Impact Evaluation of Prefabricated Buildings Cost on Game Theory-Cloud Model

Li, Na; Fan, Zhifeng

doi:https://doi.org/10.1155/2022/3635009

Journal of Mathematics

On this page

Abstract Introduction Materials and Methods Results Discussion Conclusions Data Availability Conflicts of Interest Supplementary Materials References Copyright Related Articles

Research Article | Open Access

Volume 2022 | Article ID 3635009 | https://doi.org/10.1155/2022/3635009

Impact Evaluation of Prefabricated Buildings Cost on Game Theory-Cloud Model

Na Li¹and Zhifeng Fan¹

Academic Editor: Xiaogang Liu

Received06 Jan 2022

Revised14 Mar 2022

Accepted25 Mar 2022

Published28 Apr 2022

Abstract

Prefabricated buildings have the advantages of energy-saving, high efficiency, and high quality, which is energetically promoted in China’s construction industry. But the prefabricated buildings’ high construction cost hinders their rapid development. Around the higher construction cost of prefabricated buildings, this paper starts with the full life cycle of prefabricated buildings and selects four stages: design, component production, transportation, and construction. And constructs the evaluation index system of influencing factors of the prefabricated buildings cost. Based on this, this paper proposes an evaluation framework based on the game theory-cloud model to evaluate the influencing factors of prefabricated buildings costs. Taking a prefabricated building in Tianjin as the research object, the game theory combinatorial empowerment method and cloud model are used to evaluate the impact effect of prefabricated buildings cost. Game theory is used to optimize the subjective and objective weights determined by the attribute hierarchy model and the entropy weight method and to confirm the comprehensive weight of the evaluation index. The index’s weight is scientific and accurate, and the subjective influence of a single process is avoided or does not conform to the actual situation and so on. The cloud model is used to evaluate the cost impact of prefabricated buildings comprehensively. The experimental results show that the model is feasible; the scientific and accurate evaluation results are improved; and the model is simple to operate and has some reference value.

1. Introduction

With the development of building industrialization, the traditional architecture has not conformed to the concept of a green four sections and one environmental protection advocated by the state. The traditional architecture construction method has low production efficiency, serious environmental pollution, long construction period, and so on [1, 2]. At present, national are actively promoting prefabricated buildings. The prefabricated building is a building that is finished in the factory and transported to the construction site for safe and reliable installation [3]. Prefabricated buildings have the advantages of green energy saving and high efficiency, in line with the national green, high-quality development of strategic requirements. However, prefabricated buildings’ high-cost problem has restricted the rapid development of prefabricated buildings [4, 5]. The cost of prefabricated buildings is affected by many factors. If the cost management is improper in the construction process of prefabricated buildings, it may lead to cost overruns and delays in the construction period [6, 7]. It will suspend the construction in serious cases. Therefore, we should fortify control of prefabricated buildings costs and virtually lessen the construction cost. It has important guiding significance for the development of prefabricated buildings.

At present, domestic and foreign scholars have some research results on the cost of prefabricated buildings, as shown in Table 1. Peng et al. [8] studied the cost of prefabricated buildings from the perspective of hidden cost by using the fuzzy interpretive structure model (FISM) and Bayesian network (BN) and found out the key factors leading to hidden cost. Chang and Zhang [9] analyzed the main problems existing in assembly parts production using the strategic planning table method and putting forward corresponding control countermeasures. Wu and Qi [10] used the fuzzy TOPSIS method to study the closeness between the prefabricated high-rise building project and the optimal cost in Fujian province. Xun et al. [11] used AHP and improved CRITIC methods to determine the subjective and objective weights and TOPSIS method to determine the total weight and evaluated the cost risk of actual prefabricated buildings according to the cloud model. However, the cost risk lacked the evaluation of the dynamic process. Scholars have also made many achievements in the comparison of the cost of traditional buildings and prefabricated buildings [12], the exploration of influencing factors [13, 14], cost management, and cost control [15, 16].

To sum up, we can see from the literature analysis:(1)Some achievements have been made in the cost study of prefabricated buildings. However, most of the research scope is limited to a certain stage, such as more design and construction stages, and less consideration is given to the cost impact of the entire life cycle of prefabricated buildings.(2)Scholars have adopted many methods to study the cost of prefabricated buildings. However, if there are too many factors affecting the cost, many methods will be very troublesome and time-consuming to operate. In addition, a single model is difficult to overcome subjectivity or objectivity in the research process.

Therefore, this paper proposes an evaluation framework based on the game theory-cloud model to evaluate the influencing factors of prefabricated buildings costs. The calculation process is simple and easy. The game theory is used to optimize the subjective and objective weights determined by the attribute hierarchy model and the entropy weight method and to confirm the comprehensive weight of the evaluation index. The index’s weight is scientific and accurate, and the subjective influence of a single process is avoided or does not conform to the actual situation and so on. The cloud model is used to evaluate the cost impact of prefabricated buildings comprehensively. The cloud model realizes the uncertainty mapping of each evaluation index, takes into account the randomness and ambiguity of evaluation index quantification and grade division, and makes the evaluation result objective.

In summary, this paper combine game theory with the cloud model from the perspective of starting with the full life cycle of prefabricated buildings in this study. The qualitative and quantitative analyses have been combined to analyze the cost of prefabricated buildings systematically and dynamically. Firstly, based on the extensive collection of data and questionnaire survey, this paper analyzes the influencing factors of the four stages of design, component production, transportation, and construction on the cost of prefabricated buildings and constructs the evaluation index system of the influencing factors of the cost of prefabricated buildings. Then, the subjective and objective weights are calculated by the attribute hierarchy model and entropy weight method. Based on game theory, the subjective and objective weights are optimized to determine the comprehensive weight of each influencing factor. Finally, the rating level and cloud model parameters are determined by using cloud model theory, and the impact of prefabricated buildings cost is comprehensively evaluated. Taking specific prefabricated buildings in Tianjin as an example to verify the rationality of the model, this paper proposes the corresponding cost control optimization countermeasures according to the research results to further promote the development of prefabricated buildings make them have a broader market.

This study is organized as follows: Section 2 establishes the evaluation index system and method model according to the problems raised. Subsequently, Section 3 introduces the case and implements the proposed method model. Finally, Section 4 puts forward the discussion, and Section 5 puts forward the conclusions and prospects.

2. Materials and Methods

2.1. Establishment of the Evaluation Index System

Prefabricated buildings mainly use integrated architectural design and construction, greatly saving labor resources and building materials; construction duration is short. However, the construction cost of prefabricated buildings is maybe ¥1,000/square meter, which is higher than that of traditional buildings. The cost of prefabricated buildings includes the cost of designing, producing, transporting, and hoisting prefabricated components compared to traditional buildings. Based on the reference to the existing literature [17, 18], this paper starting with the full life cycle of the prefabricated buildings and selects four stages of design, component production, transportation, and construction to study and construct the evaluation index system of influencing factors of prefabricated buildings cost, as shown in Figure 1. The evaluation index is scientific and accurate.

2.1.1. Design Stage

The cost of prefabricated buildings in the design stage mainly includes prefabricated components, technical planning, preliminary, overall, and construction of five design links. Prefabricated buildings costs are higher than traditional building costs, mainly due to prefabricated component design. Prefabricated component design is jointly designed by the design unit and the manufacturing plant according to the drawings. The cost is mainly affected by the type and complexity of prefabricated components. Therefore, the cost of prefabricated components should be reasonably designed and managed. In addition, the rationality of the overall design, the standardized design of prefabricated components, and other reasons will also directly affect the cost of subsequent prefabricated buildings construction.

2.1.2. Production Stage

The production stage of prefabricated buildings is mainly the production of prefabricated components; traditional construction requires a large number of on-site labor, whereas prefabricated buildings only need modern machinery and equipment and a small number of exceptional technical employees. The cost of production of prefabricated components in the factory is high, and the labor cost is lower. The cost of prefabricated components in the production stage is mainly component production technology, mold cost, pre-buried parts setup fee, and so on. Among them, the mold cost will be affected by the type and complexity of the prefabricated components, and the greater the type and complexity, the production cost of the mold will also increase. If the production technology of prefabricated components is not skilled, it may be operated incorrectly, resulting in the re-production of prefabricated components, which will also greatly increase production costs.

2.1.3. Transportation Stage

The transportation stage of prefabricated buildings is mainly the transportation of prefabricated components. The transportation of prefabricated components is much more complex than traditional buildings, and the cost is high. The transportation stage is divided into four steps:(i)After the factory manufactures, the vehicle goes to the factory warehouse and completes the crane operation of the prefabricated components through the lifting equipment.(ii)The vehicle sends the prefabricated components to the construction site according to the prearranged route.(iii)After arriving at the construction site, the construction personnel hoists the prefabricated components.(iv)After the hoisting is completed, the vehicle returns to the prefabricated factory.

Therefore, factory prefabrication close to the construction site should be selected. Before transport needs to plan transport routes and means of transport, timely cooperation with the destination saves some unnecessary transportation and installation costs. If the transportation route is unreasonable, it will lead to excessive use of vehicles, which will significantly increase the cost of transportation.

2.1.4. Construction Stage

The construction stage of the prefabricated buildings is mainly the setting and partial pouring, which need to be checked and repaired after installation. Compared with traditional buildings, prefabricated buildings have higher installation and hoisting engineering requirements in the construction process, resulting in increased setting up and hosting costs. Prefabricated buildings in the construction stage are mainly artificial, mechanical, hoisting, installation, and tool amortization costs. For example, because prefabricated components are heavier than standard pouring components, hoisting mechanical equipment costs increased. Good construction site management improves equipment efficiency, reduces consumables consumption, and can effectively control costs.

2.2. Combinatorial Empowerment Determines the Weight

2.2.1. AHM

Attribute Hierarchy Model (AHM) is an unstructured decision method based on analytic hierarchy process (AHP) [19, 20]. The modeling and calculation process of AHM’s subjective weight is easy without calculating feature vectors and consistency checking. The steps for the use of AHM are as follows: Step 1: Construct a judgment matrix. According to the 1–9 proportional scaling table, as shown in Table 2, the importance of the two factors influencing the cost of prefabricated buildings is compared, and the matrix composed of the comparison results is called the judgment matrix . Step 2: Calculate the attribute judgment matrix. According to the following formula, transform the constructed judgment matrix into an attribute judgment matrix . where k is a positive integer greater than 1 and β often takes 1 or 2. Step 3: Determine the subjective weight. The relative property weight W₁ of each indicator is calculated by the following formula:

2.2.2. The Entropy Weight Method

The entropy weight method is an objective weighting method that can calculate the size of information entropy by evaluation index, which is used to determine the objective weight of the evaluation index [21]. The calculation process of obtaining objective weight by the entropy weight method is simple and easy. The steps for the use of the entropy weight method are as follows: Step 1: Standardized processing. Invite n prefabricated building-related experts to evaluate the cost factors, form the evaluation index matrix and data standardization processing, and thus obtain a standardized matrix of dimensionless data. Step 2: Determine the objective weight. The information entropy E₁, E₂, …, E_k of each indicator is calculated by formulas (3) and (4), and the objective weight W₂ of the indicator is determined according to formula (5): where p_ij represents the frequency of the evaluation index j appearing in the i sample, 0 < p_ij < 1; Y_ij represents the value of the j the evaluation index of i the sample after dimensionless processing; E_j represents the information entropy of evaluation index j; and k is a constant.

2.2.3. Game Theory

Game theory is a mathematical theory and method to study two or more people’s strategies and decisions. The thinking of game theory is combining subjective weight with objective weight, taking the attribute hierarchy model method and entropy weight method as two participants of game theory, seeking the balance point of combining subjective weight and objective weight. Moreover, reach the optimal combination weight of equilibrium state, that is, the deviation between combination weight and subjective and objective weights is minimum [22, 23]. The steps for the use of game theory are as follows: Step 1: The linear combination of subjective and objective weights of W₁ and W₂ obtained by AHM and entropy weight method yields the optimal weight of W; α₁ and α₂ are linear combined coefficients. Step 2: Based on the idea of cooperative game theory, the difference between combination weight and subjective and objective weights is minimized, and α₁ and α₂ are optimized. The objective function is Step 3: According to the differential properties of the matrix, the objective function is transformed into the first derivative of the optimization by using the conditional expression (8), α₁ and α₂ take the absolute value get the best linear combination coefficient after normalization α and get the optimal combination weight W.

2.3. Cloud Model Theory

The cloud model is a kind of uncertainty conversion model between qualitative concept and quantitative representation put forward by Li and Yang [24], which combines randomness and fuzziness existing in qualitative concept to form the mapping between qualitative and quantitative, to realize qualitative and quantitative transformation. The cost impact evaluation of prefabricated buildings aims to establish the mapping between the cost impact evaluation index and qualitative conception. It shows the relationship between quantitative data and qualitative concepts and makes the transition between qualitative and quantitative.

Let U be on the domain, x₁, x₂, …, x_n is an accurate representation of quantitative domain space U. Fuzzy concept C is the qualitative concept on the domain. There is a random number μ(x)∈[0,1] for any element with a stable tendency in the existing field U. That is the membership degree. Its value is stable and random, which can directly reflect the certainty of attribute x to concept C. The distribution space of the membership degree μ(x) on the domain U is called the cloud, and each x becomes a cloud droplet, namely

In the domain space U, a large number of cloud droplets x form a cloud, which can represent the characteristics of the qualitative concept [25]. The three digital characteristics of the cloud are acted for by expected (Ex), entropy (En), and hyper entropy (He) [26], as shown in Figure 2. Expected (Ex) is the distribution of cloud droplets in the universe space, which is the most representative point of the qualitative concept; entropy (En) is the value of the comprehensive measurement of randomness and fuzziness of the stability concept, which represents the acceptable value range of cloud droplets in the qualitative concept; hyper entropy (He) is the entropy of entropy and the comprehensive reflection of entropy fuzziness and randomness. For the problem of cost impact evaluation of prefabricated buildings, if there are m evaluation indexes, the impact level is divided into n levels; set X_min is the minimum boundary value of the evaluation indicator in a level of influence criterion; and X_max is its maximum boundary value. The boundary value of the evaluation index influence level standard is a quantitative indicator variable with bilateral. For example, x [X_min, X_max], the digital characteristic formula of the cloud iswhere k is a constant. Hyper entropy (He) reflects the randomness of evaluation. The larger the number, the greater the error, and the impact of the final evaluation is more significant. This paper, based on the reference literature [27, 28], takes k = 0.01.

Cloud generation algorithms can be cured into hardware and software implementations, called cloud generator [29, 30]. The cloud generator separates into forwarding cloud generator and reverse cloud generator, as shown in Figure 3. The combination of the two can realize the mutual conversion between qualitative and quantitative concepts. The cost impact evaluation of prefabricated buildings mainly uses a forward cloud generator. Forward cloud generator generates cloud droplets based on the digital characteristics of the cloud (Ex, En, and He). Each cloud drop represents a mapping relationship between qualitative concepts and quantitative representations. The cloud model is used to transform digital cloud features and the number of cloud droplets (N) into a map composed of cloud N cloud droplets, which is output by MATLAB software.

(a)

(b)

2.4. Cloud Model Building

According to the characteristics of the impact of prefabricated buildings cost, divide the prefabricated buildings cost impact level into = {very important, important, general, less important, very less important}, and the score value is . In order to generate a comprehensive evaluation cloud map, a unified value standard is established for the cost impact evaluation level of prefabricated buildings, namely V₁ [0.8, 1], V₂ [0.6, 0.8], V₃ [0.4, 0.6], V₄ [0.2, 0.4], and V₅ [0, 0.2]. The expectations for the “general” level are centered, and 0 and 1 represent the expectations for the “very less important” and “very important” levels, respectively. According to the principle of approaching the “general” level, the expectation of “important” and “less important” levels can be calculated by formula (12) to be 0.691 and 0.309, respectively, and He = 0.01. According to formula (12), the evaluation rating criteria are converted into the digital characteristic parameters of the cloud model of the comment, as shown in Table 3. MATLAB forward cloud generator is used to grade the standard evaluation cloud map for each evaluation measure, as shown in Figure 4.

The evaluation indicator cloud of the cloud model was obtained through data evaluation. N experts were invited to score each evaluation indicator according to the situation of a specific project, input the obtained original data, and obtain the second-level index evaluation cloud through backward cloud generator calculation.

where S_j², X_ij, and Ex_j, respectively, indicate the variance, evaluation value, and expectation of the i (i = 1, 2, 3, …, n) experts on the indicator j.

Input the three digital characteristics of the cloud model into the forward cloud generator, get the cloud map of the first expert score, use the cloud map to observe the feasibility of the expert scoring data, and after the comprehensive arrangement, the results will be fed back to the experts, and the opinions will be consulted again. This will be repeated for many rounds until the expert scoring data are more scientific and accurate. The cycle is adjusted repeatedly until a satisfactory cloud map is generated. The three digital characteristics of the evaluation cloud and the comprehensive weight are calculated by formula (14) to find the integrated cloud, which is recorded as C (Ex, En, and He). Similar comparisons between the comprehensive cloud and the standard evaluation cloud are achieved through MATLAB software, to determine the impact level of prefabricated buildings cost and reflect the overall results of the evaluation index object.

3. Experiments and Results

3.1. Engineering Background

Taking a specific prefabricated building in Tianjin as the evaluation object, the total construction area is 111,573.92 square meters, and the ground floor area is 69,623.05 square meters. The construction area of the northern region is 97,408.19 square meters, and the aboveground construction area is 9,430.96 square meters. The prefabricated components are prefabricated floors and prefabricated columns. Ten prefabricated buildings experts were invited to score the cost impact of the prefabricated buildings. The total weight is obtained using the combination weighting based on game theory, and the cloud model is used to evaluate the cost impact of prefabricated buildings comprehensively.

3.2. Comprehensive Weight

3.2.1. AHM

Based on existing literature research and questionnaire survey, the factors affecting the cost of the prefabricated buildings are compared, and the judgment matrix is shown in Tables 4–8.

3.2.2. The Entropy Weight Method

Invite 10 prefabricated building-related experts to evaluate the cost factors, form the evaluation index matrix and data standardization processing, and thus obtain a standardized matrix of dimensionless data. The calculation results are shown in Tables 9 and 10.

See Tables S1–S8 in the Supplementary Materials for a comprehensive table analysis.

3.2.3. Comprehensive Weight

The weight calculation is shown in Tables 11 and 12.

3.3. Comprehensive Evaluation of Cloud Model

Based on the cost impact evaluation of the project scored by ten experts, the cloud digital characteristic value of each evaluation indicator was calculated using the cloud model, and the results were shown in Tables 13 and 14.

Comprehensive evaluation cloud C (Ex, En, He) = (0.2769, 0.1457, 0.0204). MATLAB forward cloud generator is used to generate a comprehensive cloud map. The comprehensive cloud map is displayed in the evaluation standard cloud map of the cost of prefabricated buildings, as shown in Figure 5. The similarity between each first-level index and each standard evaluation level can be seen intuitively by drawing the similarity comparison diagram between each first-level index and each standard cloud, as shown in Figure 6.

(a)

(b)

(c)

(d)

It can be seen from Figure 5 that the comprehensive cloud is between the two evaluation levels of “very less important” and “less important,” and the proportion of the “less important” level is slightly larger than that in the “very less important” level, indicating that the cost impact level of the prefabricated construction project is in the less important level, which meets the project cost requirements. From the digital characteristics of the cloud model of each index in the evaluation of prefabricated buildings cost, it can be seen that the factors such as component splitting design, standardization levels of design, designer qualification, the processing technology of prefabricated components, component production technology, mold production, field hoisting construction level, project managers and construction workers level, and so on cause have a greater impact on the cost of prefabricated buildings. Prefabricated buildings have a relatively high cost in both the design and component production stages, which need to be controlled.

4. Discussion

In previous studies, most of them used subjective methods to determine the weight (such as expert evaluation method and AHP method), while only a few studies implemented the objective weight method. However, the single-use of subjective or objective weight method cannot make the determined weight scientific and accurate. In this paper, game theory is used to combine subjective and objective weights, so the subjective influence of a single process is avoided or does not conform to the actual situation and so on. Most of the weights of the indicator involved in this article are scientific and accurate, optimization of subjective and objective weights by attribute hierarchical model method, and entropy weight method based on game theory. The subjective standard weight is determined by the attribute hierarchy model method, and the objective weight is determined by the entropy weight method.

For effect evaluation, scholars generally adopt the fuzzy evaluation method. However, compared with the cloud model, the traditional fuzzy evaluation method has some shortcomings. The evaluation results of the traditional fuzzy evaluation method do not have volatility and randomness, and the operation is relatively complex and does not reflect fuzziness [31–33]. However, as a model to deal with uncertain problems, the cloud model has randomness and fuzziness, and the operation is relatively simple. In recent years, the cloud model has been gradually improved, and fruitful research results have been achieved [34, 35]. However, the application of cloud model theory in the field of prefabricated buildings is limited.

According to the results of specific prefabricated buildings in Tianjin case studies, the research on cost control of prefabricated buildings should be carried out from the following aspects in the future.

4.1. Strengthen the Design Stage Optimization

When the prefabrication rate increases, the production scale will greatly increase; the speed of production will be accelerated; and the time will be shortened. However, the higher the coefficient, the greater the workload of site setting up, thereby increasing the workload of construction and installation entity. Therefore, designers should set a scientific and reasonable rate of prefabricated structure in the design stage to minimize costs. The design unit should make corresponding preparations before work, integrate and plan all resources, and design a reasonable general plan to reduce the transportation distance of components on the site and reasonably control the cost.

4.2. Improve Production Component Design and Mold Production

In the production stage of prefabricated components, the production necessity of the internal embedded parts location and mold shape of the prefabricated components are higher. If there is a significant error, the prefabricated components need to be corrected on a large scale. Seriously or even reordering the prefabricated components, the production cost of the prefabricated components will increase significantly. Therefore, according to the existing production experience, the design unit should put forward opinions on the design of prefabricated components, reduce the type of prefabricated components and the complication of design, and reduce the mold design and production cost on the premise of meeting the technical requirements.

4.3. Strengthen Professional Level and Train Professionals

Currently, the construction market lacks talents, but a large numeral of professional talents is necessary for the construction process of prefabricated buildings. The talent problem is one of the most crucial factors in the promotion procedure of prefabricated buildings. To farm professional talents who meet the development necessity of the prefabricated construction industry, in the future, China should focus on cultivating professional talents in the procedure of promoting prefabricated construction. Enterprises should train professionals according to their conditions, arrange more training for professionals, and strengthen the management of talents. The higher the professional level of staff, the wealthy the powerful experience, the powerful the capability, the better the effect of reducing costs, and the faster the development of prefabricated buildings.

5. Conclusions and Prospects

Prefabricated buildings have the advantages of energy-saving, high efficiency, and high quality, which is energetically promoted in China’s construction industry. But the prefabricated buildings’ high construction cost hinders their rapid development. From the perspective of the full life cycle of prefabricated buildings, this paper studies the impact evaluation of the cost of prefabricated buildings, establishes the index system of the influencing factors of the cost of prefabricated buildings, and constructs the game theory cloud model. First, the cost influencing factors of prefabricated buildings in each stage are analyzed from the four dimensions of design, component production, transportation, and construction. There is also a complex correlation between the influencing factors of the cost, and one single model is difficult to overcome these problems at the same time. Therefore, this paper proposes a method based on the game theory cloud model to evaluate the influencing factors of prefabricated buildings costs. The model not only can deal with the data with large uncertainty but also has no requirement for the size of sample data and can directly reflect the complex internal relationship of factors. According to the results of the model’s research, it can be seen that there are many cost influencing factors in the two stages of design and component production of prefabricated component buildings, which need to be controlled. Therefore, targeted measures could be taken to reduce project costs. This provides a reference for managers to manage the prefabricated buildings cost in the actual project and also provides a new idea for the research, management, and theoretical basis of prefabricated buildings cost.

But this study also has some limitations. In this paper, the influencing factors system of cost of prefabricated buildings obtained by literature analysis and questionnaire has certain subjectivity; cost influencing factors may not be specific and complete, and so on. In addition, this paper analyzes the influencing factors of prefabricated buildings cost from four aspects: design, component production, transportation, and construction, but does not consider the cost influencing factors of early investment and later operation and maintenance stage, and the research scope needs to be further studied. In future research, combined with the shortcomings of the above two aspects, we will analyze the specific impact of various indicators on the cost of prefabricated buildings through a more scientific method, to better control the cost management of prefabricated buildings projects.

Data Availability

The data used to support the results of this study are included in the article and supplementary materials.

Conflicts of Interest

The authors declare that there are no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Supplementary Materials

Table S1: ten prefabricated building experts were invited to score the indicator C1j and form the evaluation index matrix of C1j. Table S2: according to formula (1), standardize the data in the evaluation index matrix of C1j, so as to obtain the standardization matrix of C1j. , where is the normalized value. Table S3: ten prefabricated building experts were invited to score the indicator C2j and form the evaluation index matrix of C2j. Table S4: according to formula (1), standardize the data in the evaluation index matrix of C2j, so as to obtain the standardization matrix of C2j. Table S5: ten prefabricated building experts were invited to score the indicator C3j and form the evaluation index matrix of C3j. Table S6: according to formula (1), standardize the data in the evaluation index matrix of C3j, so as to obtain the standardization matrix of C3j. Table S7: ten prefabricated building experts were invited to score the indicator C4j and form the evaluation index matrix of C4j. Table S8: according to formula (1), standardize the data in the evaluation index matrix of C4j, so as to obtain the standardization matrix of C4j. (Supplementary Materials)

References

N. N. Satheeskumar, N. G. O. Tuan, G. D. Tharaka, and D. Henderson, “Performance review of prefabricated buildings systems and future research in Australia,” Buildings, vol. 9, no. 2, p. 38, 2019.
View at: Google Scholar
A. A. Baghdadi, M. Heristchian, and H. Kloft, “Design of prefabricated wall-floor building systems using meta-heuristic optimization algorithms,” Automation in Construction, vol. 114, Article ID 103156, 2020.
View at: Google Scholar
P. Tao, “The application of assembly building in modern urban architecture,” Building structure, vol. 24, 2020.
View at: Google Scholar
H. Liu, Y. He, Q. Hu, J. Guo, and L. Luo, “Risk management system and intelligent decision-making for prefabricated building project under deep learning modified teaching-learning-based optimization,” PLoS ONE, vol. 15, no. 7, Article ID e0235980, 2020.
View at: Publisher Site | Google Scholar
W. W. Chen, S. Ya, and S. Zou, “Construction cost factor analysis of prefabricated buildings based on structural equation modelr,” Journal of Civil Engineering and Management, vol. 36, no. 5, pp. 50–55, 2019.
View at: Google Scholar
A. Nasirian, M. Arashpour, B. Abbasi, E. K. Zavadskas, and A. Akbarnezhad, “Skill set configuration in prefabricated construction: hybrid optimization and multicriteria decision-making approach,” Journal of Construction Engineering and Management, vol. 145, no. 9, pp. 1–16, 2019.
View at: Publisher Site | Google Scholar
J. Yoon, J. Han, and S. C. Lee, “Issues and improvements on cost determination and cost management in construction industry,” Korean Accounting Journal, vol. 27, no. 3, pp. 255–288, 2018.
View at: Publisher Site | Google Scholar
J. Peng, J. Zhou, F. Meng, and Y. Yu, “Analysis on the hidden cost of prefabricated buildings based on FISM-BN,” PLoS One, vol. 16, no. 6, Article ID e0252138, 2021.
View at: Publisher Site | Google Scholar
C. G. Chang and Y. Zhang, “Study on the production cost control of assembly building components,” Journal of Shenyang University of Architecture (Social Science Edition), vol. 5, pp. 470–475, 2016.
View at: Google Scholar
Z. M. Wu and A. Qi, “The method of evaluating the cost of assembly building is used by fuzzy TOPSIS method,” Journal of Fuzhou University (Natural Science Edition), vol. 5, pp. 618–624, 2020.
View at: Google Scholar
Z. Y. Xun, L. M. Zhang, Z. Y. Zhao, and Y. L. Xu, “Evaluation of assembly building cost risk based on the portfolio empowerment cloud model,” Journal of Civil Engineering and Management, vol. 6, pp. 8–13, 2020.
View at: Google Scholar
Y. Chen, G. E. Okudan, and D. R. Riley, “Sustainable performance criteria for construction method selection in concrete buildings,” Automation in Construction, vol. 19, no. 2, pp. 235–244, 2010.
View at: Publisher Site | Google Scholar
L. Zhao and Q. Q. Han, “Evaluation of the factors influencing the cost of assembly construction,” Construction economy, vol. 5, pp. 25–29, 2018.
View at: Google Scholar
Z. Ken and J. S. Tsai, “Identification of critical factors influencing prefabricated construction quality and their mutual relationship,” Sustainability, vol. 13, Article ID 11081, 2021.
View at: Google Scholar
Y. Y. Chen, Z. Du, X. Y. Cao, and S. L. Bao, “Study on the impact of “reform and increase” on the cost of assembly-type construction projects,” Building structure, vol. 6, pp. 108–111, 2019.
View at: Google Scholar
H. Wang, Y. Zhang, W. Gao, and S. Kuroki, “Life cycle environmental and cost performance of prefabricated buildings,” Sustainability, vol. 12, 2020.
View at: Publisher Site | Google Scholar
Z. Q. Xu, “Research on cost management of the whole industrial chain of assembly building,” Construction economy, vol. 2, pp. 81–85, 2021.
View at: Google Scholar
J. M. Bian, Z. L. Wang, and X. Liu, “Study on the constraints of the development of assembled buildings based on the analysis of main components,” Construction economy, vol. 2, pp. 76–80, 2021.
View at: Google Scholar
J. Seyedmohammadi, F. Sarmadian, A. A. Jafarzadeh, and R. W. McDowell, “Development of a model using matter element, AHP and GIS techniques to assess the suitability of land for agriculture,” Geoderma, vol. 352, pp. 80–95, 2019.
View at: Publisher Site | Google Scholar
X. Y. Sun, T. Chao, and S. Y. Wang, “A comprehensive method of evaluating indicators based on the gray hierarchical attribute model,” Journal of System Simulation, vol. 2, pp. 699–706, 2018.
View at: Google Scholar
J. Lu, W. Wang, Y. Zhang, and S. Cheng, “Multi-objective optimal design of stand-alone hybrid energy system using entropy weight method based on HOMER,” Energies, vol. 10, no. 10, p. 1664, 2017.
View at: Publisher Site | Google Scholar
D. Y. Wang, “The application of cloud model based on improving the weight of game theory combination in urban flood vulnerability evaluation,” People’s Pearl River, vol. 11, pp. 30–36, 2020.
View at: Google Scholar
Q. C. Fang and L. Shang, “Analysis of the stability of the slope of open-pit ore rock based on game theory-cloud model,” Journal of Safety and Environment, vol. 1, pp. 8–13, 2019.
View at: Google Scholar
Z. H. Yang and D. Y. Li, “2D cloud model and its application in forecasting,” Journal of Computer Science, vol. 11, pp. 961–969, 1998.
View at: Google Scholar
M. Guo, J. W. Zhao, D. Pan, M. Sun, Y. Zhou, and B. Yan, “Normal cloud model theory-based comprehensive fuzzy assessment of wooden pagoda safety,” Journal of Cultural Heritage, vol. 55, pp. 1–10, 2022.
View at: Publisher Site | Google Scholar
J. Ren, “Linguistic-stochastic multi-criterion decision-making method based on cloud model,” Computer Integrated Manufacturing Systems, vol. 18, pp. 2792–2797, 2012.
View at: Google Scholar
Y. P. Yang, G. G. Chen, T. J. Yang, and P. S. Huang, “Based on the cloud model of flood risk evaluation of a mine purification reservoir in xiangnan based on the empowerment of game theory combination,” Journal of Safety and Environment, vol. 2, pp. 546–553, 2021.
View at: Google Scholar
J. Li, M. W. Wang, J. Y. Long, and J. L. Jin, “A comprehensive cloud evaluation model based on game theory of water eutrophication,” Environmental Engineering, vol. 6, pp. 192–197, 2021.
View at: Google Scholar
H. L. Fu, Z. Huang, H. W. Huang, and J. B. Zhang, “Health diagnosis method of shield tunnel structure based on cloud theory,” Chinese Journal of Mechanical Engineering, vol. 39, no. 5, pp. 794–801, 2017.
View at: Google Scholar
K. Liu, L. Yang, and M. Li, “Application of cloud model and bayesian network to piracy risk assessment,” Mathematical Problems in Engineering, vol. 2021, Article ID 6610339, 14 pages, 2021.
View at: Publisher Site | Google Scholar
Y. W. Du, J. Fang, and P. Wang, “Ecological security evaluation of marine ranching based on DEMATEL-Fuzzy comprehensive evaluation,” Mathematical Problems in Engineering, vol. 2021, Article ID 6688110, 14 pages, 2021.
View at: Publisher Site | Google Scholar
D. Ding, J. Y. Wu, S. W. Zhu, Y. Mu, and Y. Li, “Research on AHP-based fuzzy evaluation of urban green building planning,” Environmental Challenges, vol. 5, Article ID 100305, 2021.
View at: Publisher Site | Google Scholar
D. Tadić, A. Aleksić, M. Stefanović, and S. Arsovski, “Evaluation and ranking of organizational resilience factors by using a Two-Step Fuzzy AHP and Fuzzy TOPSIS,” Mathematical Problems in Engineering, vol. 2014, Article ID 418085, 13 pages, 2014.
View at: Publisher Site | Google Scholar
H. W. Wu, J. Zhen, and J. Zhang, “Urban rail transit operation safety evaluation based on an improved CRITIC method and cloud model,” Journal of Rail Transport Planning & Management, vol. 16, Article ID 100206, 2020.
View at: Publisher Site | Google Scholar
Y. Zhou, J. Cai, Y. Xu, Y. Wang, C. Jiang, and Q. Zhang, “Operation performance evaluation of green public buildings with AHP-fuzzy synthetic assessment method based on cloud model,” Journal of Building Engineering, vol. 42, Article ID 102775, 2021.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2022 Na Li and Zhifeng Fan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies

Views

552

Downloads

639

Citations