Fuzzy risk assessment model for off-site construction

Abstract

The invention provides a fuzzy risk assessment model for off-site construction, and relates to the technical field of off-site construction risk assessment. The method comprises the following steps: firstly, identifying potential risk factors related to off-site construction by adopting a Delphi method; then, an interval value intuitionistic fuzzy IVIF-DEMATEL method is used in combination with Choquet integration, the relation between adopted risk factors ARFs is analyzed, and the method comprises the steps of data collection, decision maker weight determination, matrix construction and the like; and finally, determining the individual weight of each decision maker by using an intuitionistic fuzzy TOPSIS method, carrying out aggregation evaluation to construct a matrix, calculating an ideal solution, a distance index and a proximity coefficient, and carrying out priority ranking on risk factors. According to the method, the defects of a traditional risk assessment model are effectively overcome, and the complexity and uncertainty of off-site construction risks are comprehensively considered. By integrating multiple methods, the key risk factors and the interrelation thereof can be identified more accurately, a scientific and comprehensive risk assessment basis is provided for decision makers, and making of a more effective risk coping strategy is facilitated.

Description

Technical Field

[0001] The present invention relates to the technical field of off-site construction risk assessment, and particularly to a fuzzy risk assessment model for off-site construction. Background Art

[0002] In recent years, off-site construction (OSC) has played an increasingly important role in the development of the construction industry. By transferring some parts of the construction process to a controlled environment such as a factory, it effectively improves construction efficiency, enhances sustainability, and shortens the project delivery cycle. For example, in some urban construction projects, the use of OSC technology has significantly reduced on-site construction time and the impact of construction on the surrounding environment. However, it faces many challenges in the process of popularization and application.

[0003] From the perspective of supply chain management, OSC highly depends on suppliers and manufacturers. Once problems occur in the supply chain, such as delayed raw material supply, unstable quality, etc., it will affect the project progress. In the logistics link, the transportation and distribution of large precast components are difficult, and the risks of damage during transportation and delivery delay are relatively prominent. In terms of quality control, due to the coordination of multiple links, it becomes a difficult problem to ensure the quality consistency of precast components during production, transportation, and installation. At the same time, the regulatory policies vary greatly in different regions, lacking unified and perfect standards, which brings obstacles to the cross-regional operation of OSC enterprises.

[0004] Traditional risk assessment models are mostly constructed based on precise data and fixed variables, and it is difficult to adapt to the complex characteristics of OSC projects. In practical applications, these models cannot fully consider the uncertainty and ambiguity factors in the projects, resulting in insufficient decision-making basis. For example, in the face of risk factors such as supplier reputation and market fluctuations in OSC projects that are difficult to accurately quantify, traditional models often cannot accurately evaluate their impact degree.

[0005] In this field, although there have been many studies on OSC risks, there are still many deficiencies. On the one hand, most of the existing studies do not focus on specific stakeholders, especially those who have decision-making power in the adoption of OSC projects, making the application of research results in actual decision-making limited. On the other hand, there is a lack of in-depth exploration of the interaction and comprehensive impact between different risk factors, and it is impossible to provide decision-makers with comprehensive risk information. Therefore, it is urgent to develop a more accurate, comprehensive, and applicable risk assessment model for OSC projects. Summary of the Invention

[0006] To address the challenges in aspects such as supply chain management, logistics, quality control, and regulatory policies faced by off-site construction in the promotion and application of existing technologies, the inability of traditional risk assessment models to adapt to the complexity and uncertainty of off-site construction projects, and the technical problems that relevant research does not focus on specific stakeholders and lacks in-depth exploration of the interaction of risk factors, the present invention provides a fuzzy risk assessment model for off-site construction.

[0007] The technical solution provided by the present invention is as follows:

[0008] A fuzzy risk assessment model for off-site construction provided by the present invention includes:

[0009] S1: Risk identification, using the Delphi method to identify potential risk factors related to the adoption of off-site construction (OSC);

[0010] S2: Analysis of the relationship between risk factors, using the interval-valued intuitionistic fuzzy (IVIF)-DEMATEL method combined with the Choquet integral to analyze the relationship between adopted risk factors (ARFs);

[0011] S3: Determination of the priority of risk factors, using the intuitionistic fuzzy TOPSIS method to determine the priority of each risk factor.

[0012] The beneficial effects brought by the technical solution provided by the present invention at least include:

[0013] (1) In the present invention, by using the Delphi method to identify risk factors, expert opinions can be widely collected, and potential risks in the process of adopting off-site construction can be determined comprehensively and accurately. This method effectively overcomes the difficulties brought by limited data and complex risk factors, lays a solid foundation for subsequent risk assessment, ensures that key risk points are not missed, and improves the comprehensiveness and accuracy of risk assessment;

[0014] (2) In the present invention, the IVIF-DEMATEL method combined with the Choquet integral deeply analyzes the complex relationship between risk factors. It can not only clarify the importance of each factor but also reveal the causal relationship, presented in an intuitive causal relationship diagram. This helps decision-makers clearly grasp the risk context, prioritize key risks, reasonably allocate resources, and enhance the pertinence and effectiveness of risk response;

[0015] (3) In the present invention, the intuitionistic fuzzy TOPSIS method determines the priority of risk factors, comprehensively considering various factors, making the evaluation result more scientific. By calculating the positive and negative ideal solutions and the proximity coefficient for ranking, it provides a quantitative basis for decision-making. Decision-makers can formulate more reasonable risk response strategies accordingly, plan in advance, focus on preventing high-priority risks, enhance the overall risk resistance ability of off-site construction projects, and ensure the smooth progress of the projects. Description of the Drawings

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention, the following will briefly introduce the accompanying drawings required for the description of the embodiments. Obviously, the accompanying drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0017] Figure 1 It is a schematic flow chart of a fuzzy risk assessment model for off-site construction provided by an embodiment of the present invention;

[0018] Figure 2 It is a schematic diagram of the causal relationship between ARFs of a fuzzy risk assessment model for off-site construction provided by an embodiment of the present invention;

[0019] Figure 3 It is a schematic diagram of analyzing the sensitivity of ARFs through weight adjustment of a fuzzy risk assessment model for off-site construction provided by an embodiment of the present invention;

[0020] Figure 4 It is a schematic diagram of the overall ranking of ARFs of a fuzzy risk assessment model for off-site construction provided by an embodiment of the present invention. Detailed implementation manners

[0021] The following will describe the technical solutions in the present invention with reference to the accompanying drawings.

[0022] In the embodiments of the present invention, words such as "exemplarily" and "for example" are used to represent examples, illustrations or explanations. Any embodiment or design solution described as an "example" in the present invention should not be construed as being more preferred or having more advantages than other embodiments or design solutions. Exactly speaking, the use of the word "example" aims to present concepts in a specific way. In addition, in the embodiments of the present invention, the meaning expressed by "and / or" can be both, or either one of the two.

[0023] In the embodiments of the present invention, "image" and "picture" can sometimes be used interchangeably. It should be noted that when the difference is not emphasized, the meanings they express are the same. "(of)", "corresponding", and "corresponding" can sometimes be used interchangeably. It should be noted that when the difference is not emphasized, the meanings they express are the same.

[0024] In the embodiments of the present invention, sometimes subscripts such as W1 may be miswritten as non-subscript forms such as W1. When the difference is not emphasized, the meanings they express are the same.

[0025] To make the technical problems, technical solutions, and advantages to be solved by the present invention clearer, the following will be described in detail with reference to the accompanying drawings and specific embodiments.

[0026] Refer to the attached Figure 1 figures, which show a schematic flow diagram of a fuzzy risk assessment model for off-site construction provided by an embodiment of the present invention.

[0027] An embodiment of the present invention provides a fuzzy risk assessment model for off-site construction, and the processing flow may include the following steps:

[0028] S1: Risk identification, using the Delphi method to identify potential risk factors related to off-site construction (OSC);

[0029] S2: Analysis of risk factor relationships, using the interval-valued intuitionistic fuzzy (IVIF)-DEMATEL method combined with the Choquet integral to analyze the relationships between adopted risk factors (ARFs);

[0030] S3: Determination of risk factor priorities, using the intuitionistic fuzzy TOPSIS method to determine the priorities of each risk factor.

[0031] In a possible implementation manner, the specific implementation process of the Delphi method in S1 is as follows: In the case of limited direct data or complex and uncertain risk factors, organize multiple rounds of expert surveys. In each round of the survey, experts evaluate and provide feedback on possible risk factors based on their professional knowledge and experience. By continuously collecting and summarizing expert opinions, gradually clarify and screen out potential risk factors closely related to off-site construction, laying a foundation for subsequent risk analysis and assessment.

[0032] In a possible implementation manner, when using the IVIF-DEMATEL method combined with the Choquet integral to analyze risk factor relationships in S2, the following specific refinement steps are included:

[0033] S21: Data collection, collecting data using fuzzy terms according to five linguistic categories from "no relationship" to "very high relationship", and having experts subjectively evaluate and score the relationships between adopted risk factors (ARFs) according to these linguistic categories, so as to obtain preliminary information on the degree of association of risk factors;

[0034] S22: Determination of decision-maker weights, assigning weights to each decision-maker (DMs) using intuitionistic fuzzy sets (IFS) based on linguistic expressions from "critical" to "not considered". Considering the differences in professional fields, experience levels, etc. among different decision-makers, in this way, the importance of each decision-maker's opinion can be more reasonably reflected;

[0035] S23: Preference integration. Using the IVIF weighted average operator, according to the weight of each decision maker, integrate their evaluation preferences for the relationships of risk factors, so that the opinions of all decision makers can be comprehensively considered to obtain a comprehensive evaluation result on the relationships of risk factors;

[0036] S24: Matrix construction and normalization. Apply the IVIF entropy method to construct matrix N, which reflects a certain correlation structure between risk factors. Subsequently, calculate the normalized value of the matrix through a specific calculation method for more accurate analysis in the follow-up;

[0037] S25: Total impact matrix construction. Based on the results obtained from the previous steps, use relevant rules to construct the total impact matrix, which comprehensively reflects the comprehensive impact relationships between various risk factors and is the key basis for analyzing the causal relationships and importance of risk factors;

[0038] S26: Relationship evaluation. Use the Choquet integral to calculate the Choquet integral values of the columns (ChInc) and rows (ChInr) of the total impact matrix. Through further calculation of these integral values, obtain the values of ChInr + ChInc and ChInr – ChInc, so as to determine the importance levels of each risk factor and their causal relationships;

[0039] S27: Causal relationship diagram drawing. Use ChInr + ChInc as the horizontal axis to represent importance and ChInr - ChInc as the vertical axis to represent the impact of criterion i to draw the causal relationship diagram, which intuitively shows the interaction and influence directions between risk factors and helps decision makers better understand the complex relationships between risk factors.

[0040] In a possible implementation manner, when using the intuitionistic fuzzy TOPSIS method to determine the risk factor priorities in S3, it includes:

[0041] When collecting data using fuzzy terms in S21, to ensure the accuracy and consistency of the evaluation, there are clear definitions and descriptions for each language category. "No relationship" means that there is almost no mutual influence between two risk factors; "Very high relationship" means that there is a strong mutual correlation and influence between two risk factors. At the same time, it is required that experts follow unified standards and processes during the evaluation process to reduce subjective biases.

[0042] In a possible implementation manner, when assigning weights to decision makers using intuitionistic fuzzy sets in S22, considering factors such as the decision makers' professional knowledge, experience richness in different fields, and understanding of the project, for decision makers with profound professional knowledge and rich practical experience in relevant fields, higher weights are assigned; while for decision makers with less understanding of the project or lower professional relevance, relatively lower weights are assigned.

[0043] In a possible implementation, when integrating the decision-maker preferences using the IVIF weighted average operator in S23, this operator can fully consider the weights of each decision-maker and their specific evaluation values regarding the relationships of risk factors. Through the weighted average method, different opinions of multiple decision-makers are effectively fused, making the final comprehensive evaluation result better reflect the collective wisdom and judgment of all decision-makers.

[0044] In a possible implementation, when using the intuitionistic fuzzy TOPSIS method to determine the risk factor priorities in S3, it specifically includes the following detailed steps:

[0045] S31: Determination of individual weights. Based on the linguistic expressions from "major" to "unimportant", determine the individual weights of each decision-maker in the decision-making group consisting of l participants. Convert these linguistic expressions into intuitionistic fuzzy values. The evaluation value of the k-th decision-maker is represented as the intuitionistic fuzzy number I = [ωk, σk, ηk], and the corresponding weights are obtained through a specific calculation method. In this way, the opinions of decision-makers can be reasonably weighted according to their importance levels.

[0046] S32: Construction of the collective decision matrix. Aggregate the evaluations of decision-makers. Using the IFWA function, integrate the evaluation results of each decision-maker on risk factors to construct the collective decision matrix Z(k) = (zij(k))m×n. This matrix synthesizes the opinions of all decision-makers and reflects the performance of risk factors under various evaluation indicators.

[0047] S33: Calculation of standard weights. Aggregate the evaluations of each decision-maker on the importance of standards. Use the IFWA function to calculate the standard weight Ф. Considering that the importance of different evaluation standards may vary in the entire risk assessment system, determining the standard weights in this way can more accurately measure the impact of each standard on the risk factor priorities.

[0048] S34: Creation of the comprehensive matrix and the decision matrix. Using the assigned weights, create the comprehensive matrix and construct the decision matrix according to certain rules. The comprehensive matrix combines the evaluation values of risk factors and the standard weights, and the decision matrix provides the basic data for subsequent calculation of the positive and negative ideal solutions.

[0049] S35: Calculation of the positive and negative ideal solutions. Calculate the positive ideal solution and the negative ideal solution. B1 and B2 correspond to the benefit and cost standards respectively. N* represents the positive ideal solution, and N represents the negative ideal value. The positive ideal solution represents the situation where the optimal state is achieved under all evaluation indicators, and the negative ideal solution represents the situation where the worst state is achieved under all evaluation indicators.

[0050] S36: Distance index calculation. Using the normalized Euclidean distance, calculate the distances between each solution and the positive and negative ideal solutions. These distance indices reflect the proximity of each risk factor to the optimal and worst cases, and are important bases for evaluating the priorities of risk factors.

[0051] S37: Closeness coefficient calculation. Calculate the closeness coefficient to the ideal solution through a specific formula. This coefficient comprehensively considers the distances between the risk factor and the positive and negative ideal solutions, and can more comprehensively measure the advantages and disadvantages of each risk factor in the entire risk system.

[0052] S38: Risk factor ranking. Rank the solutions according to the calculated closeness coefficient. The larger the closeness coefficient, the closer the risk factor is to the positive ideal solution, and the higher its priority; conversely, the smaller the closeness coefficient, the closer the risk factor is to the negative ideal solution, and the lower its priority.

[0053] In a possible implementation, when determining the individual weights of decision-makers in S31, there is a clear quantitative standard for each linguistic expression. For example, "major" indicates that the opinion of the decision-maker has a very important influence, and the corresponding intuitionistic fuzzy value is relatively high; "unimportant" indicates that the opinion of the decision-maker has a relatively small influence, and the corresponding intuitionistic fuzzy value is relatively low. Through this quantitative method, the actual importance of the decision-maker can be more accurately reflected.

[0054] In a possible implementation, when using the IFWA function to construct the collective decision matrix in S32, this function can effectively aggregate the evaluation results of multiple decision-makers, taking into account the weights of each decision-maker. During the aggregation process, the information of the original evaluation data is fully retained, enabling the collective decision matrix to more truly reflect the comprehensive evaluation of all decision-makers on risk factors.

[0055] In a possible implementation, the three steps of S1, S2, and S3 are interrelated and work synergistically. The potential risk factors identified in S1 provide the object for the relationship analysis in S2, and the risk factor relationships obtained from the analysis in S2 provide the basis for determining the priorities in S3. Through this systematic evaluation process, the risks during the off-site construction adoption process can be comprehensively and accurately evaluated, providing strong support for decision-makers to formulate scientific and reasonable risk response strategies.

[0056] It should be noted that the Delphi method is a structured communication technique commonly used to collect expert opinions through a series of surveys. It is particularly suitable for situations where direct data is limited or the subject involves complex uncertain factors, such as risk identification in off-site construction (OSC). In this embodiment, the Delphi method is used to systematically identify and validate the potential risks of adopting OSC in China. It consists of two parts: the combination of Choquet integral and (IVIF)-DEMATEL, and the intuitionistic method of intuitionistic fuzzy TOPSIS.

[0057] Combination of Choquet integral and (IVIF)-DEMATEL:

[0058] Step 1: Collect data using fuzzy terms: Formulas (1) to (3) are used to create IVIFNs. Table 1 defines five linguistic categories, from "no relationship" to "very high relationship", which are used to evaluate and assign scores to ARFs.

[0059]

[0060]

[0061] Table 1. Linguistic scoring of IVIF-DEMATEL

[0062]

[0063] Step 2: Determine the weights of decision-makers (DMs): Use the intuitionistic fuzzy set (IFS) to assign the weight of each DM, denoted as S U =(ωh,σh,ηh), and the calculation of these weights follows equations (1)-(3). Table 2 shows the linguistic scores representing the weights of DMs using IVIFNs.

[0064] Table 2. Linguistic expressions for assigning DM weights

[0065]

[0066] Step 3: Use the IVIF weighted average operator to determine the combined preference of decision-makers. The degree of influence of criterion i on j is represented by the value of IVIFNs assigned by the uth decision-maker. The preferred options of DMs are combined using formula (4). The combined value is as follows:

[0067]

[0068] where ζ i is the weight of δ i

[0069] Step 4: Apply the IVIF entropy method together with equation (5) to construct matrix N:​

[0070]

[0071] Among them, n represents the total number of IVIF components.

[0072] Step 5: Calculate the normalized value of the matrix using formula (6):

[0073]

[0074] Among them, ij is an element of matrix N.

[0075] Step 6: Construct the total matrix of influence using equation (7):

[0076]

[0077] Among them, T = S(I - S) -1 , where I is the identity matrix.

[0078] Step 7: Evaluate the relationship using the Choquet integral. According to formulas (8) to (10), calculate the Choquet integral values of the columns (ChInc) and rows (ChInr) in the overall influence matrix. Subsequently, calculate the values of ChInr + ChInc and ChInr - ChInc respectively:

[0079] T = [τ ij n×n i, j = 1,..., n (8)

[0080]

[0081] Step 8: Create a graph to represent the causal relationship. The horizontal axis represents the importance level (ChInr + ChInc), while the vertical axis represents the influence of criterion i (ChInr - ChInc).

[0082] Intuitionistic approach of intuitionistic fuzzy TOPSIS:

[0083] Applying the method of intuitionistic fuzzy TOPSIS includes calculating the relative importance of criteria through the IVIF-DEMATEL method combined with the Choquet integral, so as to obtain the ranking of alternative solutions. Implementing this method requires the following steps:

[0084] Step 1: Determine the individual weights assigned to each decision maker. Assume that the decision-making group consists of l participants. These decision makers are represented by linguistic terms, and these linguistic terms are represented as intuitionistic fuzzy values. Table 3 provides the linguistic terms used to evaluate the importance of alternative solutions.

[0085] Table 3. Evaluating alternative solutions through IFN numbers

[0086]

[0087]

[0088] Express the evaluation value of the \(k\)-th decision maker as an intuitionistic fuzzy number \(I = [\omega_k, \sigma_k, \eta_k]\), and the weight corresponding to the \(k\)-th DM is:

[0089]

[0090] where,

[0091] Aggregate the evaluations provided by the decision makers to construct a collective decision matrix. \(Z^{(k)}=(z_{ij}^{(k)})_{m\times n}\) represents each decision maker. Then combine the individual evaluations into a single aggregated matrix. To achieve this goal, the IFWA function is used.

[0092] \(Z^{(k)}=(z_{ij}^{(k)})_{m\times n}\)

[0093] where,

[0094]

[0095] The following is the description of the decision matrix:

[0096]

[0097] Step 2: Define the criterion weights. \(\varPhi\) represents a series of importance levels. The importance of these criteria may not be exactly equal. The evaluations of each decision maker on the criterion importance must be aggregated to determine the overall weights. Then use the IFWA function to calculate the weights of the criteria.

[0098]

[0099] where, \(\varPhi\) j \( = [\omega\) j , \sigma\) j , \eta\) j , \(j = 1,\cdots,n\).

[0100] Step 3: Create a comprehensive matrix using the assigned weights. This matrix is formed according to the following outline:

[0101]

[0102] The decision matrix is formulated as follows:

[0103]

[0104] is an element of the matrix.

[0105] Step 4: Calculate the values of the positive and negative ideal solutions. B1 and B2 correspond to the gain and expenditure criteria respectively, N* represents the positive ideal solution, and N represents the negative ideal value. The derivation of these solutions is as follows:

[0106] N - =(ω N-Φ (q j ),σ N-Φ (q j ))

[0107] Where:

[0108]

[0109]

[0110] Step 5: Distance metric, using the extended forms of Hamming distance and Euclidean distance, and their normalized versions to evaluate the similarity or difference between options. Specifically, the normalized Euclidean distance is applicable to the following situations:

[0111]

[0112] Step 6: Calculate the closeness coefficient to the ideal solution. Use the formula in formula (23) to calculate the closeness coefficient:

[0113]

[0114] Where,

[0115]

[0116] Step 8: Sort the alternative solutions according to the ranking. After calculating the Cli* values, sort the alternative solutions in descending order.

[0117] The construction industry in China faces many challenges, such as rapid urbanization, population growth, and the need to achieve sustainable development goals. In Beijing and Shanghai, the government launched a large-scale prefabricated housing project that adopted the OSC method. The project aims to quickly provide affordable housing to meet the growing urban demand. The risk assessment was carried out by a panel of fifteen professionals from different departments, including project consultants, project managers, and site engineers. Each expert has at least five years of relevant experience and the necessary technical expertise (see Table 4). The panel identified fourteen risk factors associated with the adoption of OSC. These potential risk factors are listed in Table 5.

[0118] Table 4. Distribution of experts by experience and job role

[0119]

[0120] The IVIF-DEMATEL method is used to establish the relationships among ARFs. The experts evaluated the degree of interdependence among ARFs according to the fuzzy scales in Tables 1 and 2. The results of this analysis, including the causal diagram of ARFs, are as Figure 2 shown. The significance scores ChInr + ChInc of ARFs help to determine their relative importance. The results show that the importance levels of ARFs are as follows: ARF2 > ARF8 > ARF11 > ARF13 > ARF12 > ARF6 > ARF3 > ARF4 > ARF1 > ARF5 > ARF14 > ARF10 > ARF9 > ARF7. ARF1 In the project, ARF 1 is the most critical risk factor. Figure 2 It shows that ARF 1, as the core factor driving other risks, is the basis and key element for solving the remaining factors. The ARFs in the cause group affect other factors, and the strength of this causal relationship is measured by the positive difference between ChInr and ChInc. The results show that the ranking of the nine causal risk factors is as follows: ARF2 > ARF8 > ARF11 > ARF5 > ARF13 > ARF12 > ARF3 > ARF1 > ARF10.

[0121] Table 5. Adopted Risk Factors (ARFs) for Off-Site Construction (OSC) Projects

[0122]

[0123]

[0124] The results show that in the causal group, ARF1 has the highest value. The influence group of ARFs is determined by the negative value of ChInr - ChInc. Among the elements in this influence group, ARF7 is most affected, indicating its significant sensitivity to causal ARFs. The order of the five influence parameters is as follows: ARF7 > ARF4 > ARF6 > ARF14 > ARF9. The IVIF-DEMATEL method is used to identify the relationships among ARFs. The final weights are determined by combining the values obtained by the IVIF-DEMATEL method with the IF-TOPSIS method. These combined weights, together with the identified relationships, are used to set priorities. The priority rankings and final values of ARFs are shown in Table 6.

[0125] Table 6. Cause and Result Values and Priority Rankings of ARFs

[0126]

[0127]

[0128] A sensitivity analysis was conducted to examine the changes in the ARF scores and how different percentage adjustments of 10%, 20%, 30%, and up to 90% affected the priority rankings. Figure 3 The results of combining the IVIF-DEMATEL and IF-TOPSIS methods are presented. It should be noted that all values were normalized to ensure that the sum of the total weights was 1. The dark blue bars represent stable values, while the light blue bars highlight the variations between one or more alternatives. The chart shows that ARF-1, ARF-3, ARF-10, and ARF-14 exhibit the highest stability, while ARF-8 and ARF-11 are the most sensitive, especially when applying the FDEMATEL-FTOPSIS method. This method uses an improved IF-TOPSIS technique to determine the ranking of alternatives, which improves the efficiency of the risk assessment process compared to FTOPSIS. The results of the sensitivity analysis indicate that the proposed method provides a more reliable and stable output than the FDEMATEL-FTOPSIS method, especially when considering the differences between different ARFs.

[0129] To demonstrate the efficiency and advantages of the proposed risk assessment method, a comparative analysis was conducted using F TOPSIS, FIS system, and FDEMATEL-FTOPSIS. Figure 4 The overall rankings of the ARFs obtained by four different methods are shown. ARF-7 is ranked as the highest priority, while ARF-12 is in the lowest position among all methods. Additionally, the rankings of ARF-1, ARF-2, ARF-3, ARF-5, ARF-6, ARF-7, ARF-10, ARF-11, ARF-12, and ARF-13 are consistent between the proposed method and the other three methods, which confirms the robustness of the proposed risk assessment framework. However, there are differences in the rankings of ARF-4, ARF-8, ARF-9, and ARF-14 between the proposed method and other techniques. These differences can be attributed to the following limitations: First, the FDEMATEL-FTOPSIS method does not consider the integration role of individual expert judgments in determining the importance of ARFs. Second, the FIS method uses a fuzzy inference system to establish the risk factor priorities but does not consider the relative weights or interdependencies of the risk criteria. Finally, the fuzzy TOPSIS method cannot combine all individual expert opinions while considering the interdependencies between ARFs.

[0130] The effectiveness analysis is carried out by the following method. The comprehensive ranking is obtained by combining the results of various decision-making techniques. The most effective method is the one that best matches the comprehensive priority ranking. Table 7 shows the risk priority matrix of fourteen ARFs, showing the frequency with which each ARF is assigned to different priority levels. Subsequently, Table 8 is formed by summing up the data in the previous column and placing it in the ranking column of Table 7. Using the data in Table 7, the optimal priority values are determined using the linear programming model described below:

[0131]

[0132] The above LP problem is solved using LINGO software. The priority ranking of ARFs is as follows: ARF-4 > ARF-7 > ARF-11 > ARF-1 > ARF-10 > ARF-5 > ARF-13 > ARF-2 > ARF-8 > ARF-9 > ARF-14 > ARF-6 > ARF-3 > ARF-12. Next, the priority differences between the four previously discussed methods and the comprehensive ranking method are calculated using formula (25).

[0133]

[0134] where S p represents the priority score assigned to ARFi by each method, and Ai represents the aggregated ranking order of ARFi. The deviation values of fuzzy TOPSIS, FIS, FDEMATEL-FTOPSIS, and the proposed method are 1.811, 1.709, 1.801, and 1.619, respectively. Obviously, this method produces the smallest deviation, providing more accurate and reliable results for risk assessment.

[0135] Table 7. Frequency of ARFs Assigned to Different Priorities

[0136]

[0137]

[0138] Table 8. Allocation of Refined ARFs at Different Priority Levels (Ω gp )

[0139]

[0140] An embodiment of the present invention proposes a new method for evaluating risk factors in off-site construction (OSC) projects, aiming to address the limitations found in the prior art. The proposed technique combines the advanced interval-valued intuitionistic fuzzy (IVIF) DEMATEL method with the Choquet integral, enabling a comprehensive examination of the interdependent relationships among various risk factors. In addition, the IVIF entropy method and the IVIF weighted average (IVIFWA) operator are used to synthesize expert opinions and evaluate the importance of each risk factor. Subsequently, the combined IVIF-DEMATEL-intuitionistic fuzzy-TOPSIS framework is used to prioritize the risk factors. A real case of risk assessment for off-site construction projects is also presented, including sensitivity tests, comparison tests, and validation tests, to evaluate the effectiveness of the proposed method. The results show that the method provides a more consistent and reliable risk assessment, making it an effective tool for evaluating risk factors in off-site construction projects.

[0141] The beneficial effects brought by the technical solution provided by the embodiment of the present invention at least include:

[0142] (1) In the present invention, the Delphi method is used to identify risk factors, which can widely collect expert opinions and comprehensively and accurately determine the potential risks in the process of adopting off-site construction. This method effectively overcomes the difficulties brought by limited data and complex risk factors, lays a solid foundation for subsequent risk assessment, ensures that key risk points are not missed, and improves the comprehensiveness and accuracy of risk assessment;

[0143] (2) In the present invention, the IVIF-DEMATEL method is combined with the Choquet integral to deeply analyze the complex relationships among risk factors. It can not only clarify the importance of each factor but also reveal the causal relationships, which are presented in an intuitive causal relationship diagram. This helps decision-makers clearly grasp the risk context, prioritize the handling of key risks, reasonably allocate resources, and enhance the pertinence and effectiveness of risk response;

[0144] (3) In the present invention, the intuitionistic fuzzy TOPSIS method determines the priority of risk factors, comprehensively considering various factors, making the evaluation results more scientific. By calculating the positive and negative ideal solutions and the proximity coefficient for ranking, it provides a quantitative basis for decision-making. Decision-makers can formulate more reasonable risk response strategies accordingly, plan in advance, focus on preventing and controlling high-priority risks, improve the overall risk resistance of off-site construction projects, and ensure the smooth progress of the projects.

[0145] The above content is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claimed rights.

[0146] The following points need to be explained:

[0147] (1) The accompanying drawings of the embodiments of the present invention only relate to the structures involved in the embodiments of the present invention, and other structures may refer to the usual designs.

[0148] (2) For clarity, in the accompanying drawings used to describe the embodiments of the present invention, the thickness of layers or regions is enlarged or reduced, that is, these drawings are not drawn to actual scale. It can be understood that when an element such as a layer, film, region or substrate is referred to as being "on" or "under" another element, the element can be "directly" on or under the other element or there may be intermediate elements.

[0149] (3) Without conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other to obtain new embodiments.

[0150] The above is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. The protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A fuzzy risk assessment model for off-site construction, characterized in that, Including: S1: Risk identification, using the Delphi method to identify potential risk factors related to the adoption of off-site construction (OSC); S2: Risk factor relationship analysis, using the interval-valued intuitionistic fuzzy (IVIF)-DEMATEL method combined with the Choquet integral to analyze the relationships among the adopted risk factors (ARFs); S3: Risk factor priority determination, using the intuitionistic fuzzy TOPSIS method to determine the priorities of each risk factor.

2. The fuzzy risk assessment model for off-site construction according to claim 1, wherein Including: The specific implementation process of the Delphi method in S1 is as follows: In the case of limited direct data or complex and uncertain risk factors, multiple rounds of expert surveys are organized. In each round of the survey, experts evaluate and provide feedback on the possible risk factors based on their professional knowledge and experience. By continuously collecting and summarizing expert opinions, the potential risk factors closely related to the adoption of off-site construction are gradually clarified and screened, laying a foundation for subsequent risk analysis and assessment.

3. A fuzzy risk assessment model for off-site construction according to claim 1, characterized in that When using the IVIF-DEMATEL method combined with the Choquet integral to analyze the risk factor relationships in S2, the following specific refinement steps are included: S21: Data collection, collecting data using fuzzy terms according to five linguistic categories from "no relationship" to "very high relationship". Experts subjectively evaluate and score the relationships among the adopted risk factors (ARFs) based on these linguistic categories, thereby obtaining preliminary information on the degree of association of risk factors; S22: Decision maker weight determination, using intuitionistic fuzzy sets (IFS) to assign weights to each decision maker (DMs) based on linguistic expressions from "critical" to "not considered". Considering the differences among decision makers in terms of professional fields, experience levels, etc., in this way, the importance of each decision maker's opinion can be more reasonably reflected; S23: Preference integration, using the IVIF weighted average operator to integrate the evaluation preferences of decision makers on risk factor relationships according to the weights of each decision maker. In this way, the opinions of all decision makers can be comprehensively considered to obtain a comprehensive evaluation result on risk factor relationships; S24: Matrix construction and normalization, applying the IVIF entropy method to construct matrix N, which reflects a certain association structure among risk factors. Subsequently, the normalization value of the matrix is calculated through specific calculation methods for more accurate analysis in the follow-up; S25: Total impact matrix construction, based on the results obtained from the previous steps, using relevant rules to construct the total impact matrix, which comprehensively reflects the comprehensive impact relationships among various risk factors and is the key basis for analyzing the causal relationships and importance of risk factors; S26: Relationship evaluation, using the Choquet integral to calculate the Choquet integral values of the columns (ChInc) and rows (ChInr) of the total impact matrix. By further calculating these integral values, the values of ChInr + ChInc and ChInr – ChInc are obtained, thereby determining the importance levels of each risk factor and their causal relationships. S27: Draw a causal relationship diagram. Use ChInr + ChInc as the horizontal axis to represent importance, and ChInr - ChInc as the vertical axis to represent the impact of criterion i. Draw a causal relationship diagram, which intuitively shows the interaction and impact direction among risk factors, helping decision-makers better understand the complex relationships among risk factors.

4. The fuzzy risk assessment model for off-site construction according to claim 3, characterized in that, When using the intuitionistic fuzzy TOPSIS method to determine the priority of risk factors in S3, it includes: When collecting data using fuzzy terms in S21, to ensure the accuracy and consistency of the evaluation, each linguistic category has clear definitions and descriptions. "No relationship" means that there is almost no mutual influence between two risk factors; "Very high relationship" means that there is a strong mutual correlation and influence between two risk factors. At the same time, experts are required to follow unified standards and procedures during the evaluation process to reduce subjective biases.

5. The fuzzy risk assessment model for off-site construction according to claim 3, wherein, It includes: When assigning weights to decision-makers using intuitionistic fuzzy sets in S22, considering factors such as the decision-makers' professional knowledge, experience level in different fields, and their understanding of the project, decision-makers with profound professional knowledge and rich practical experience in relevant fields are given higher weights; while decision-makers with less understanding of the project or lower professional relevance are given relatively lower weights.

6. The fuzzy risk assessment model for off-site construction according to claim 3, characterized in that It includes: When integrating decision-makers' preferences using the IVIF weighted average operator in S23, this operator can fully consider the weights of each decision-maker and their specific evaluation values of the relationships among risk factors. Through weighted averaging, different opinions of multiple decision-makers are effectively integrated, making the final comprehensive evaluation result better reflect the collective wisdom and judgment of all decision-makers.

7. The fuzzy risk assessment model for off-site construction according to claim 1, wherein When using the intuitionistic fuzzy TOPSIS method to determine the priority of risk factors in S3, it specifically includes the following detailed steps: S31: Determine individual weights. Based on the linguistic expressions from "major" to "unimportant", determine the individual weights of each decision-maker in a decision-making group consisting of l participants. Convert these linguistic expressions into intuitionistic fuzzy values. The evaluation value of the k-th decision-maker is represented as the intuitionistic fuzzy number I = [ωk, σk, ηk]. The corresponding weights are obtained through specific calculation methods, so that the opinions of decision-makers can be reasonably weighted according to their importance levels. S32: Construct a collective decision matrix. Aggregate the evaluations of decision-makers. Use the IFWA function to integrate the evaluation results of each decision-maker on risk factors and construct a collective decision matrix Z(k) = (zij(k))m×n. This matrix synthesizes the opinions of all decision-makers and reflects the performance of risk factors under each evaluation index. S33: Calculate criterion weights. Aggregate the evaluations of each decision-maker on the importance of criteria. Use the IFWA function to calculate the criterion weights Ф. Considering that the importance of different evaluation criteria may vary in the entire risk assessment system, determining the criterion weights in this way can more accurately measure the impact of each criterion on the priority of risk factors. S34: Creation of the comprehensive matrix and the decision matrix. Using the assigned weights, create the comprehensive matrix and construct the decision matrix according to certain rules. The comprehensive matrix combines the evaluation values of risk factors and the standard weights, and the decision matrix provides the basic data for the subsequent calculation of the positive and negative ideal solutions. S35: Calculation of the positive and negative ideal solutions. Calculate the positive ideal solution and the negative ideal solution. B1 and B2 correspond to the benefit and cost criteria respectively. N* represents the positive ideal solution, and N represents the negative ideal value. The positive ideal solution indicates the situation where the best is achieved under all evaluation indicators, while the negative ideal solution indicates the situation where the worst is achieved under all evaluation indicators. S36: Calculation of the distance metrics. Using the normalized Euclidean distance, calculate the distances between each solution and the positive and negative ideal solutions. These distance metrics reflect the degree of proximity of each risk factor to the best and worst cases, and are important bases for evaluating the priorities of risk factors. S37: Calculation of the closeness coefficient. Calculate the closeness coefficient to the ideal solution through a specific formula. This coefficient comprehensively considers the distances between the risk factor and the positive and negative ideal solutions, and can more comprehensively measure the advantages and disadvantages of each risk factor in the entire risk system. S38: Ranking of risk factors. Rank the solutions according to the calculated closeness coefficient. The larger the closeness coefficient, the closer the risk factor is to the positive ideal solution, and the higher its priority. Conversely, the smaller the closeness coefficient, the closer the risk factor is to the negative ideal solution, and the lower its priority.

8. A fuzzy risk assessment model for off-site construction according to claim 7, characterized in that, Including: When determining the individual weights of decision-makers in S31, there are clear quantitative criteria for each linguistic expression. For example, "major" indicates that the opinion of this decision-maker has a very important influence, corresponding to a relatively high intuitionistic fuzzy value; "unimportant" indicates that the opinion of this decision-maker has a relatively small influence, corresponding to a relatively low intuitionistic fuzzy value. Through this quantitative method, the actual importance of decision-makers can be more accurately reflected.

9. The fuzzy risk assessment model for off-site construction according to claim 7, wherein Including: When using the IFWA function to construct the collective decision matrix in S32, this function can effectively aggregate the evaluation results of multiple decision-makers, taking into account the weights of each decision-maker. During the aggregation process, the information of the original evaluation data is fully retained, making the collective decision matrix more truly reflect the comprehensive evaluation of all decision-makers on risk factors.

10. A fuzzy risk assessment model for off-site construction according to claim 1, characterized in that, Including: The three steps of S1, S2, and S3 are interrelated and interact synergistically. The potential risk factors identified in S1 provide the objects for the relationship analysis in S2, and the risk factor relationships obtained from the analysis in S2 provide the basis for determining the priorities in S3. Through this systematic evaluation process, the risks in the off-site construction adoption process can be comprehensively and accurately evaluated, providing strong support for decision-makers to formulate scientific and reasonable risk response strategies.

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