Cost-effective evaluation of air purifiers based on entropy weight method combined with TOSIS

: With the rapid development of the economy, people pay more and more attention to the improvement of air quality, and we tend to choose air purifiers to clean the air in our living space as a way to take care of the health of our own lungs. This paper establishes a screening model, based on the screening principles and screening principles, and obtains the effective five indicators are: selling price, particulate CADR, formaldehyde CADR, noise range, and power rating. Then the TOPSIS model was established to get the processed decision matrix, and the scores of each evaluation object were obtained by using the decision matrix. After that, the entropy weighting method was combined to find out the occupied weight of each index. Finally, the TOPSIS method was combined to re-solve the scores to obtain the ranking of each air purifier.


Introduction
[3][4] .They are widely used in industry, homes, government and general construction.Over the years, air pollution has caused an increasing number of human diseases such as tuberculosis, lung cancer, nasal cancer and even leukemia.Therefore, the research, invention and manufacture of a qualified and effective air purifier is a top priority in the current scientific development and human health research.
The performance of air purifiers can often be evaluated by several attributes, such as purification efficiency, noise level, and energy consumption.Entropy weight TOPSIS is able to synthesize these attributes and take their weights into account.Through this method, the relative importance between each attribute can be synthesized to assess the cost-effectiveness of different air purifiers in a more comprehensive way.In this paper, entropy weight combined with TOPSIS [5][6] is used to comprehensively evaluate the cost-effectiveness of air purifiers to provide effective decision-making for the rational selection of air purifiers in the market.

Data collection
For the mixed market of air purifier products, we selected ten air purifiers with large sales and good evaluation on e-commerce platforms such as Jingdong and Taobao as research samples.Their data come from Jingdong and Taobao shopping platforms.Finally, the information of the ten air purifiers selected in this paper is shown in Table 1 1, this paper for the ten air purifiers found a total of six major evaluation indicators, in order to make these indicators contain the maximum amount of information to avoid the redundancy of the information, this paper needs to establish a model to screen the indicators.

Screening of evaluation indicators
Based on the daily use of air purifiers and the high screen indicators of the classic viewpoints of domestic and foreign authorities, this paper establishes a set of evaluation sea selection indicators based on the above data sources.Before screening the indicators, the unavailable data are eliminated according to the observability of the data [7] .

Screening principles
(1) Coefficient of variation: Screening out the indicators that have a greater impact on the comprehensive evaluation of air purifiers and the information contained in different indicators reflects the discriminative ability of the differences in the indicator data on the evaluation of air purifiers -the greater the variability of the indicator data, the stronger the discriminative ability of the indicator on the rating of air purifiers, and vice versa, the weaker the discriminative ability.Therefore, this paper screens out the indicators with the strongest discriminatory ability among various types of data through the coefficient of variation to ensure that the screened indicators have the greatest impact on air purifier ratings.
(2) Correlation coefficient: eliminating indicators with redundant response information.If the indicator system contains more redundant indicators, the more confusing the information reflected in the evaluation results.Therefore, this paper analyzes the correlation coefficients to eliminate the indicators with large correlation coefficients in the same criterion layer, so as to avoid the duplicity of the information reflected by the indicators.

Principle of indicator screening
The correlation coefficient between two indicators at the same criterion level is calculated through correlation analysis to reflect the set of indicators with redundant information, i.e., those with larger correlation coefficients, and then the coefficient of variation is calculated to calculate the information content of each indicator reflecting redundant information, so as to select the indicators with the largest information content in the same category, and then to finally eliminate those indicators with a large information content.As can be seen from the analysis of Figure 1, this paper ensures that the screened indicators have the greatest impact on the evaluation of air purifiers in the market, and also avoids the duplication of information in the response of the indicator system.The three indicators finally established are: functional level, efficiency level and energy consumption level.
After the above principle this paper screens the following results:

Establishment of TOPSIS modeling
The TOPSIS method, also known as the ideal solution method, is an effective multi-indicator evaluation method [8] .It first constructs the positive ideal solution (optimal solution) and negative ideal solution (worst solution) of the evaluation problem, and then calculates the similarity closeness (i.e., the degree of proximity to the positive ideal solution and the degree of distance from the negative ideal solution) of each solution to the ideal solution, in order to score the solutions and select the optimal solution.
(1).The establishment of initialization decision matrix: After obtaining the data of ten air purifiers, these ten air purifiers are used as the evaluation object, and five indexes are screened out as evaluation indexes.They are selling price, particulate CADR value, formaldehyde CADR value, noise range, and power rating.A total of m (m=10) evaluation objects and n (n=5) evaluation indexes are used to establish the initialized decision matrix of TOPSIS model.
(2).Normalization of the matrix Very large indicators: particulate matter CADR value, formaldehyde CADR value; Very small indicators: selling price, noise range (replaced by arithmetic mean), power rating; Very small indicators are converted by max-x, and the conversion formula is as follows min max min The transformed matrix is: (3).Normalization of the matrix The normalized matrix is normalized to eliminate the effect of factors such as magnitude.The normalized matrix is denoted as: ) evaluation object to normalize the score Finally, this paper calculated the scores of each evaluation object through the Excel table to get the following Table 3.  3, this paper concludes that based on the TOPSIS algorithm, the ranking results calculated in this paper should prove the ranking of the advantages and disadvantages of the products: 352X86C, JA32 of Midea, JF1568 of Smith, AC-MD2-SC of Xiaomi, Blueair570EF, Xiaomi X, Xiaomi 4, PHILIPSAC2936, Huawei C400, E33 of Midea.
(4).In this paper, the weights of these five indicators were calculated using MATLAB: According to Figure 2 analysis found that: particulate matter CADR value and formaldehyde CADR value accounted for a larger weight, and the impact on the evaluation object is also large.In addition, the three indicators of selling price, noise range and rated power account for a smaller weight, and the degree of influence on the evaluation object is also small.

Optimization of the air purifier evaluation model
For the above method, this paper finds the score of each evaluation object.Due to the different weights of each evaluation object, there will be an error between the actual score and the calculated score, so this paper introduces the entropy weight method to eliminate the error [9] .According to the definition and principle of entropy, when the system can be in several different states, the probability of each state is i p ( 1, 2 ) im  . Then the entropy of the system can be defined as: According to the above conditions, there are m evaluation objects and n evaluation indicators ( 10, 4) mn  ( 1, 2 ; 1, 2 ) Calculate the entropy of the i indicator: Calculation of the coefficient of variation for indicator i : For the j indicator, the larger j e is, the less variation there is in the value of the indicator Calculation of the weight of indicator j : Then redefine the distance of the ( 1, 2 ) im  evaluation object from the maximum value:

Conclusion
In order to provide a comprehensive and objective evaluation of air purifiers collected in the market, this paper chooses to use TOPSIS combined with the entropy weight method to evaluate the collected air purifiers, which combines the entropy weight method into the original TOPSIS method, so that the evaluation results are free from external interference, and improves the comprehensiveness of the evaluation results.Finally, the cost-effective evaluation results of air purifiers are obtained.
However, the model is sensitive to changes in initial data and different standardization methods,

Figure 2 :
Figure 2: Percentage of weights for each indicator ., the weight of the ith evaluation object on the value of the jth indicator Count: paper obtains a graph comparing the two evaluation scores of the original TOPSIS and the TOPSIS with the introduction of the entropy weighting method.

Figure 3 :
Figure 3: Comparison of TOPSIS in two states

Figure 3
Figure 3 can be analyzed to conclude that the TOPSIS with the introduction of entropy weighting method has a significant deviation from the original TOPSIS calculation score, indicating that the indicators have different weights and the final scores are quite different.352X86C, PHILIPSAC29, Blueair570EF and Huawei C400 are four air purifiers whose scores have undergone a sudden change.

Table 1 :
below: Information related to ten air purifiers

Table 2 :
Screening results screening evaluation metrics obtained from Table2are: selling price, particulate CADR, formaldehyde CADR, noise range, and power rating.

Table 3 :
Scores for each purification machine