.000
1.110
1.130
1.090
1.740
Soil impact
1.000
1.040
1.190
1.077
1.630
Water impact
1.000
0.880
1.160
1.014
1.600
Vegetation impact
1.000
1.004
1.190
1.077
1.630According to formula (4), the normalization process is performed as shown in Table 5.Table 5
Normalized matrix table.
Plan
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Price (yuan/ton)
0.495
0.491
0.500
0.035
0.512
Snow-melting speed
0.447
0.447
0.396
0.596
0.298
Deicing rate
0.464
0.437
0.451
0.431
0.453
Suitable working temperature (°C)
0.577
0.385
0.385
0.577
0.192
Road damage
0.391
0.391
0.387
0.633
0.379
Degree of metal corrosion
0.399
0.407
0.392
0.626
0.360
Soil impact
0.385
0.440
0.398
0.603
0.370
Water impact
0.386
0.368
0.515
0.515
0.907
Vegetation impact
0.372
0.402
0.513
0.531
0.908The evaluation matrix is weighted according to formula (5), and the distance values are obtained according to formulas (6) and (7): the optimal distance S+ and the worst distance S− are shown in Table 6.Table 6
Positive and negative ideal solution distance table.
Name
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Alpine and highly sensitive
Positive ideal solution distance
0.098
0.066
0.065
0.072
0.073
Negative ideal solution distance
0.073
0.100
0.081
0.080
0.100
Low sensitivity to high and cold
Positive ideal solution distance
0.077
0.041
0.047
0.050
0.198
Negative ideal solution distance
0.198
0.201
0.192
0.195
0.078
Low cold and high sensitivity
Positive ideal solution distance
0.083
0.068
0.061
0.068
0.105
Negative ideal solution distance
0.105
0.111
0.105
0.105
0.085
Hyposensitive
Positive ideal solution distance
0.060
0.044
0.042
0.046
0.222
Negative ideal solution distance
0.223
0.218
0.214
0.218
0.062


## 3.2. Calculation of Grey Relational Degree

According to formulas (8), (9), (10), and (11), the grey correlation degree is calculated for the evaluation matrix, and the resolution coefficient is taken as 0.5, as shown in Table 7.Table 7
Grey correlation table of positive and negative ideal solutions.
Name
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Alpine and highly sensitive
Positive ideal solution distance
0.642
0.727
0.701
0.677
0.926
Negative ideal solution distance
0.910
0.803
0.761
0.807
0.637
Low sensitivity to high and cold
Positive ideal solution distance
0.856
0.901
0.887
0.878
0.926
Negative ideal solution distance
0.922
0.868
0.868
0.882
0.853
Low cold and high sensitivity
Positive ideal solution distance
0.725
0.782
0.774
0.755
0.926
Negative ideal solution distance
0.914
0.844
0.815
0.849
0.720
Hyposensitive
Positive ideal solution distance
0.879
0.908
0.902
0.895
0.926
Negative ideal solution distance
0.922
0.886
0.882
0.894
0.876


## 3.3. Relative Proximity

According to formula (12), the positive and negative ideal solutions and the grey relational degree are dimensionless, and the positive and negative ideal solutions and grey relational degree after comprehensive dimensionlessization using formulas (13) and (14) are shown in Table 8.Table 8
Proximity table of positive and negative ideal solutions.
Name
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Alpine and highly sensitive
Positive ideal solution proximity
0.713
0.890
0.782
0.765
1.000
Negative ideal solution proximity
1.000
0.777
0.749
0.809
0.723
Low sensitivity to high and cold
Positive ideal solution proximity
0.955
0.987
0.957
0.960
0.693
Negative ideal solution proximity
0.693
0.574
0.589
0.605
0.963
Low cold and high sensitivity
Positive ideal solution proximity
0.866
0.922
0.891
0.882
0.885
Negative ideal solution proximity
0.893
0.785
0.734
0.787
0.894
Hyposensitive
Positive ideal solution proximity
0.975
0.980
0.968
0.972
0.638
Negative ideal solution proximity
0.635
0.578
0.573
0.588
0.975The relative proximity calculation formula (15) can obtain the proximity as C, as shown in Table 9.Table 9
Table of relative proximity C values.
Name
Sodium chloride
Calcium chloride
Magnesium chloride
Chloride mixed type
Calcium magnesium acetate
Alpine and highly sensitive
Relative proximity
0.416
0.534
0.511
0.486
0.580
Low sensitivity to high and cold
Relative proximity
0.579
0.632
0.619
0.613
0.418
Low cold and high sensitivity
Relative proximity
0.492
0.540
0.548
0.528
0.497
Hyposensitive
Relative proximity
0.605
0.629
0.628
0.623
0.396


## 4. Alternatives

The relative proximity radar chart is shown in Figure1. It can be seen that in the high-cold and high-risk environment of A1, the C value of the proximity of the scheme is calcium magnesium acetate > calcium chloride > magnesium chloride > chloride salt mixed type > sodium chloride; the scheme p5 (calcium acetate magnesium (CMA)) is the best solution among the five solutions, mainly because (1) in alpine areas, CMA has a good effect of deicing and melting snow; (2) in high-sensitivity areas, the CMA snow-melting agent is corrosive to metals after the snow melts, resulting in less negative impact on infrastructure, flora and fauna, and the surrounding ecological environment; these reasons make CMA the best solution.Figure 1
Relative proximity radar.In the A2 high-cold and low-risk environment, the program proximity value C is calcium chloride > magnesium chloride > chloride salt mixed type > sodium chloride > calcium magnesium acetate, and the program p2 (calcium chloride) is the best of the five programs, mainly because (1) in the low-risk environment, the advantages of the CMA snow-melting agent are not so great, the impact of calcium chloride and magnesium chloride on the environment is not too great, and the price is more advantageous than CMA; (2) the environmental impact of sodium chloride is too large in the alpine environment. The performance is not as good as calcium chloride and magnesium chloride. The above reasons make calcium chloride the best solution in high cold and low sensitivity.In the A3 low-temperature and high-risk environment, the project close value C for magnesium chloride > calcium chloride > chloride mixture type > magnesium acetate > sodium chloride, plan p3 (magnesium chloride) is the best of the five plans, mainly because (1) in the high-risk environment, the CMA snow-melting agent environmental impact is small, but due to the high price of CMA, it is difficult to achieve large-scale use of the CMA environmental snow-melting agent [9]. Although calcium chloride and magnesium chloride have more environmental impacts than CMA, the price is more favorable than CMA, and magnesium chloride has less effect on the environment than calcium chloride. (2) Calcium chloride and magnesium acetate have little performance advantages in low-cold areas. The best solution to use magnesium chloride at low temperature and with high sensitivity is defined based on the differences between five snowmelt agents, sodium chloride, calcium chloride, magnesium chloride, salt mixed snowmelt, and magnesium acetate.In the A4 low-cold and high-risk environment, the program proximity value C is calcium chloride > magnesium chloride > chloride salt mixed type > sodium chloride > calcium and magnesium acetate, and the program p2 (calcium chloride) is the best of the five programs, because in low-risk environments, CMA and magnesium chloride snow-melting agents have little environmental impact and have little advantages and are more expensive; the above reasons make calcium chloride the best solution in low-cold and high-sensitivity areas.


## 5. Conclusion

In order to select the economic, practical performance, and small environmental impact from the source control, the combined weighting method is used to determine the weight and introduces the TOPSIS evaluation and analysis model combined with grey correlation. Five snow-melting agents (sodium chloride, calcium chloride, magnesium chloride, salt chloride mixed snow-melting agent, and magnesium acetate) respectively adopt cold, high-cold, low-cold, and low-sensitivity areas. The evaluation results show that (1) CMA is the best solution in the A1 high-cold and high-sensitivity area, (2) calcium chlorine is the best solution in the A2 high-cold and low-sensitivity area, (3) magnesium chlorine is the best solution in the A3 low-cold and high-sensitivity area, (4) calcium chlorine is the best solution in the low-cold and low-sensitivity area of A4. The construction of the model judgment matrix needs to be combined with a specific environment, and the judgment matrix has different habitual constructors. Therefore, using the unique function formula, the process of this model is simple and accurate and the order of the matrix can be adjusted at will to test the matrix and provide the possibility of further expansion. The combination of theory and practice provides a feasible snow-melting agent. Follow-up studies should focus on reducing the harm of using snow-melting agents. Because a model judgment matrix needs to combine a specific environment, and the judgment matrix has different customary constructors, it is necessary to combine theory and practice to provide a feasible snowmelt agent. Follow-up research should focus on reducing the harm of using snowmelt agents. The use of snow-melting agents also has a certain impact on the environment. Therefore, it is necessary to reduce the use of snow-melting agent and gradually develop a new green snow-melting agent [26]. Therefore, it is necessary to strengthen the research and development of an environmentally protective snow-melting agent, improve the use and management system of snow-melting agents, learn from foreign experience, and use scientific decision-making methods to guide the proper use of snow-melting agents.



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*Source: 3882031-2022-05-06.xml*