1. Research Purpose

3. Carbon Neutrality Capacity Evaluation Mechanism—The Entropy Weight TOPSIS Method

3.3. Entropy Weight TOPSIS Evaluation Model

The entropy weight TOPSIS method is an objective approach that employs the original data and removes subjectivity. This method reflects the weight coefficients of the index layer and the gap between the data of the evaluation object and the ideal solution. This method designates scores to the evaluation object, which in this case is the carbon neutrality ability of the construction industry in each region. The goal is to obtain accurate assessment results through quantitative analysis, facilitating better adjustment and enhancing the carbon neutrality capacity target [21].

3.3.1. Standardised Processing of Indicator Data

This work concentrates on determining the initial matrix ${T=w}_{tj}$for the indicator data, where $w_{tj}$ is the $\mathrm{j}$TH initial value of the t leading county. Fuzzy membership degrees are employed to standardise the index [22]. Through the standardisation of indicators, the value of the original data is regulated within 0–1; that is, compared with the original data, it has the same scale, and the entropy weight TOPSIS method is more impartial and sound for the determination of the entropy weight of indicators and the assessment of the implementation influence of the annual carbon neutrality policy. The standardisation of indicators can be split into positive standardisation and negative standardisation. The positive indicator indicates that the higher the value of the indicator, the better the implementation of the carbon neutrality policy. The negative index is the opposite. According to the indicators of this subject, except for the business income of the leisure construction industry and the Engel coefficient of county residents, the other indicators are positive indicators. Based on this method [23], $y_{tj}$ is set as the standardised value of the t index of the JTH evaluation object, and n is the number of objects to be assessed. Then, the indicators can be standardised through the normalisation formula (1) for positive indicators and the standardisation formula (2) for negative indicators.

$$y_{tj}={\displaystyle \frac{\begin{array}{c}{w}_{tj}-min{w}_{tj}\\ 1\le j\le n\end{array}}{\begin{array}{c}max{w}_{tj}-min{w}_{tj}\\ 1\le j\le n1\le j\le n\end{array}}}$$

(1)

$$y_{tj}={\displaystyle \frac{\begin{array}{c}max{w}_{tj}-w_{tj}\\ 1\le j\le n\end{array}}{\begin{array}{c}max{w}_{tj}-min{w}_{tj}\\ 1\le j\le n1\le j\le n\end{array}}}$$

(2)

With the aid of the initially gathered indicator data, the data were preprocessed according to the above standardised data processing method. Part of the data after the preprocessing of the indicator data is presented in Table 2.

3.3.2. Entropy Value of Carbon Neutrality Capacity Evaluation System Index

Based on the quantitative requirements of the carbon neutrality capacity evaluation system for the work evaluation of the regional construction industry and given the mutual independence of the indicators, the entropy weight method was employed to obtain the entropy value of the indicators. In information theory, entropy is a measure of uncertainty. The higher the uncertainty, the higher the entropy and the more information it contains. In the entropy weight method, the characteristics of the entropy value can be employed to determine the dispersion degree of the carbon neutrality capacity degree index. The higher the dispersion degree of the index, the higher the effect of the index on the evaluation system of the regional construction industry, that is, the higher the weight. This type of quantitative determination of the importance of indicators has greater accuracy and more powerful objectivity. Based on the relationship between the actual situation and the indicators collected [24], 9 of the 30 indicators were chosen as the evaluation index system with accurate data sources and long-term development goals, such as the proportion of prefabricated assembly rate in counties and districts, the penetration rate of harmless toilets and the proportion of households that conducted energy conservation assessment after placing into use in the community. The composition system of the index layer of entropy weight is shown in Figure 2.

The equation for obtaining the corresponding entropy and weight coefficient of an index is as follows: Let $e_j$ be the entropy of the $\mathrm{j}$TH index, and $S_{tj}$ be the characteristic gravity of the JTH index in the $i$TH system.

$$S_{tj}={\displaystyle \frac{w_{tj}}{\sum _{i=1}^n{w}_{tj}}}{e}_j=-{\displaystyle \frac{1}{\ln n}}\sum _{i-1}^n{s}_{tj}\ln S_{tj}$$

(3)

where $\sum _{i=1}^n{w}_{tj}$ is the sum of all system observation data of the JTH index.

Let the difference coefficient of indicator $\mathrm{j}$ be $q_j$ and the weight coefficient of 30 indicators be $s_j$. The equation is expressed as follows:

$$q_j=1-e_j{s}_j={\displaystyle \frac{q_j}{\sum _{j=1}^{30}{w}_{tj}}}$$

(4)

With the aid of preprocessing indicator data, Python software was used to compute the difference coefficient and weight coefficient of indicators, and the outcomes are presented in Table 3.

The weight coefficient of the proportion of collectively economically powerful areas/counties is the greatest, representing its highest importance in the evaluation system for carbon neutrality capability [25]. Conversely, the weight coefficient of the county–district point ratio for the reuse of construction waste is the smallest, demonstrating its lesser effect on the evaluation system. The notion of entropy weight is confirmed by these results, where higher weights are assigned to indicators with greater data dispersion. This outcome emphasises the value of accurate, diverse data in attaining indicator importance within the assessment system.

3.3.3. Scores of Carbon Neutrality Capacity Evaluation of the Construction Industry in Each Region

To reflect the carbon neutrality capacity development index of the leading county quantitatively, the weighted value of each indicator data can be known by multiplying the index data and the index weight, stressing the variation in the importance of each indicator and optimising and enhancing the carbon neutrality capacity evaluation mechanism. $Z_{ij}$ is set as the weighted value of the standardised data of the $j$TH indicator in the $i$ leading area, the normalised value of the observation value of the $j$TH indicator in the $i$ leading area and $S_j$ the weight coefficient. According to the above weighted method, the following equation is derived:

$$Z_{ij}=Q_{ij}{s}_j$$

(5)

With the help of standardised index data and index weights, the data matrix weighted by evaluation indicators can be computed, and the results are presented in Table 4.

Based on the actual condition of the evaluation system, the TOPSIS method is employed to determine the close degree between the development indicators and the ideal solution. In the index system, the maximum value of the positive evaluation index and the minimum value of the negative evaluation index are chosen to develop the ideal optimal solution in the evaluation system and vice versa, and the worst solution is formed. The ideal optimal solution and the worst solution are also positive and negative ideal solutions [26].

Let $d_i^{+}$ be the Euclidean distance between the $i$th leading county and the positive ideal solution, and $d_i^{-}$ be the Euclidean distance between the $i$th leading county and the negative ideal solution. Then, the following equations are derived:

$$d_i^{+}=\sqrt{{(y_1^{+}-y_{i1})}^2+{(y_2^{+}-y_{i2})}^2+\cdots +{(y_{30}^{+}-y_{i30})}^2}$$

(7)

$$d_i^{-}=\sqrt{{(y_1^{-}-y_{i1})}^2+{(y_2^{-}-y_{i2})}^2+\cdots +{(y_{30}^{-}-y_{i30})}^2}$$

(8)

Using the above formula, the distance to the positive and negative ideal solution corresponding to each leading county can be determined.

Table 5. Distance from the antecedent zone to the positive and negative ideal solutions.

Table 5. Distance from the antecedent zone to the positive and negative ideal solutions.

Pioneer County	Distance to the Positive Ideal Solution	Distance to the Negative Ideal Solution
Jiaojiang District, Taizhou	0.251	0.402
Huangyan District, Taizhou	0.402	0.275
Road Bridge District, Taizhou	0.288	0.432
Tiantai County, Taizhou	0.392	0.367
Wenling City, Taizhou	0.410	0.248
Lucheng District, Wenzhou	0.382	0.322
Longwan District, Wenzhou	0.122	0.559
Cangnan County, Wenzhou	0.289	0.392
Taishun County, Wenzhou	0.277	0.447
Longgang City, Wenzhou	0.281	0.421
Nanhu District, Jiaxing	0.312	0.488
Xiuzhou District, Jiaxing	0.381	0.317
Jiashan County, Jiaxing	0.512	0.240
Pinghu City, Jiaxing	0.381	0.317
Haining City, Jiaxing	0.342	0.391

In the carbon neutrality capability assessment system, to determine the development of each leading county quantitatively, that is, the carbon neutrality development index of the leading county, the notion of relative proximity degree is presented, and $f_i$ is set as the proximity degree to the positive ideal solution of each indicator system of the $i$ pioneer county, whose $f_i$ value is the carbon neutrality development index of each leading county. The formula is as follows:

$$f_i={\displaystyle \frac{d_i^{-}}{d_i^{-}+d_i^{+}}},$$

(10)

where $i$ = 1,2,..., n. For the carbon neutrality development index, if the index system of the leading county is close to the positive ideal solution and far from the negative ideal solution, then $f_i$→ 1, and its carbon neutrality ability development index is higher; conversely, if $f_i$→ 0, then its carbon neutrality ability development index is lower. Therefore, based on the value of $f_i$ in descending order, the precedence counties are ranked. The higher the $f_i$ value, the higher the ranking, signifying higher development level of carbon neutrality capacity of the leading county; the smaller the $f_i$ value, the lower the ranking, representing lower development level of carbon neutrality capacity of the leading county [27]. With the data, weights and post standardisation of indicators, Python software was used to compute the scores of the leading counties and districts. Finally, the carbon neutrality ability evaluation index results were derived, as detailed in Table 6.

Examining the carbon neutrality ability evaluation index of the leading counties reveals that Jiaojiang District of Taizhou has the highest score, followed by Huangyan District of Taizhou and Cangnan County of Wenzhou. In the middle are Jiashan County of Jiaxing, Taizhou Luqiao District, Haining City of Jiaxing and Pinghu City of Jiaxing.

4. Analysis and Suggestion of Carbon Neutrality Capacity Evaluation System

5. Conclusions

References

1. [Huang Li, Deng Shijing, Zhou Zhixiu, et al. Construction of evaluation index system of regional red cultural tourism resources based on G1-entropy weight method.] Journal of Ningde Normal University (Philosophy and Social Sciences Edition), 2021,139 (4) : 42-50.
2. Li Gang, Chi Guotai, Cheng Yanqiu. Evaluation model of human all-round Development based on entropy weight TOPSIS [J]. Journal of Systems Engineering, 2011,26 (3) : 400-407. (in Chinese).
3. Lam, W.H., Lam, W.S., Liew, K.F., & Lee, P.F. (2023). Decision Analysis on the Financial Performance of Companies Using Integrated Entropy-Fuzzy TOPSIS Model. Mathematics.
4. Forouzandeh, S., Rostami, M., & Berahmand, K. (2022). A Hybrid Method for Recommendation Systems based on Tourism with an Evolutionary Algorithm and Topsis Model. Fuzzy Information and Engineering, 14, 26 - 50. [CrossRef]
5. Bai, Y. (2023). Forest management based on the TOPSIS model. Highlights in Science, Engineering and Technology. [CrossRef]
6. Fai, L.K., Lam, W.S., & Lam, W.H. (2022). Financial Network Analysis on the Performance of Companies Using Integrated Entropy–DEMATEL–TOPSIS Model. Entropy, 24.
7. Rahman, A., Fitri, Z., Zulkifli, Z., Ula, M., & Suhendra, B. (2022). Analysis of the Teacher’s Role in Evaluation of Student Learning Performance Using the TOPSIS Model (Case Study of Smk Negeri 1 Lhokseumawe). JOURNAL OF INFORMATICS AND TELECOMMUNICATION ENGINEERING. [CrossRef]
8. Ali, J., Bashir, Z., & Rashid, T. (2021). On distance measure and TOPSIS model for probabilistic interval-valued hesitant fuzzy sets: application to healthcare facilities in public hospitals. Grey Syst. Theory Appl., 12, 197-229. [CrossRef]
9. Wang, Y., Chardonnet, J., & Mérienne, F. (2021). Enhanced cognitive workload evaluation in 3D immersive environments with TOPSIS model. Int. J. Hum. Comput. Stud., 147, 102572. [CrossRef]
10. Mandal, T., Saha, S., Das, J., & Sarkar, A. (2021). Groundwater depletion susceptibility zonation using TOPSIS model in Bhagirathi river basin, India. Modeling Earth Systems and Environment, 8, 1711 - 1731. [CrossRef]
11. Banihashemi, S.A., & Khalilzadeh, M. (2021). Evaluating Efficiency in Construction Projects with the TOPSIS Model and NDEA Method Considering Environmental Effects and Undesirable Data. Iranian Journal of Science and Technology, Transactions of Civil Engineering, 46, 1589-1605. [CrossRef]
12. Ortíz-Barrios, M.A., Petrillo, A., De Felice, F., Jaramillo-Rueda, N., Jiménez-Delgado, G., & Borrero-López, L. (2021). A Dispatching-Fuzzy AHP-TOPSIS Model for Scheduling Flexible Job-Shop Systems in Industry 4.0 Context. Applied Sciences, 11, 5107. [CrossRef]
13. Forouzandeh, S., Berahmand, K., Nasiri, E.S., & Rostami, M. (2020). A Hotel Recommender System for Tourists Using the Artificial Bee Colony Algorithm and Fuzzy TOPSIS Model: A Case Study of TripAdvisor. Int. J. Inf. Technol. Decis. Mak., 20, 399-429. [CrossRef]
14. Pazhuhan, M., & Shiri, N. (2020). Regional tourism axes identification using GIS and TOPSIS model (Case study: Hormozgan Province, Iran). Journal of Tourism Analysis: Revista de Análisis Turístico.
15. Oz, N.E., Mete, S., Serin, F., & Gul, M. (2018). Risk assessment for clearing and grading process of a natural gas pipeline project: An extended TOPSIS model with Pythagorean fuzzy sets for prioritizing hazards. Human and Ecological Risk Assessment: An International Journal, 25, 1615 - 1632. [CrossRef]
16. Yurdakul, M., & Iç, Y.T. (2019). Comparison of Fuzzy and Crisp Versions of an AHP and TOPSIS Model for Nontraditional Manufacturing Process Ranking Decision. Journal of Advanced Manufacturing Systems. [CrossRef]
17. Aikhuele, D.O., & Turan, F.M. (2017). An Integrated Fuzzy Dephi and Interval-Valued Intuitionistic Fuzzy M-Topsis Model for Design Concept Selection. Pakistan Journal of Statistics and Operation Research, 13, 425-438. [CrossRef]
18. Najafabadi, R.M., Ramesht, M.H., Ghazi, I., Khajedin, S.J., Seif, A., Nohegar, A., & Mahdavi, A. (2016). Identification of natural hazards and classification of urban areas by TOPSIS model (case study: Bandar Abbas city, Iran). Geomatics, Natural Hazards and Risk, 7, 100 - 85. [CrossRef]
19. Sofuoğlu, M.A. (2019). A Fuzzy Behavioral TOPSIS Model in Manufacturing Environment. Advanced Engineering Forum, 31, 70 - 80. [CrossRef]
20. Mukherjee, A.B., Krishna, A.P., & Patel, N. (2018). Application of Remote Sensing Technology, GIS and AHP-TOPSIS Model to Quantify Urban Landscape Vulnerability to Land Use Transformation.
21. Raihan, A. (2023). The contribution of economic development, renewable energy, technical advancements, and forestry to Uruguay’s objective of becoming carbon neutral by 2030. Carbon Research, 2.
22. Huovila, A., Siikavirta, H., Antuña Rozado, C., Rökman, J., Tuominen, P., Paiho, S., Hedman, Å., & Ylén, P. (2022). Carbon-neutral cities: Critical review of theory and practice. Journal of Cleaner Production. [CrossRef]
23. Wen, L., Zhang, J., & Song, Q. (2022). A scenario analysis of Chinese carbon neutral based on STIRPAT and system dynamics model. Environmental Science and Pollution Research, 29, 55105 - 55130. [CrossRef]
24. Chen, Z., Dayananda, B., Fu, B., Li, Z., Jia, Z., Hu, Y., Cao, J.Z., Liu, Y., Xie, L., Chen, Y., & Wu, S. (2022). Research on the Potential of Forestry’s Carbon-Neutral Contribution in China from 2021 to 2060. Sustainability. [CrossRef]
25. Mallapaty, S. (2020). How China could be carbon neutral by mid-century. Nature, 586, 482 - 483. [CrossRef]
26. Rosa, L., Sanchez, D.L., & Mazzotti, M. (2021). Assessment of carbon dioxide removal potential via BECCS in a carbon-neutral Europe. Energy & Environmental Science.
27. Maurya, P.K., Mondal, S., Kumar, V., & Singh, S.P. (2021). Roadmap to sustainable carbon-neutral energy and environment: can we cross the barrier of biomass productivity? Environmental Science and Pollution Research International, 28, 49327 - 49342.
28. Algarvio, H. (2021). The Role of Local Citizen Energy Communities in the Road to Carbon-Neutral Power Systems: Outcomes from a Case Study in Portugal. Smart Cities, 4, 840-863. [CrossRef]
29. Causone, F., Tatti, A., & Alongi, A. (2021). From Nearly Zero Energy to Carbon-Neutral: Case Study of a Hospitality Building. Applied Sciences. [CrossRef]
30. Nieuwenhuijsen, M.J. (2020). Urban and transport planning pathways to carbon neutral, liveable and healthy cities; A review of the current evidence. Environment international, 105661. [CrossRef]
31. Vaka, M., Walvekar, R., Rasheed, A.K., & Khalid, M. (2020). A review on Malaysia’s solar energy pathway towards carbon-neutral Malaysia beyond Covid’19 pandemic. Journal of Cleaner Production, 273, 122834 - 122834. [CrossRef]
32. Ravetz, J., Neuvonen, A., & Mäntysalo, R. (2020). The new normative: synergistic scenario planning for carbon-neutral cities and regions. Regional Studies, 55, 150 - 163. [CrossRef]
33. Bedulli, C., Lavery, P.S., Harvey, M., Duarte, C.M., & Serrano, O. (2020). Contribution of Seagrass Blue Carbon Toward Carbon Neutral Policies in a Touristic and Environmentally-Friendly Island. Frontiers in Marine Science. [CrossRef]
34. Mandova, H., Patrizio, P., Leduc, S., Kjärstad, J., Wang, C., Wetterlund, E., Kraxner, F., & Gale, W.F. (2019). Achieving carbon-neutral iron and steelmaking in Europe through the deployment of bioenergy with carbon capture and storage. Journal of Cleaner Production. [CrossRef]
35. Balany, F., Muttil, N., Muthukumaran, S., Wong, M.S., & Ng, A.W. (2022). Studying the Effect of Blue-Green Infrastructure on Microclimate and Human Thermal Comfort in Melbourne’s Central Business District. Sustainability. [CrossRef]
36. Aksulu, I., & Wang, R. (2012). Contribution of Integrated Green District Heating to the Sustainable Cities: A Case Study of Ferrara, Italy.