Analysis of the Practice of Dengue Prevention and Sustainable Control with Multi-attribute Decision-making

Dengue fever is one of the most common insect-borne diseases in the world, and epidemics mostly occur in tropical and subtropical regions. In the past, the grey multi-attribute decision-making method has been combined with the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method to predict which areas in southern Tainan may easily trigger dengue epidemics. As many studies have shown that the extent of human communication and active government is crucial in dengue prevention, this study aims to propose dengue prevention and control methods before and after the occurrence of dengue cases. This study found that, when dengue fever cases begin to appear, the relevant county and city government departments must hire vector control companies to carry out regional indoor and outdoor spraying. Before the emergence of dengue cases, the green and sustainable-oriented remediation strategies, as promoted by the Environmental Protection Administration (EPA), can be adopted. Remediation of soil and groundwater pollution sites can reduce the source of vector mosquitoes, in order that the green environment can achieve sustainable development.


Introduction
The most effective method is to improve the drainage gradient of roads and drains in the city, remove the waste tires and potted plants, large water tanks and fill the pool in the idle courtyard to reduce the occurrence of water accumulation, in order to completely isolate the mosquitoes and people. Life field. Infections most often occur in urban environments. In recent decades, due to the expansion of rural areas, towns and cities, dengue fever is common in these places, and the increase in mobility has increased the number of infectious diseases and epidemic viruses. Therefore, dengue fever, which was confined to infectious diseases in South Asia, has now spread to countries in southern for dengue fever. The findings can can provide reference for the prevention and control of dengue fever to government departments, vector mosquito control operators, and environmental remediation workers, before and after the occurrence of dengue fever cases, in the hope of reducing the risk and scale of dengue fever through prevention and treatment measures [9][10][11][12][13][14].

Literature review
Once people are infected with the dengue virus, they become the main source and breeder of the virus, meaning they become a source of the virus for uninfected mosquitoes.
The virus circulates in the blood of infected people for 2-7 days, which is about the same period as the human fever. Patients who have been infected with dengue virus may spread the virus through mosquitoes after the first symptom (4-5 days; up to 12 times) [15][16].
Preventive measures against dengue virus can improve the environment of families and communities, and make it difficult for mosquitoes to breed. Efforts should be made to educate the public through various channels, raise public awareness of the dangers of dengue fever, prevent them from being exposed to the disease, formulate public guidelines for controlling the environment and removing mosquito breeding grounds, promote the prevention of dengue fever and medical technology development, and establish effective medical and health workforces to provide effective treatment for patients with dengue fever [17].
In the context of scarce natural resources and growing environmental problems, such as global warming, the world has gradually paid attention to environmental remediation and introduced the concept of Green and Sustainable Remediation (GSR).
Each country, as based on natural law and social demands, has introduced different definitions of GSR. The Interstate Technology & Regulatory Council (ITRC) defined GSR as a strategy to remediate pollution sites, set standards for remediation techniques, procedures, or methods, and strike a balance among community goals, economic impacts, and overall environmental impact. GSR applies the principle of "sustainable development" to the management of pollution sites and lands, and sustainable development is defined as the principle of meeting current contemporary needs without compromising the ability of future generations to meet their needs [18]. GSR is often described as a combination of remedies, and its net benefits are maximized through the rational use of limited resources.
GSR is a process-and goal-based implementation process that focuses on assessing the composition of remediation items in order to strike a balance and achieve sustainable remediation. That is, during the improvement process of pollution sites, relevant knowledge should be integrated into the green and sustainable remediation strategy by measuring the three indicators of environment, society, and economymeaning a triple bottom line, thereby, reducing the secondary pollution caused by environmental remediation [19]. Green and sustainable remediation is not merely about improving polluted sites; instead, from the perspective of sustainable development and current and future environmental use, the "green and sustainable remediation" strategy states that the method most suitable for improving the polluted sites should be selected.
Regarding most real-world decision-making problems, the degree of information clarity is often in the grey stage. In this regard, the grey theory serves as a useful tool in decision-making under incomplete and uncertain scenarios [7], as it is an effective method to address uncertain problems. In addition, it can be used to analyze and construct limited and incomplete information [20].

Research method
This study used the open database of the Center for Disease Control, and Tainan City Government as the main data source. Grey Relational Analysis (GRA) together with TOPSIS were employed to analyze various factors, such as dengue outbreaks and prevention measures. In addition, the dengue epidemic situations in various areas of Tainan City were analyzed by grey multi-attribute decision-making analysis [21][22].
Grey relational analysis GRA is one of the extended theories of the grey system theory, which can address uncertain and nonlinear problems. Unlike statistical methods and the fuzzy theory, it does not require a large number of samples or distribution hypotheses, problems subjects are regarded as a whole, and the value of data is explored for analysis. These features make it suitable for data with complex structures and insignificant distributions [23].
GRA is a quantitative analysis method used to explore the similarities and differences among various factors in a system, by proposing dependence to measure the degree of correlation between factors: the higher the similarity, the more relevant the factors are.
GRA uses grey relation to measure the degree of relationship among factors, and extracts and ranks the relevant parts of each factor to provide systematic and reliable information [24].
As GRA conducts analysis based on the development trend of each factor, it does not need a large amount of regularly distributed raw data. In addition, with a small calculation amount, it is less likely that the quantitative analysis result will be inconsistent with the qualitative analysis result. Relevance refers to the measure of the degree of correlation between factors that exist between systems in the context of time change or different objects. In the process of system development, if the degree of change between the two subsystems or factors is high, the degree of correlation between the two systems is considered to be high [8,24].
The main procedure of GRA is to convert all data into comparable sequences, define the standard sequences, compare the sequences, and then, calculate the grey relation coefficient between all comparable sequences and the standard sequence. Finally, based on these grey relation coefficients, the grey relation degree between the standard sequence and each compared sequence is calculated [25]. GRA includes data normalization, definition reference sequence, grey relation coefficient, and grey relation degree calculation steps. The equation is written as follows: Step 1: Standardize the data, as expressed in Eq. (1): Step 2: Define standard sequence 0 and comparison sequence , compare the absolute difference between the two sequences 0 ( ) and ( ), and calculate the difference sequence ∆ 0 ( ), as expressed in Eq. (2): Step 3: Obtain the maximum difference ∆ and the minimum difference ∆ between the two poles, as defined by Eq. (3) and Eq. (4): Step Step 5: Calculate the grey relation between each comparison sequence and the standard sequence. The definition of grey relation is Eq. (6): Step 6: According to GRA, the grey relation degree of the operation results is ranked, where grey relation degree 0 refers to the degree of association between standard sequence 0 and comparison sequence , wherein 0 < Γ 0 ≤ 1. When the 0 value becomes closer to 1, it indicates that the degree of relation between the factor and the system is larger; when the 0 value is closer to 0, it indicates that the factor is less related to the system, thus, the order of the relatively important factors affecting the development trend of the system are arranged according to the 0 value.
Grey multi-attribute decision-making analysis People encounter many multi-attribute decision-making problems in daily life, which are different from single attribute decision making. The purpose of multi-attribute decision-making is to consider multiple "attributes", "targets", or "evaluation standards", in order to select the optimal solutions from various "options", "policies", "actions", or "alternatives". However, when considering various "attributes", "targets", or "standards", it is usually easy to cause conflicts and contradictions; therefore, efforts should be made to strike a balance between these conflicting attributes. There are several commonly used methods for multi-attribute decision-making, such as simple weighted summation (SAW), TOPSIS, the analytic hierarchy process (AHP), and grey multi-attribute decision-making Grey multi-attribute decision-making refers to a decision-making system composed of all possible uncertain or incomplete decision elements in the multi-attribute decision-making process. After obtaining the effect of the actual decision-making system by calculating the effect measure of the grey theory, the optimal solution may be selected according to the decision matrix [8].
The key point of grey multi-attribute decision-making is, "When event (A) occurs, strategy (B) is its countermeasure", and the result is called a situation (S). Event A represents an event collection or a property set, and an element or attribute in the A collection is called , = 1,2,3,⋅⋅⋅, . Strategy B is a collection of alternatives. B represents a set of countermeasures for event A, and an element in the set of countermeasures is called a solution , = 1,2,3,⋅⋅⋅, . The result of each solution under the attribute is called a situation S, and the results can be established into a situation matrix (also known as the result matrix) = ( , ) [8,24].
The application of GRA to perform grey multi-attribute decision-making analysis process is, as follows:

Effect measure
In GRA, a sequence is defined as a standard sequence, and serves as the analysis target.
Each comparable sequence is compared with the standard sequence to generate a difference sequence ∆ ( ), and then, the grey relation coefficient ( ) with the standard sequence is calculated. The effect measure of grey multi-attribute decision-making is divided into three types: upper limit effect measure, lower limit effect measure, and specific center effect measure. The following is an introduction of each effect measure [8].
Upper limit measure: Measure the extent to which the data deviates from the maximum value, and the larger the expected target value the better, such as financial performance, quality, return on investment, etc. In this regard, when is used to represent the maximum of all solutions under a certain sequence or certain attribute , the upper limit effect measure is defined as Eq. (7): Lower limit effect measure: Measure the extent to which the data deviates from the minimum value, and the smaller the expected target value the better, such as production cost, environmental impact, personnel change, etc., In this regard, when is used to represent the minimum of all solutions under a certain sequence or a certain attribute , the lower limit effect measure is defined as Eq. (8): Specific center effect measure: Applicable to the expected target value within a specified interval, such as age, temperature, etc. Hence, * is used to represent a specific sequence value of all solutions under a certain sequence or a certain attribute . The definition of a specific central effect measure is shown in Eq. (9): Effect measure is the effect degree of attribute and solution . When the value of effect measure is greater than 0 and less than or equal to 1, that is 0 < ≤ 1. When is closer to 1, the better the effect of solution under attribute . When is closer to 0, the worse the effect of solution under attribute [8].

Multi-attribute decision-making matrix
Decision matrix D is established by effect measure , where is an element in the matrix, and represents that the matrix has n attributes, namely , = 1,2,3,⋅⋅⋅, ; represents that there are m solutions, namely , = 1,2,3,⋅⋅⋅, . Then, the representation of decision matrix D( × ) is shown in Eq. (10):

Decision standard
After decision matrix D is formed, the optimal solution can be selected according to the decision standard. The decision standard of grey multi-attribute decision-making analysis refers to the effect of selecting the optimal solution under attribute , as shown in Eq. (11). In short, it means that is the most suitable decision under the consideration of attribute . As the decision standard is to find the largest element value in each row, it can also be called a "row decision" [8]. * = max = { 1 , 2 ,⋅⋅⋅, } Finally, the optimal solution shall be solution with the largest value under the total comprehensive result .
In the multi-attribute decision-making analysis method, the relative weight of the attribute has considerable influence on the choice of the alternative, meaning different attribute weights may lead to different results. Attribute weights can be mainly divided into subjective weight method, compromise weight method, and objective weight method.
The subjective weight method is based on the subjective consciousness or subjective preference of decision-makers themselves; the objective weight method is known through the results of the computing system; the compromise weight method is a combination of the subjective weight method and objective weight method. Common weighting methods include expert evaluation, weighted least square (WLS), AHP, and TOPSIS [8].
Technique for order preference by similarity to an ideal solution Multi-attribute decision-making is designed to evaluate and select the most qualified solution, as based on the metrics of each attribute of each alternative. The multi-attribute decision-making method solves problems in many fields, and is widely used in engineering, economic, management, and social fields. There are two ways to analyze multi-attribute decision-making: (1) Methods that depend on human subjective preferences, such as the AHP and the Best Worst Method (BWM); (2) Mathematical methods that depend on mathematical operations, such as the TOPSIS method and the weighted sum method (SAW). The TOPSIS method is the most commonly used method in mathematics [8,26].
The weight of the grey multi-attribute decision-making analysis method in this study is based on the TOPSIS method, as first proposed by Hwang and Yoon in 1981. The core concept is to define the positive ideal solution and negative ideal solution, in order to help decision-makers find the best alternative. In addition, the alternative must maintain the shortest distance from the "positive ideal solution" and the longest distance from the "negative ideal solution". The positive ideal solution refers to the value with the largest benefit standard and the lowest cost standard; while the negative ideal solution is the value with the largest cost standard and the smallest interest rate [8,27]. The calculation process of TOPSIS is, as follows: Step 1: Standardize the raw data, that is, is calculated by Eq. (13), where is expressed as the value of attribute under solution : = √∑ 2 =1 , = 1,2,3,⋅⋅⋅, , = 1,2,3,⋅⋅⋅, Step 2: Calculate the weighted standardized evaluation value, that is, is calculated by Eq. (14), where is the weight value of the decision matrix: Step Step 4: Calculate the Euclidean distance between each alternative and its positive and negative ideal solutions, meaning the distance from the positive ideal solution ( + ) and the distance from the negative ideal solution ( − ), as shown in Eqs. (17) and (18), respectively.
Step 5: Calculate the relative approximation of each alternative to the ideal solution, as in Eq. (19).
Step 6: Prioritize the various alternatives, arrange them according to the * value, and judge the decision maker's preference for the alternatives.  providing an environment for the breeding of vector mosquito larvae. In Taiwan, when the average monthly temperature is lower than 16 °C, no larvae of vector mosquitoes are found; when the monthly average temperature is higher than 21 °C, the density of vector larvae begins to appear in towns above 2; when the monthly average temperature is higher than 23 °C, the vector mosquitoes The density of larvae began to appear in towns and towns greater than grade 3. However, temperature is not the only environmental factor affecting the density of vector mosquito larvae. But, no mention of diurnal temperature range [3,[15][16][17][28][29][30][31][32][33][34][35]. This study used the data concerning dengue epidemics on the Tainan City Government open data platform from 2012 to 2015 as the data source, and then, analyzed the data with GRA.   Table 2, while the calculation process is shown in Appendix A~D. According to the GRA results of Table 2, the factors that affect the number of positive households suffering dengue fevers are, as follows: Spray times, number of containers of respondents, number of vector control operators, number of sprayers, population density, soil and groundwater pollution fields, annual average rainfall (mm), annual average temperature (°C), environmental protection volunteers in attendance, and farms breeding over 2,000 waterfowl. According to the results of GRA (Table 2), the most significant factors affecting the number of households suffering dengue fever are spray times, number of containers, and number of vector control operators. The dengue fever vector density survey conducted by the Ministry of Health and Welfare indicates that, an average of about 30% of breeding sources are found in indoor water containers. Therefore, the government should guide the public to reduce number of containers with standing water and clean indoor containers to reduce breeding sources. In case of any dengue fever cases, the relevant county and city departments should engage vector control operators to carry out regional spraying as soon as possible to avoid vector mosquitoes escaping to other areas [3,[15][16][17][28][29][30][31][32][33][34][35]. Thus, a large number of vector control operators may conduct a wide range of pesticide spraying in a timely manner. The more the spraying times, the more vector mosquitoes can be extinguished to reduce the incidence and scale of dengue fever. Although the GRA results show that spray times, number of containers of respondents, and number of vector control operators are the most influential factors, these three have never been able to make Taiwan a dengue fever-free area. The more times the pesticide is sprayed, the stronger the resistance of mosquitoes, and the worse the future anti-epidemic effect on dengue.
Moreover, the use of these environmental pesticide will result in poor environmental conditions, and expand the scale of the future dengue epidemic. Therefore, this study aims to reduce the incidences of mosquito-borne breeding and dengue fever through certain sustainable prevention and treatment measures before dengue fever cases occur.
Grey multi-attribute decision-making analysis Through grey multi-attribute decision analysis, this study intends to understand which areas of Tainan may become dengue-prone areas in the future, discusses the factors that may affect a dengue fever epidemic in the future, provides a sustainable remediation method based on the influencing factors, and offers relevant suggestions for county and city government departments. Previous scholars have widely applied the TOPSIS method and grey theory in engineering, economics, management, agriculture, and other fields [36][37].
Grey multi-attribute decision-making analysis must include the impact factors after the effect measure into the corresponding weights to obtain the results. In assessing the corresponding weights of each impact factor, this study reviewed relevant research and literature on environmental sustainability and dengue fever in Taiwan In order to avoid deviations in the interview process and prevent important research topics from being missed during the interview process, the interview content was provided to respondents before the interview, in order that respondents could understand the research and participate in the interview at the stipulated time period. According to the recommendations of the experts and based on the number of positive households, this study employed the TOPSIS method to calculate the corresponding weight of each impact factor , = 1,2,3, ⋯ ,10, as described in Table 3.

Effect measure
This study employed grey multi-attribute decision-making analysis to determine which areas of Tainan City are prone to dengue fever. According to the factors in Table 1, this study adopted the suggestions of relevant experts and conducted corresponding measure of effect for each factor. The effect measure is divided into three types: upper limit effect measure, that is, the larger the target effect the better; lower limit effect measure, that is, the smaller the target effect the better; specific center effect measure, that is, the target effect is a specific target, as described in Tables 4~6, respectively. Annual average rainfall The greater the average annual rainfall, the more likely it is to cause mosquito breeding. 3 Population density The higher the population density, the higher the risk of dengue infection 4

Number of containers of respondents
The more the number of containers of respondents, the easier it is to accumulate water and cause mosquito breeding. 8 Soil and groundwater pollution sites The more the number of pollution sites in the area, the more likely it is to cause mosquito breeding. 10 Farms breeding over 2,000 waterfowl The dirtier the farm environment, the more likely it is to cause mosquito breeding.

Spray times
The fewer the spray times, the more likely it is to cause mosquito breeding.

Results of grey multi-attribute decision-making analysis
This study calculated the results of the corresponding weights of each factor according to Table 3. According to the effect measures in Table 6, and through No.7 and No.10 items, this study reached the calculation results shown in Table 7. The calculation process is shown in the appendix. According to the results of grey multi-attribute decision-making analysis, it can be seen that the East District, Nanxi District, and North District in Tainan are prone to dengue fever, which is mainly due to the corresponding weights of positive household factors in Table 3. The ranking of the corresponding weights of positive households are, as follows: soil and groundwater pollution sites, spray times, number of containers of respondents, number of sprayers, number of vector control operators, population density, annual average temperature (°C), annual average rainfall (mm), environmental protection volunteers in attendance, and farms breeding over 2,000 waterfowl. Since the weight of soil and groundwater pollution sites is relatively high, its influence is relatively high, thus, to prevent dengue fever, it is necessary to improve the soil and groundwater pollution sites.
This study proposes relevant suggestions based on the green and sustainable remediation strategy, as promoted by the Environmental Protection Administration, in order to reduce the incidences of vector mosquitoes, reduce the incidences of dengue fever, and improve environmental protection.

Discussion
This study analyzed the data of dengue epidemics and prevention methods, as  Table 2. The top three factors are spray times, number of containers of respondents, and number of vector control operators; in the second part, this study adopted the grey multi-attribute decision-making analysis of the grey system theory and the TOPSIS method for analysis. According to the results in Table 7, the top three areas that are prone to dengue fever epidemic in Tainan area are the East District, Nanxi District, and the North District [8,17,26].
When the epidemic slows down or there are no new cases, efforts should be made to block overseas immigration and encourage the public to adopt scientific behaviors to prevent dengue fever. The World Health Organization (WHO) also pointed out that dengue fever prevention must be carried out by relevant government departments and community members, and proper vector mosquito control strategies should be adopted.
Since there is no effective vaccine or drug treatment for dengue fever, various government agencies should publicize the prevention and treatment measures of dengue fever to enhance people's self-prevention measures [15][16].
Before any dengue fever cases occur, county and city governments should carry out long-term cooperation with vector prevention and control operators, and pre-construct a dengue fever prevention system to spray environmental pesticides to eliminate vector mosquitoes and train sprayers, in order to facilitate operations in the event of an emergency; under the circumstance of any dengue fever case, the county and city governments can carry out regional indoor and outdoor spraying according to the actual situation of the epidemic. In order to prevent vector mosquitoes from escaping to unsprayed areas during pesticide spraying, vector control operators should be of sufficient number, in order to expand the range of the spray and improve spraying speed. Dengue fever is an environmental and community infectious disease. According to the survey, an average of about 30% of breeding sources are found in containers with standing water per year. "Checking, pouring, clearing, and brushing" are the only ways to eliminate breeding sources and have a clean home environment, thus, county and city governments should publicize regular cleaning of water containers used in households, and try to reduce the number of containers. The government can also use garbage trucks, various news media, and dengue prevention lectures for the purpose of publicity. In addition, they should establish the concept of basic prevention and control among the public, and strive to improve people's self-protection and prevention awareness in a bid to effectively inhibit the rapid spread of dengue fever [9][10].
At present, the only way to prevent dengue fever in Taiwan, besides cleaning, is to spray pesticides; however, spraying pesticides has a negative impact on the human body, other living things, and the environment. Mosquito vectors will also develop pesticideresistance, thus, the next dose must increase the amount of pesticidein the next spraying. Under such a vicious circle, human health will be affected and the ecological environment will be destroyed. In the past, people had no concept of sustainable development or environmental protection, and farmers sprayed pesticides, and factories discharged waste water or dumped toxic wastes, which caused soil and groundwater to be polluted, destroyed the habitats of other creatures, and created serious ecological imbalances. As the natural enemies of mosquitoes are gradually disappearing, this study hopes to promote the development of green and environmental sustainability, achieve a balance of the ecosystem in the future, and address dengue epidemics through the natural enemies of mosquitoes, rather than chemical prevention and control [3,6].
Dengue fever is a kind of "community disease" and "environmental disease". If there is a breeding source of mosquito vectors in a community environment, it will easily cause dengue fever. If a community has a high population density, it may cause a large-scale dengue fever outbreak, thus, to prevent dengue fever, efforts should be made to protect the environment and remove breeding sources. The East District has the second-highest population in the Tainan area, and if one person has been infected with dengue fever, the disease may easily spread, thus, the East District should make great efforts to avoid dengue fever sources. In addition to physical control methods, official units, such as the city government and the Environmental Protection Administration, should identify pollution sites and rectify them through GSR strategies [3,6,28].
Regarding the remediation strategy for soil and groundwater pollution sites, this study suggests that the government should regularly conduct surveys at these sites, including controlling pollution sites in the control area, selecting a suitable remediation strategy, and assessing a balance among environment, society, and economy. When the remediation plan is implemented, the government can also use its environmental carbon footprint to analyze or detect whether secondary pollutants have been produced, in order

Conclusion and Suggestions
This study used GRA and grey multi-attribute decision-making to analyze the data.
Based on the analysis results, this study provides dengue fever remediation strategies for relevant county and city government departments, and offers reference for follow-up research and environmental remediation. warming, as well as the formation of the "one-day living circle" in Taiwan, meaning people can move north and south in one day, may lead to the northward migration of dengue fever in the future. In terms of data, this study referred to the related data concerning the dengue epidemic in the Tainan area from 2012 to 2015, and does not include other data, thus, the results may be subject to change due to differences in the study area. Therefore, future research can include dengue-related data from the various regions of Taiwan, in order to understand the factors affecting the dengue fever epidemic in Taiwan, and to explore counties and cities other than Tainan, such as Taichung and Taipei,. The regional dengue prevention and control methods have made subsequent researches on the prevention and treatment of dengue fever perfect [10,[15][16]28].
This study used the grey theory as the research method, and the TOPSIS method was applied as the weighting method. According to previous research, in addition to the TOPSIS method, the grey theory can be combined with multiple weighting methods, such as theAHP, weighted sum method (SAW), etc. It is suggested that future research can use the grey theory and multiple weighting methods to compare the results of various weighting methods, and further explore which weighting methods are more suitable for the analysis of dengue fever [8,36].
Authors' contributions MHL conceived the research idea, designed the study, and wrote the results, STW revised the manuscript, CCL assisted in the literature review and analysis, WCC wrote and proofread the manuscript, contributed to the discussion, and prepared the manuscript for submission. All authors read and approved the final manuscript.

Funding
This research received no external funding.

Availability of data and materials
This study of the dengue fever epidemic original data in Tainan City Government, Taiwan.
Ethics approval and consent to participate No administrative permissions were required to access and use the mediation records described in our study.