A Five-Dimensional Model for Risk Assessment during the Operation Period of Cross-Border Transportation Infrastructure

Abstract

The present invention relates to the technical field of cross-border transportation infrastructure, and specifically to a five-dimensional model for risk assessment during the operation period of cross-border transportation infrastructure. It includes the design of a five-dimensional model for comprehensive risk assessment. For the risks during the operation period of cross-border transportation infrastructure, a five-dimensional evaluation model including four stages is proposed. The four stages are as follows: The first stage: identification of risk factors; The second stage: analysis of the dependence effect of risk factors; The third stage: calculation of the objective weights of the five-dimensional indicators for risk assessment; The fourth stage: comprehensive assessment of risk factors under the five-dimensional indicators. The present invention proposes a brand-new "four-stage - five-dimensional" risk assessment model for the operation period of cross-border transportation infrastructure projects considering the risk dependence effect, and introduces the four implementation stages and specific calculation formulas of this model.

Description

Technical Field

[0001] The present invention relates to the technical field of cross-border transportation infrastructure, and specifically to a five-dimensional model for risk assessment during the operation period of cross-border transportation infrastructure. Background Art

[0002] Due to connecting different countries or regions, cross-border transportation infrastructure (hereinafter referred to as CBTI) faces differences in various aspects such as different political systems, legal systems, culture and religion during the operation period, resulting in a series of unique and difficult-to-ignore operation period risks. In addition, due to the influence of "cross-border", CBTI faces a more complex natural and social environment, making the operation period risks it faces not only more, but also have a dependence effect, that is, the interaction and spread among risk factors. Further, the various types of operation period risks that cannot be ignored during the operation period of CBTI and their dependence effects also greatly increase the difficulty of risk assessment for such engineering risks by risk managers. Therefore, for this special type of project, systematic research on the analysis of risk dependence effects and comprehensive risk assessment during the operation period is of great significance for comprehensively identifying, reasonably assessing, effectively preventing its risks, and achieving sustainable operation. Summary of the Invention

[0003] The present invention proposes a brand-new "four-stage - five-dimensional" risk assessment model for the operation period of cross-border transportation infrastructure projects considering risk dependence effects, and introduces the four implementation stages and specific calculation formulas of this model.

[0004] The technical solution adopted by the present invention is as follows:

[0005] A five-dimensional model for risk assessment during the operation period of cross-border transportation infrastructure, characterized in that: it includes the design of a five-dimensional model for comprehensive risk assessment, and for the risks during the operation period of cross-border transportation infrastructure, a five-dimensional evaluation model including four stages is proposed; the four stages are as follows:

[0006] The first stage: identification of risk factors, including two parts: (1) pre-identification of risk factors, initially identifying possible risk factors through literature analysis; (2) final determination of risk factors and construction of a risk factor index system. This part requires the establishment of an expert team and is finally determined based on the long-term experience and accumulation of experts.

[0007] The second stage: analysis of the dependence effect of risk factors, based on the scores given by experts in the questionnaire collected in the first stage on the mutual relationship between risk factors, calculating the dependence effect of risk factors, including ranking the intensity of the dependence effect of risk factors and classifying the causal relationship of risk factor transmission.

[0008] First, consider a risk assessment model that contains n risk factors, F = {F1, F2,..., F n}(i ∈ {1, 2,..., n}), and there are m experts who score the risk factors, E = {E1, E2,..., E m}(k ∈ {1, 2,..., m}). Assume that each expert has equal importance in this risk assessment process, and this paper will use linguistic terms to represent the experts' evaluations of the strength of the dependence effects among various risk factors, and convert the linguistic terms into trapezoidal fuzzy numbers as their mathematical expressions for substitution into the mathematical operations of subsequent steps. Let represent the evaluation of the strength of the influence of risk factor Fi on risk factor Fj given by the m-th expert, where i, j = 1, 2,..., n, k = 1, 2,..., m. In particular, when

[0009] Third stage: Calculation of the objective weights of the five-dimensional indicators for risk evaluation,

[0010] The calculation method for the objective weights of the five-dimensional indicators is as follows:

[0011] Let be the fuzzy personal risk assessment matrix represented by trapezoidal fuzzy numbers, which reflects the evaluations of each risk factor under each indicator by each expert. Here, k represents each expert, and d represents the indicators of each dimension.

[0012] Fourth stage: Comprehensive assessment of risk factors under the five-dimensional indicators. The comprehensive performance of risk factors during the operation period of cross-border transportation infrastructure under the five indicators will be scored and ranked. These five indicators include: possibility, loss, controllability, measurability, and dependence.

[0013] The five dimensions mentioned above refer to the indicators used to evaluate risk factors, which are divided into five dimensions, namely: the possibility of risk occurrence, the loss caused by risk occurrence, the mutual dependence among risk factors, the controllability of risk, and the measurability of risk, abbreviated as: possibility, loss, dependence, controllability, and measurability.

[0014] The four stages mentioned above respectively refer to:

[0015] First stage, identification of risk factors; through the literature analysis of existing relevant research, a preliminary list of risk factors is established. Then, the expert team combines the specific engineering situation and their own experience to construct the final list of risk factors. At the same time, by distributing questionnaires to experts, the scores of each expert for each risk factor in terms of dependence effect and the other four evaluation indicators are collected as the basic data for subsequent risk assessment.

[0016] In the second stage, the dependence effect analysis of risk factors will be carried out. The DEMATEL method under a fuzzy environment will be used to calculate the mutual dependence effects among risk factors, which will include two parts of calculation results: (1) calculating the causal classification of different risk factors; (2) calculating the strength of dependence of different risk factors and generating a ranking. Among them, the result of the second part will be used as the initial data of "risk dependence" in the "five-dimensional" evaluation index and substituted into the subsequent calculation of the comprehensive evaluation of risk factors.

[0017] In the third stage, the objective weights of the five-dimensional indicators for risk evaluation will be calculated. By using the entropy weight method, the objective weights of the five-dimensional indicators will be calculated.

[0018] In the fourth stage, the comprehensive evaluation of risk factors under the five-dimensional indicators will be carried out. In this stage, the VIKOR method under a fuzzy environment will be used to comprehensively score the major risk factors under the five-dimensional indicators and obtain the final comprehensive ranking. At the same time, in this stage, management suggestions based on this result will also be given and a sensitivity analysis will be carried out.

[0019] The specific steps of the second stage are as follows:

[0020] Step 1. Construct the individual initial fuzzy direct influence matrix

[0021] According to the scores given by experts on the direct influence of each risk factor, the individual initial fuzzy direct influence matrix is obtained as follows:

[0022]

[0023] In this application, trapezoidal fuzzy numbers are used to represent the meaning of linguistic terms in a mathematical form. That is, can be converted to where Therefore, the initial fuzzy direct influence matrix can be converted to where k = 1, 2,..., m, i, j = 1, 2,..., n. In particular, is converted to

[0024] Step 2. Construct the group fuzzy direct influence matrix

[0025] To obtain the comprehensive evaluation of each expert, the individual initial fuzzy direct influence matrices are arithmetically averaged to obtain the group fuzzy direct influence matrix as follows:

[0026]

[0027] Step 3. Obtain the standard group fuzzy direct influence matrix

[0028] Next, perform normalization calculation on the group fuzzy direct influence matrix to obtain the standard matrix The normalization calculation process is as follows:

[0029]

[0030] where and

[0031] Step 4. Obtain the crisp value matrix X 1 , X 2 , X 3 , X 4 .

[0032] Decompose the standard group fuzzy direct influence matrix to obtain four crisp value matrices X 1 , X 2 , X 3 and X 4 , that is

[0033] (4)

[0034] Step 5. Calculate the fuzzy comprehensive dependence effect matrix

[0035] The risk dependence effect includes the direct influence and indirect influence between risk factors. The indirect influence is caused by the cascade propagation between risk factors. The direct influence is obtained by direct scoring from experts, and the indirect influence can be calculated by the fuzzy DEMATEL method. According to the FDEMATEL method, the fuzzy comprehensive dependence effect matrix can be calculated by the following formula:

[0036]

[0037] and can be expressed as

[0038]

[0039] where

[0040] Step 6. Calculate the influence coefficient, centrality, and reason degree of risk factors

[0041] Let represent the sum of the influence strength of risk factor Fi on other risk factors, which can be calculated by the following formula:

[0042]

[0043] Let Denote the sum of the strengths of the influence of risk factor Fi by other risk factors, which can be calculated by the following formula:

[0044]

[0045] Let Denote the fuzzy centrality of risk factor Fi, which can be calculated by the following formula:

[0046]

[0047] Let Denote the fuzzy causality degree of risk factor Fi, which can be calculated by the following formula:

[0048]

[0049] In order to obtain the ranking of the strengths of each risk factor in the dependence effect and their causal classification, the fuzzy centrality and the fuzzy causality degree can be converted into clear values and are respectively denoted as p i and r i , and their calculation formulas are as follows:

[0050]

[0051] Risk factor F i 's ranking of dependence strength and causal classification can be obtained through the clear values of the centrality p i and the causality degree r i . The value of p i represents the quantified value of the role of risk factor F i in the propagation of all risk factors. The higher the centrality p i of risk factor F i , the stronger its dependence effect with other risk factors. The value of r i represents the classification of risk factor F i . If r i > 0, then risk factor F i is a cause risk factor; if r i < 0, then this risk factor is an effect risk factor.

[0052] The weight calculation steps for the risk evaluation index during the operation period of cross-border transportation infrastructure in the third stage are as follows, with the step numbers following step 6:

[0053] Step 7. Calculate the fuzzy group risk evaluation matrix

[0054] Aggregate the fuzzy individual risk assessment matrix to obtain the fuzzy group risk evaluation matrix The trapezoidal fuzzy numbers are processed by weighted average, and the calculation method is as follows:

[0055]

[0056] Step 8. Defuzzification and normalization

[0057] Next, the fuzzy group risk evaluation matrix is defuzzified to obtain the group risk evaluation matrix S = [s id n×5 .

[0058] Then, it is further normalized to obtain the standard group risk evaluation matrix Y = [y id n×5 . The normalization method here is to divide each element in the matrix by the sum of the elements in its column. The specific calculation formula is as follows:

[0059]

[0060] Step 9. Calculate the objective weights of the five-dimensional indicators

[0061] The objective weights of the five-dimensional indicators are calculated by the entropy weight method. "Entropy" can be used to measure the utility of data information under a certain indicator. The larger the "entropy" value ed, the more chaotic the data; the smaller the utility value hd, so the weight value wd of this indicator is smaller. In particular, when the "entropy" value e = 1, the utility is 0. The specific calculation formula is as follows:

[0062]

[0063] The specific steps of the fourth stage are as follows, with the step numbers following step 9:

[0064] Step 10. Calculate the maximum and minimum values of risk factors in a single dimension

[0065] The calculation methods for the optimal and worst values of risk factors in the five single dimensions are as follows:

[0066]

[0067] where i = 1, 2,..., n, d = 1, 2, 3, 4, 5

[0068] Step 11. Calculate the S, Q, and R values

[0069]

[0070] where i = 1, 2,..., n, d = 1, 2, 3, 4, 5, S + = min i S i ; S​​- = max i S i ; R + = min i R i ; R - = max i R i In addition, v represents the weight value of the group utility, and 1 - v represents the individual regret value.

[0071] Step 12. Calculate the ranking of risk factors

[0072] The comprehensive ranking of risk factors under the five - dimensional index can be calculated from the Q, S, and R values obtained by the above formula. Since there are conflicts among the five - dimensional indexes, the probability that a certain risk factor satisfies the optimal solution under all indexes is relatively low. Therefore, to obtain a unique compromise solution, the following two conditions need to be met:

[0073] Condition 1: Acceptable advantage

[0074]

[0075] where F′ is the first - ranked risk factor in the ranking of risk factors with the Q value as the standard, and F″ is the second - ranked.

[0076] Condition 2: Acceptable decision stability

[0077] The risk factor F′ must also be ranked first when ranked by S or / and R as the standard.

[0078] Only when the above two conditions are met simultaneously can a unique compromise solution be obtained. However, in many cases, due to the insufficient difference between risk factors, the above two conditions cannot be met simultaneously. In this case, a set of compromise solutions will be generated and output as the result. The calculation method is as follows:

[0079] If only Condition 2 cannot be met, the set of compromise solutions is {F′, F″};

[0080] If Condition 1 cannot be met either, the set is {F′, F″,... F (M)}, where M is the maximum value that makes hold.

[0081] Advantages of the present invention:

[0082] The present invention fills the gap in the systematic research in the field of risk assessment during the operation period of cross-border transportation infrastructure. Specifically, it has the following research significance: (1) Theoretical contribution; (2) Method innovation. By combining the three major methods of FDEMATEL method, entropy weight method and FVIKOR method, an innovative hybrid method for the new risk assessment framework under the five-dimensional indicators of this paper is formed, enabling it to effectively calculate the comprehensive risk assessment during the operation period of cross-border transportation infrastructure, which fits the innovative framework proposed in this paper. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] Figure 1 It is a schematic diagram of the framework of a five-dimensional model for risk assessment during the operation period of a cross-border transportation infrastructure of the present invention.

[0084] Figure 2 It is a causal diagram of risk factors of a five-dimensional model for risk assessment during the operation period of a cross-border transportation infrastructure of the present invention.

[0085] Figure 3 It is a radar chart of S, R, and Q values of each risk factor of a five-dimensional model for risk assessment during the operation period of a cross-border transportation infrastructure of the present invention. DETAILED IMPLEMENTATION MANNER

[0086] The present invention will be further described below.

[0087] A five-dimensional model for risk assessment during the operation period of cross-border transportation infrastructure, characterized in that it includes the design of a five-dimensional model for comprehensive risk assessment, and a five-dimensional evaluation model including four stages is proposed for the risks during the operation period of cross-border transportation infrastructure; the four stages are as follows:

[0088] The first stage: identification of risk factors, including two parts: (1) Preliminary identification of risk factors, and possible risk factors are initially identified through literature analysis; (2) Final determination of risk factors and construction of a risk factor index system. This part requires the establishment of an expert team, which is finally determined based on the long-term experience and accumulation of experts.

[0089] The second stage: analysis of the dependence effect of risk factors. Based on the scores of experts on the mutual relationship between risk factors in the questionnaire collected in the first stage, the dependence effect of risk factors is calculated, including the ranking of the dependence effect intensity of risk factors and the classification of the causal relationship of risk factor propagation.

[0090] Among the numerous methods for studying dependence effects, the DEMATEL method only requires experts to evaluate the direct influence relationships between factors, and calculates the indirect and comprehensive influence relationships by multiplying the matrix by itself and summing, which makes the initial evaluation of risk dependence effects more intuitive and avoids the intricate interrelationships from affecting experts' judgments, thus possibly leading to errors in the final results. The DEMATEL method is usually applied to calculate the interrelationships between factors in complex systems with fuzzy backgrounds where the data source is expert experience and the relationships between factors are uncertain. Therefore, it is suitable for studying risk interdependence and has been widely used in correlation studies among various factors.

[0091] Meanwhile, since it is relatively difficult to evaluate the risks of cross-border transportation infrastructure projects, the evaluations given by experts are usually fuzzy and unclear. Therefore, this paper will adopt the FDEMATEL method under fuzzy environment proposed by Suo et al. to calculate and analyze the dependence effects of risk factors during the operation period of cross-border transportation infrastructure.

[0092] First, consider a risk assessment model that contains n risk factors, F = {F1, F2,..., F n}(i ∈ {1, 2,..., n}), and there are m experts scoring the risk factors E = {E1, E2,..., E m}(k ∈ {1, 2,..., m}). Assume that each expert has the same importance in this risk assessment process, and this paper will use linguistic terms to represent the experts' evaluations of the strength of the dependence effects between various risk factors, and convert the linguistic terms into trapezoidal fuzzy numbers as their mathematical expressions for substituting into the subsequent mathematical operations. Let represent the evaluation of the strength of the influence of risk factor Fi on risk factor Fj given by the m-th expert, where i, j = 1, 2,..., n, k = 1, 2,..., m. In particular, when

[0093] Third stage: Calculation of the objective weights of the five-dimensional indicators for risk evaluation,

[0094] It is a common method in traditional risk assessment for experts to directly assign weights to the five evaluation indicators of "likelihood - loss - dependence - controllability - measurability". Calculating the weights of different indicators based on the degree of dispersion of the data distribution in the risk assessment questionnaire is closer to reality compared to experts' direct weight assignment.

[0095] The concept of "entropy" in thermodynamics, which is used to judge the degree of dispersion of substances, was first proposed by C.E. Shannon and introduced into information theory to calculate the weight of information, and then developed into the entropy weight method (EWM). Therefore, this paper uses the entropy weight method to calculate the weights of the five indicators to more objectively reflect the actual importance of each indicator. In the entropy weight method, according to the evaluation scores of experts on each risk factor under the five indicators, the weight values of each indicator are calculated. Among them, the scores of each risk factor under the indicator of "risk dependence" are determined by the result centrality p obtained in the previous stage i and the scores of each risk factor under the other four indicators (i.e., possibility, loss, controllability, and measurability) are directly evaluated by experts.

[0096] The calculation method of the objective weights of the five-dimensional indicators is as follows:

[0097] Let be the fuzzy personal risk assessment matrix represented by trapezoidal fuzzy numbers, which reflects the evaluation of each expert on each risk factor under each indicator. Where k represents each expert and d represents the indicators of each dimension.

[0098] The fourth stage: The comprehensive evaluation of risk factors under the five-dimensional indicators will calculate the scores and rankings of the comprehensive performance of risk factors during the operation period of cross-border transportation infrastructure under the five indicators. These five indicators include: possibility, loss, controllability, measurability, and dependence.

[0099] Since the five indicators of risk assessment are not comparable; at the same time, the probability that a certain risk factor can show the strongest risk characteristics under the five-dimensional indicators is also very low, that is, it is difficult to obtain an optimal (worst) solution. Therefore, the VIKOR method proposed by Opricovic is used to determine the comprehensive ranking order of all risk factors and find a group of factors with the highest risk. The VIKOR method can obtain a compromise solution when there are conflicts between indicators and no optimal solution can be obtained, and at the same time reflects the group utility and personal regret value of experts, and has superiority in comprehensive evaluation. At the same time, due to the fuzzy and complex environment faced by cross-border transportation infrastructure, this paper will finally select the fuzzy VIKOR method (i.e., the FVIKOR method) to comprehensively evaluate the risk factors under the five-dimensional indicators and obtain the ranking of the overall risk performance from strong to weak.

[0100] The five dimensions mentioned above refer to that the indicators for evaluating risk factors are divided into five dimensions, namely: the possibility of risk occurrence, the loss of risk occurrence, the mutual dependence between risk factors, the controllability of risk, and the measurability of risk, abbreviated as: possibility, loss, dependence, controllability, and measurability.

[0101] The four stages mentioned above respectively refer to:

[0102] The first stage is the identification of risk factors. Through the literature analysis of existing relevant research, a preliminary list of risk factors is established. Subsequently, the expert team combines the specific engineering situation and their own experience to construct the final list of risk factors. At the same time, by distributing questionnaires to experts, the scores given by experts for each risk factor under the dependence effect and the other four evaluation indicators are collected as the basic data for subsequent risk assessment.

[0103] The second stage is the analysis of the dependence effect of risk factors. The DEMATEL method under a fuzzy environment will be used to calculate the mutual dependence effects between risk factors, which will include two parts of calculation results: (1) calculating the causal classification of different risk factors; (2) calculating the strength of dependence of different risk factors and generating a ranking. Among them, the result of part (2) will be used as the initial data of "risk dependence" in the "five-dimensional" evaluation index and substituted into the subsequent calculation of the comprehensive evaluation of risk factors.

[0104] The third stage is the calculation of the objective weights of the five-dimensional risk evaluation indicators. By using the entropy weight method, the objective weights of the five-dimensional indicators are calculated.

[0105] The fourth stage is the comprehensive evaluation of risk factors under the five-dimensional indicators. In this stage, the VIKOR method under a fuzzy environment will be used to synthesize the scores of each major risk factor under the five-dimensional indicators and obtain the final comprehensive ranking. At the same time, in this stage, management suggestions based on this result will also be given and a sensitivity analysis will be carried out.

[0106] The specific steps of the second stage are as follows:

[0107] Step 1. Construct an individual initial fuzzy direct influence matrix

[0108] According to the scores given by experts on the direct influence of each risk factor, an individual initial fuzzy direct influence matrix is obtained as follows:

[0109]

[0110] In this application, trapezoidal fuzzy numbers are used to represent the meaning of linguistic terms in a mathematical form. That is, can be converted to where Therefore, the initial fuzzy direct influence matrix can be converted to where k = 1, 2,..., m, i, j = 1, 2,..., n. In particular, is converted to

[0111] Step 2. Construct a group fuzzy direct influence matrix

[0112] To obtain the comprehensive evaluation of each expert, the arithmetic mean of the individual initial fuzzy direct influence matrix is calculated to obtain the group fuzzy direct influence matrix as follows:

[0113]

[0114] Step 3. Obtain the standard group fuzzy direct influence matrix

[0115] Next, the group fuzzy direct influence matrix is normalized to obtain the standard matrix The normalization calculation process is as follows:

[0116]

[0117] where and

[0118] Step 4. Obtain the crisp value matrix X 1 , X 2 , X 3 , X 4 .

[0119] Decomposing the standard group fuzzy direct influence matrix, four crisp value matrices X 1 , X 2 , X 3 and X 4 can be obtained, that is

[0120]

[0121] Step 5. Calculate the fuzzy comprehensive dependence effect matrix

[0122] The risk dependence effect includes the direct and indirect effects between risk factors, where the indirect effect is caused by the cascade propagation between risk factors. The direct effect is obtained by the experts' direct scoring, and the indirect effect can be calculated by the fuzzy DEMATEL method. According to the FDEMATEL method, the fuzzy comprehensive dependence effect matrix can be calculated by the following formula:

[0123]

[0124] and can be expressed as

[0125]

[0126] where

[0127] Step 6. Calculate the influence coefficient, centrality, and causal degree of risk factors

[0128] Let represent the sum of the influence strengths of risk factor Fi on other risk factors, and it can be calculated by the following formula:

[0129]

[0130] Let represent the sum of the influence strengths of risk factor Fi being affected by other risk factors, and it can be calculated by the following formula:

[0131]

[0132] Let represent the fuzzy centrality of risk factor Fi, and it can be calculated by the following formula:

[0133]

[0134] Let represent the fuzzy causal degree of risk factor Fi, and it can be calculated by the following formula:

[0135]

[0136] In order to obtain the ranking of the strength of each risk factor in the dependence effect and their causal classification, the fuzzy centrality and the fuzzy causal degree can be converted into clear values and are respectively represented as p i and r i , and their calculation formulas are as follows:

[0137]

[0138] The ranking of the dependence strength and causal classification of risk factor F i can be obtained through the clear values of the centrality p i and the causal degree r i . The value of p i represents the quantified value of the role of risk factor F i in the propagation of all risk factors. The higher the centrality p i of risk factor F i , the stronger the dependence effect between it and other risk factors. The value of r i represents the classification of risk factor F i . If r i >0, then risk factor F i is a cause risk factor; if r i <0, then this risk factor is an outcome risk factor.

[0139] The steps for calculating the weights of the risk assessment indicators during the operation period of cross-border transportation infrastructure in the third stage are as follows, with the step number following step 6:

[0140] Step 7. Calculate the fuzzy group risk assessment matrix

[0141] Aggregate the fuzzy individual risk assessment matrix to obtain the fuzzy group risk assessment matrix For trapezoidal fuzzy numbers, use the weighted average method, and its calculation method is as follows:

[0142]

[0143] Step 8. Defuzzification and normalization

[0144] Next, defuzzify the fuzzy group risk assessment matrix to obtain the group risk assessment matrix S = [s id n×5 .

[0145] Then, further normalize it to obtain the standard group risk assessment matrix. Y = [y id n×5 . The normalization method here is to divide each element in the matrix by the sum of the elements in its column. The specific calculation formula is as follows:

[0146]

[0147] Step 9. Calculate the objective weights of the five-dimensional indicators

[0148] The objective weights of the five-dimensional indicators are calculated by the entropy weight method. "Entropy" can be used to measure the utility of data information under a certain indicator. The larger the "entropy" value ed, the more chaotic the data; the smaller the utility value hd, so the weight value wd of this indicator is smaller. In particular, when the "entropy" value e = 1, the utility is 0. The specific calculation formula is as follows:

[0149]

[0150] The specific steps of the fourth stage are as follows, with the step number following step 9:

[0151] Step 10. Calculate the maximum and minimum values of risk factors in a single dimension

[0152] The calculation methods for the optimal and worst values of risk factors in the five single dimensions are as follows:

[0153]

[0154] where i = 1, 2,..., n, d = 1, 2, 3, 4, 5 ​​

[0155] Step 11. Calculate S, Q, and R values

[0156]

[0157] Where i=1,2,…,n,d=1,2,3,4,5,S + =min i S i ;S - =max i S i ; R + =min i R i ; R - =max i R i In addition, v represents the weight value of group utility, and 1-v represents the individual regret value.

[0158] Step 12. Calculate the ranking of risk factors

[0159] The comprehensive ranking of risk factors under the five-dimensional indicators can be calculated using the Q, S, and R values obtained from the above formula. Due to the conflicts between the five-dimensional indicators, the probability of a risk factor meeting the optimal solution under all indicators is low. Therefore, obtaining a unique compromise solution requires meeting the following two conditions:

[0160] Condition 1: Acceptable Advantage

[0161]

[0162] Among them, F′ is the first risk factor in the risk factor ranking based on Q value, and F″ is the second.

[0163] Condition 2: Acceptable decision stability

[0164] The risk factor F' must also be ranked first when sorting by S and / or R.

[0165] Only when both of the above conditions are met can a unique compromise solution be obtained. However, in many cases, the differences between the risk factors are not large enough, so the above two conditions cannot be met simultaneously. In this case, a set of compromise solutions will be generated as the output. The calculation method is as follows:

[0166] If only condition 2 cannot be satisfied, the set of compromise solutions is {F′, F″};

[0167] If condition 1 is also not satisfied, then the set is {F′,F″,…F (M)}, where M is such that The maximum value that can be established.

[0168] The following conducts a risk assessment and analysis during the operation period in combination with cross-border transportation:

[0169] I. Risk identification and index system establishment during the operation period of cross-border transportation:

[0170] Corresponding to the first stage in the five-dimensional model of risk assessment during the operation period of cross-border transportation infrastructure and applying it. The establishment of the risk index system for cross-border transportation during the operation period is also divided into two steps: pre-identifying risk factors based on the literature analysis method; finally determining risk factors based on the expert interview method.

[0171] Based on literature analysis and expert discussions, the risk factors are reorganized into 5 major risk categories (primary risks) and 15 risk factors (secondary risks), namely cross-border passage risks (including risk factors F1, F2, F3), major project or environmental risks (including risk factors F4, F5, F6), cross-border economic or political risks (including risk factors F7, F8, F9, F 10 ), cross-border legal risks (including risk factors F 11 , F 12 ), cross-border social risks (including risk factors F 13 , F 14 , F 15 ).

[0172] While establishing the risk list during the operation period, the members of the expert team need to fill in Questionnaire 1 (Risk Dependence Effect Assessment Questionnaire) and Questionnaire 2 (Risk Comprehensive Assessment Questionnaire):

[0173] In the Risk Dependence Effect Assessment Questionnaire (Questionnaire 1), experts are required to give an evaluation of the direct influence size between two risk factors F i and F j (excluding the influence between each risk factor and itself), that is, experts are required to pairwise analyze the direct influence of 15 risk factors. The measurement index is the possibility that risk factor F i triggers risk factor F j . The questionnaire uses a language term set, and experts give one of the 5 levels of "extremely low possibility, relatively low possibility, general possibility, relatively high possibility, extremely high possibility" according to the influence degree. The conversion between the language term set and trapezoidal fuzzy numbers is shown in Table 1. At the same time, this paper establishes a 15χ15 risk factor matrix to store the size scores of experts on the pairwise interaction between risk factors.

[0174] Table 1 Correspondence between language term set and trapezoidal fuzzy numbers

[0175]

[0176]

[0177] After the questionnaires are collected, reliability tests (α - coefficient consistency tests) should be conducted on the questionnaire results. If the value of the α - coefficient is greater than 0.7, it indicates that the questionnaire results meet the consistency test.

[0178] In Questionnaire 2, experts evaluate the risks during the operation period under five indicators. The five - dimensional indicators are: possibility, loss, dependence, controllability, and measurability. The language term sets used in this questionnaire have 5 levels under each indicator. The specific language terms are shown in Table 2. Among them, the performance ranking of risks under the dependence indicator is obtained from the above - mentioned risk - dependence effect analysis and is not directly scored by experts. The data obtained from Questionnaire 2 are used for the calculation and analysis of the comprehensive risk assessment during the operation period.

[0179] Table 2 Language term sets used in Questionnaire 2

[0180] Possibility Consequence Controllability Measurability Corresponding trapezoidal fuzzy number Very low Very insignificant Very poor Very difficult (0,0,1 / 9,2 / 9) Low Insignificant Poor Difficult (1 / 9,2 / 9,3 / 9,4 / 9) Medium Medium Medium Medium (3 / 9,4 / 9,5 / 9,6 / 9) High Severe Strong Simple (5 / 9,6 / 9,7 / 9,8 / 9) Very high Very severe Very strong Very simple (7 / 9,8 / 9,1,1)

[0181] For the original matrix of experts' personal scoring obtained, reliability tests should be conducted. If the obtained consistency index α - coefficient is greater than 0.7, it proves that the original data meets the consistency test.

[0182] II. Analysis of risk - dependence effect during the operation period of cross - border transportation:

[0183] Corresponding to the second stage in the five - dimensional model of risk assessment during the operation period of cross - border transportation infrastructure: analysis of risk - dependence effect and its application to cases.

[0184] (1) Analysis of the strength of risk - dependence effect

[0185] Calculate the indirect influence between all risk factors according to formulas (2) - (5) and establish a fuzzy comprehensive influence matrix. Calculate the centrality and reasonability of 15 risk factors according to formulas (6) - (10) and convert the fuzzy values into clear values for convenient result analysis. The calculation results of centrality and reasonability are shown in Table 3.

[0186] Table 3 Calculation results of centrality, reasonability of each risk factor and its risk - dependence ranking

[0187]

[0188]

[0189] Meanwhile, according to the calculation results of centrality and reasonability, this paper classifies the 15 risk factors causally and draws a causal diagram of risk factors, as shown in Figure 2 .

[0190] Risk factor F i 's centrality pi It's F i The sum of the impact of all other risk factors plus F i The sum of the influence of all other risk factors reflects the F i The performance and importance of the risk-dependent effect. Figure 2 It can be seen that the factor with the strongest risk dependence effect is F10, with a centrality value of 3.694. The other risk factors with strong dependence effects are: F7, F9, F3, and F11, with centralities of 3.687, 3.188, 3.162, and 3.061 respectively. This shows that these risk factors have a stronger interdependence effect with other risk factors, and are more likely to trigger other risks or be triggered by other risks. Figure 2 It can be seen more intuitively that the further to the right a risk factor is in the graph, the stronger its dependency effect. The risk factors with the weakest dependency effects are F15 and F6, with centralities of 1.98 and 1.984, respectively.

[0191] (2) Causal analysis of risk-dependent effects

[0192] Risk Factor F i The reason for i It's F i The sum of the impacts of all other risk factors minus F i The sum of the influence of all other risk factors represents F i The degree to which F affects other risk factors reflects i Is it a cause risk factor or an effect risk factor, r i If the value is greater than 0, it is a cause risk factor, which is reflected in Figure 2 Above the x-axis, the opposite is the result risk factor.

[0193] All risk factor classifications can be determined by the degree of cause.

[0194] Cause risk factors: From Table 3 and Figure 2 As shown in Figure 2, the cause degree of F2, F4, F5, F8, F13, and F14 is greater than 0, and they can be classified as cause risk factors. Figure 2 They are marked with blue diamonds. Such risks are more likely to trigger other risks, and attention should be paid to the cascade transmission between risks.

[0195] Result risk factors: F1, F3, F6, F7, F9, F10, F11, F12, and F15 have a cause degree less than 0 and can be classified as result risk factors. Figure 2 The risks are marked with grey squares. These risks are easily triggered by other risks. We should pay attention to avoid the risk sources and minimize the occurrence of such risks.

[0196] III. Results and Conclusions:

[0197] (1) Calculation of the objective weights of the five-dimensional indicators

[0198] 1. Comprehensive risk assessment results under five single indicators:

[0199] Taking the centrality value obtained from the risk dependence effect analysis in the previous section as the basis for measuring the "dependence" of risk factors, a 5*15 individual original evaluation matrix as shown in formula (12) is formed. The matrix is comprehensively processed, normalized, defuzzified, etc. according to formulas (13) - (16) to obtain the comprehensive risk assessment table as shown in the figure.

[0200] Table 4 Comprehensive Risk Assessment Table

[0201] Possibility Consequence Controllability Measurability Dependency F1 0.038 0.041 0.048 0.044 0.046 F2 0.062 0.064 0.065 0.065 0.056 F3 0.091 0.085 0.083 0.087 0.090 F4 0.055 0.060 0.056 0.056 0.052 F5 0.038 0.046 0.045 0.044 0.042 F6 0.044 0.044 0.053 0.054 0.043 F7 0.096 0.092 0.086 0.090 0.099 F8 0.085 0.084 0.075 0.077 0.082 F9 0.074 0.070 0.074 0.075 0.078 F10 0.085 0.084 0.082 0.079 0.092 F11 0.079 0.077 0.077 0.077 0.080 F12 0.050 0.049 0.056 0.054 0.057 F13 0.062 0.071 0.060 0.059 0.059 F14 0.068 0.065 0.066 0.068 0.060 F15 0.073 0.067 0.073 0.071 0.063

[0202] 2. Calculate the objective weights of the five-dimensional indicators based on the comprehensive risk assessment results:

[0203] According to formulas (17) - (18) and based on the evaluation matrix, objective weights are assigned to the five indicators. First, calculate the information entropy of each indicator, then calculate its information utility, and finally, the weights of the five indicators are obtained as follows:

[0204] (1) Likelihood of risk occurrence: 0.2697

[0205] (2) Severity of consequences of risk occurrence: 0.1977

[0206] (3) Controllability of risk: 0.1259

[0207] (4) Measurability of risk: 0.1561

[0208] (5) Mutual dependence between risk factors: 0.2505

[0209] From the above calculation results, it can be seen that among the five risk evaluation indicators, the most important evaluation indicator is "likelihood", followed by "dependence", then "consequences", and finally "measurability" and "controllability".

[0210] This result shows that each indicator occupies a certain weight, indicating that the five risk assessment indicators proposed in this paper are meaningful and valuable; secondly, as the second most important evaluation indicator, "dependence" is even more important than "consequences", fully demonstrating that the study of risk dependence effects in the risk assessment of the operation period of cross-border transportation infrastructure cannot be ignored.

[0211] (2) Risk assessment results during the operation period

[0212] After calculating the objective weights of the five-dimensional indicators, the comprehensive performance evaluation of risks under the five-dimensional indicators can be calculated.

[0213] According to the method proposed in Chapter 3 of this paper, the importance degrees of the performances of 15 risk factors during the operation period are ranked, and the compromise solutions are obtained. According to formula (19), the ideal solution and the negative ideal solution under each indicator can be obtained. Then, according to formulas (20)–(22), the S, R, and Q values of each risk factor can be calculated, as shown in Table 5. Generally speaking, the lower the obtained value, the higher the risk degree of the risk factor; the closer the value is to 1, the lower the risk degree.

[0214] Table 5 S, R, and Q values of each risk factor

[0215] F1 F2 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 F13 F14 F15 S 0.707 0.589 0.354 0.591 0.700 0.727 0.282 0.355 0.474 0.339 0.428 0.632 0.504 0.551 0.538 R 0.270 0.188 0.145 0.207 0.270 0.242 0.156 0.110 0.104 0.118 0.112 0.213 0.173 0.168 0.159 Q 0.977 0.598 0.205 0.656 0.970 0.917 0.157 0.098 0.215 0.105 0.189 0.722 0.456 0.497 0.454

[0216] Next, based on Table 5, radar charts of the S, R, and Q values of each risk factor are drawn to more clearly display the risk performances of each risk factor, as Figure 3 shown.

[0217] According to Figure 3 and Table 5, we find that the risk factors with the highest risks are: F8, F10, and F7.

[0218] The Q value of F8 is 0.098; the second highest risk degree is F10, whose Q value is 0.105; the third highest is F7, whose Q value is 0.157. According to the FVIKOR method, these three risk factors are the finally obtained compromise solutions, that is to say, the risk degrees of these three major risk factors are the most serious and should be focused on. It should be noted that F10 and F7 not only have a high comprehensive risk degree, but also have the strongest dependence effects, and certain measures should be taken for them.

[0219] In addition, some of the remaining risk factors are also relatively important and cannot be ignored, such as: F11, F3, and F9. In comparison, risk factors such as F15, F13, F14, F2, F4, and F12 are relatively serious and need to be given certain attention, while F6, F5, and F1 have the highest Q values, and their severity is still within the acceptable range and should be given general attention.

[0220] Due to the characteristics of cross-border transportation infrastructure, it faces multiple non-negligible risks during the operation period, the dependence effect between risks, and a more difficult and complex risk assessment process. Against this background, this paper constructs a five-dimensional model and an evaluation framework for the operation period risks of cross-border transportation infrastructure projects considering the dependence effect, and for the first time attempts to introduce the analysis of the dependence effect into the risk assessment framework, and innovatively proposes five-dimensional indicators for risk assessment. This paper first identifies and establishes a two-layer index system for the operation period risks of cross-border transportation infrastructure, and then independently writes a MATLAB program to realize the analysis of the dependence effect between risk factors, as well as the comprehensive ranking and overall evaluation of all risk factors under the five-dimensional indicators, and obtains the overall risk performance results.

[0221] The proposal of this five-dimensional evaluation framework fills the gap in the systematic research in the field of risk assessment during the operation period of cross-border transportation infrastructure. Specifically, it has the following research significances: (1) Theoretical contribution; (2) Method innovation.

[0222] (1) Theoretical contribution

[0223] First, by proposing an operation period risk assessment framework applicable to the specific context of cross-border transportation infrastructure, it supplements and improves the theoretical research on the risk assessment of infrastructure projects. The existing research objects of risk assessment at home and abroad mainly focus on transportation infrastructure within a country or region, the risks during the construction period, or single risk categories such as technical risks and disaster risks during the operation period. There are few studies on comprehensively evaluating various types of risks faced by cross-border transportation infrastructure during the operation period, and most of them ignore the mutual propagation effect between risk factors (i.e., the risk dependence effect). Therefore, the research of this paper makes up for these deficiencies to a certain extent, provides a risk assessment framework with robustness and superiority for transportation engineering in more complex contexts, promotes the research in the field of transportation infrastructure risks, and also provides more references for the research of subsequent scholars.

[0224] Second, by introducing the dependence effect analysis into the risk assessment during the operation period of cross-border transportation infrastructure, this paper not only proposes a method for realizing the dependence effect analysis in the assessment framework, but also for the first time attempts to substitute the analysis results into the final comprehensive assessment model for integration. This is a new application mode of the dependence effect analysis in the risk assessment framework. Through the verification of actual cases of cross-border transportation, the research on the risk dependence effect in cross-border transportation projects is of significant importance; compared with single risk assessment, the results of the comprehensive risk assessment considering the dependence effect analysis are more in-depth, and the identification of important risk points is also more reliable. This new risk assessment method provides a new direction and model reference for the research of subsequent scholars, and also broadens the research ideas of infrastructure risk assessment.

[0225] Thirdly, for the first time, on the basis of conventional evaluation indicators (likelihood of occurrence, loss), three new evaluation indicators, namely controllability, measurability, and interdependence, are added to form a comprehensive and integrated evaluation of the five dimensions of risk factors, which is an innovation in the research on multi-dimensional indicators of risk assessment. The risk assessment model based on five-dimensional indicators effectively evaluates the overall performance of major risk factors during the operation period of cross-border transportation infrastructure under various types of indicators. The proposal of the three new evaluation indicators makes up for the deficiencies in previous risk assessment studies, such as the incomplete grasp of risk information by the two-dimensional evaluation matrix and the inability to fully analyze the feasibility and expected effects of risk avoidance and prevention measures, improving the rationality and credibility of the overall evaluation and expanding the research on the construction of multi-dimensional indicator models for risk assessment.

[0226] (2) Innovation in methods

[0227] Firstly, based on the proposed brand-new risk assessment framework, this paper adopts a hybrid method formed by two methods, FDEMATEL and FVIKOR, to fit the comprehensive risk assessment model considering the risk dependence effect. This paper first conducts a study on the risk dependence effect through the FDEMATEL method, and on this basis, brings the research results of "risk dependence" into the subsequent FVIKOR method to calculate the ranking of the comprehensive performance of risk factors under five-dimensional indicators, so as to realize the systematic research on the risks during the operation period of cross-border transportation infrastructure.

[0228] Secondly, the calculation of the objective weight based on the entropy weight method. In existing research based on expert experience, the weights of major evaluation indicators are usually directly given by experts or the subjective weights of evaluation indicators are calculated using methods such as the analytic hierarchy process. In order to be closer to the real situation and actual engineering background, this paper uses the entropy weight method to objectively calculate the weights of the five major risk assessment dimensions. "Entropy" was originally a concept in thermodynamics to judge the degree of dispersion of substances, and later was introduced into information theory by C.E. Shannon to calculate the weight of information, and has gradually developed into the entropy weight method. In this application, this method calculates the effectiveness of the information contained in the data based on the scores of experts on all risk factors under the five major evaluation indicators, so as to calculate the weight values between indicators. This method avoids the subjectivity and error of human beings in the weights of indicators and is an improvement on the traditional expert subjective weighting method.

[0229] Therefore, the combination of the three methods, FDEMATEL method, entropy weight method, and FVIKOR method, forms an innovative hybrid method for the brand-new risk assessment framework under five-dimensional indicators in this paper, enabling it to effectively calculate the comprehensive risk assessment during the operation period of cross-border transportation infrastructure and fitting the innovative framework proposed in this paper.

[0230] The above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A five-dimensional model for risk assessment during the operation period of cross-border transportation infrastructure, characterized in that: Design of a five - dimensional model for comprehensive risk assessment. A five - dimensional evaluation model consisting of four stages is proposed for the risks during the operation period of cross - border transportation infrastructure. The four stages are as follows: The first stage: Identification of risk factors, including two parts: (1) Preliminary identification of risk factors. Through literature analysis method, risk factors are initially identified. (2) Final determination of risk factors and construction of a risk factor index system. An expert team needs to be established for this part. Based on the long - term experience and accumulation of experts, the final determination is made. The second stage: Analysis of the dependence effect of risk factors. Based on the scores given by experts in the questionnaire collected in the first stage regarding the inter - relationships between risk factors, calculate the dependence effect of risk factors, including ranking the intensity of the dependence effect of risk factors and classifying the causal relationships of risk factor propagation. First, consider a risk assessment model that contains n risk factors, F = {F1, F2,..., F n}(i ∈ {1, 2,..., n}), and there are m experts who score the risk factors E = {E1, E2,..., E m}(k ∈ {1, 2,..., m}); assume that each expert has the same importance in this risk assessment process, and this paper will use linguistic terms to represent the evaluation of the strength of the dependence effect between various risk factors by experts, and convert the linguistic terms into trapezoidal fuzzy numbers as their mathematical expressions to substitute into the subsequent mathematical operations; represents the evaluation of the strength of the influence of the risk factor Fi on the risk factor Fj given by the m-th expert, where i, j = 1, 2,..., n, k = 1, 2,..., m; in particular, when it means that there is no mutual influence and dependence effect between any risk factor and itself; The third stage: Calculation of the objective weights of the five - dimensional indicators for risk assessment The calculation method of the objective weights of the five - dimensional indicators is as follows: Let $i = 1, 2, \ldots, n$ be the fuzzy personal risk assessment matrix represented by trapezoidal fuzzy numbers, which reflects the evaluation of each expert on each risk factor under each index; Where k represents each expert, and d represents the indicators of each dimension. The fourth stage: Comprehensive assessment of risk factors under the five - dimensional indicators. The comprehensive performance of risk factors during the operation period of cross - border transportation infrastructure under the five indicators will be scored and ranked. These five indicators include: possibility, loss, controllability, measurability, and dependence.

2. The five-dimensional model for risk assessment during the operation period of cross-border transportation infrastructure according to claim 1, wherein: The so - called five - dimensional means that the indicators for evaluating risk factors are divided into five dimensions, namely: the possibility of risk occurrence, the loss caused by risk occurrence, the mutual dependence between risk factors, the controllability of risk, and the measurability of risk, abbreviated as: possibility, loss, dependence, controllability, and measurability.

3. The five-dimensional model for risk assessment during the operation period of cross-border transportation infrastructure according to claim 1, characterized in that: The so - called four stages respectively refer to: The first stage, identification of risk factors; through literature analysis of existing relevant research, a preliminary list of risk factors is established; then the expert team combines the specific engineering situation and their own experience to construct the final list of risk factors; at the same time, by distributing questionnaires to experts, collect the scores given by experts for each risk factor in terms of dependence effect and under the other four evaluation indicators, as the basic data for subsequent risk assessment. The second stage, analysis of the dependence effect of risk factors; The DEMATEL method under a fuzzy environment will be used to calculate the mutual dependence effect between risk factors, which will include two parts of calculation results: (1) Calculate the causal classification of different risk factors. (2) Calculate the strength of dependence of different risk factors and generate a ranking; among them, the result of part (2) will be used as the initial data of "risk dependence" in the "five - dimensional" evaluation indicators and substituted into the subsequent calculation of the comprehensive evaluation of risk factors. The third stage, calculation of the objective weights of the five - dimensional indicators for risk assessment; by using the entropy weight method, calculate the objective weights of the five - dimensional indicators. The fourth stage, comprehensive assessment of risk factors under the five - dimensional indicators; in this stage, the VIKOR method under a fuzzy environment will be used to synthesize the scores of major risk factors under the five - dimensional indicators and obtain the final comprehensive ranking; at the same time, in this stage, management suggestions based on this result will also be given and sensitivity analysis will be carried out.

4. The five-dimensional model for risk assessment during the operation period of cross-border transportation infrastructure according to claim 1, characterized in that: The specific steps of the second stage are: Step 1. Construct the individual initial fuzzy direct influence matrix According to the scores given by experts on the direct impacts of various risk factors, the individual initial fuzzy direct impact matrix is obtained as follows: Convert to where the initial fuzzy direct influence matrix is converted to where \(k = 1, 2, \ldots, m\), \(i, j = 1, 2, \ldots, n\); in particular, convert to Step 2. Construct the group fuzzy direct influence matrix To obtain the comprehensive evaluation of each expert, the arithmetic mean of the individual initial fuzzy direct influence matrix is calculated to obtain the group fuzzy direct influence matrix As follows: Step 3. Obtain the standard group fuzzy direct influence matrix Next, perform normalization calculation on the group fuzzy direct influence matrix to obtain the standard matrix The normalization calculation process is as follows: Among them, and i, j = 1, 2, …, n; Step 4. Obtain the clarity value matrix X 1 , X 2 , X 3 , X 4 ; Decompose the standard population fuzzy direct influence matrix to obtain four clear value matrices X 1 , X 2 , X 3 and X 4 , namely Step 5. Calculate the fuzzy comprehensive dependence effect matrix The risk dependence effect includes the direct and indirect effects among risk factors, where the indirect effect is caused by the cascade propagation among risk factors; the direct effect is obtained by direct scoring by experts, and the indirect effect is calculated by the fuzzy DEMATEL method; according to the FDEMATEL method, the fuzzy comprehensive dependence effect matrix is calculated by the following formula: And is represented as Among them Step 6. Calculate the impact coefficient, centrality, and reasonability of risk factors Let represent the sum of the degrees of influence of the risk factor Fi on other risk factors, and it is calculated according to the following formula: Let represent the sum of the strengths by which the risk factor Fi is affected by other risk factors, and is calculated according to the following formula: Let represent the fuzzy centrality of the risk factor Fi, which is calculated according to the following formula: Let represent the fuzzy causal degree of the risk factor Fi, which is calculated by the following formula: In order to obtain the ranking of the strength of each risk factor in the dependence effect and their causal classification, the fuzzy centrality and the fuzzy cause degree are converted into clear values and are respectively denoted as p i and r i , and their calculation formulas are as follows: Risk factor F i The ranking of the strength of dependence and causal classification of i are obtained through the clarity values of the centrality p i and the causality degree r i ; The value of p i represents the quantitative value of the role of risk factor F i in the propagation of all risk factors. The higher the centrality p i of risk factor F i , the stronger the dependence effect between it and other risk factors; The value of r i represents the classification of risk factor F i ; If r >0, then risk factor F i is a cause risk factor; If r i <0, then the risk factor is an outcome risk factor.

5. The five-dimensional model for risk assessment during the operation period of cross-border transportation infrastructure according to claim 4, characterized in that: The weight calculation steps for the risk assessment indicators during the operation period of cross-border transportation infrastructure in the third stage are as follows, with the step numbers following Step 6: Step 7. Calculate the fuzzy group risk assessment matrix Aggregate the fuzzy individual risk assessment matrix to obtain the fuzzy group risk evaluation matrix For trapezoidal fuzzy numbers, use the weighted average method, and its calculation method is as follows: Step 8. Defuzzification and normalization Next, defuzzify the fuzzy group risk evaluation matrix to obtain the group risk evaluation matrix S = [s id n×5 ;​ Further normalize it to obtain a standard population risk assessment matrix; Y = [y id n×5 ; The normalization method here is to divide each element in the matrix by the sum of the elements in its corresponding column; the specific calculation formula is as follows:​ Step 9. Calculate the objective weights of the five-dimensional indicators The objective weights of the five-dimensional indicators are calculated by the entropy weight method; "entropy" is used to measure the utility of data information under a certain indicator. The larger the "entropy" value \(e_d\), the more chaotic the data; then the smaller the utility value \(h_d\), so the weight value \(w_d\) of this indicator is smaller. Particularly, when the "entropy" value \(e = 1\), the utility is 0. The specific calculation formula is as follows: h d = 1 - e d , d = 1, 2, 3, 4, 5 (16) 6. The five-dimensional model for risk assessment during the operation period of cross-border transportation infrastructure according to claim 5, wherein: The specific steps of the fourth stage are as follows, with the step numbers following Step 9: Step 10. Calculate the maximum and minimum values of risk factors in a single dimension The calculation methods for the optimal and worst values of risk factors in the five single dimensions are as follows: where \(i = 1, 2, \ldots, n\), \(d = 1, 2, 3, 4, 5\) Step 11. Calculate the values of \(S\), \(Q\), and \(R\) where \(i = 1, 2, \ldots, n\), \(d = 1, 2, 3, 4, 5\), \(S\) + = min i \(S\) i ; \(S\) - = max i \(S\) i ; \(R\) + = min i \(R\) i ; \(R\) - = max i \(R\) i ; Additionally, \(v\) represents the weight value of the group utility, and \(1 - v\) represents the individual regret value; Step 12. Calculate the ranking of risk factors The comprehensive ranking of risk factors under the five-dimensional indicators is calculated through the \(Q\), \(S\), and \(R\) values obtained from the above formula. Since there are conflicts among the five-dimensional indicators, the probability that a certain risk factor satisfies the optimal solution under all indicators is relatively low. Therefore, to obtain a unique compromise solution, the following two conditions need to be met: Condition 1: Acceptable advantage where \(F'\) is the first risk factor in the ranking of risk factors based on the \(Q\) value, and \(F''\) is the second one; Condition 2: Acceptable decision-making stability The risk factor \(F'\) must also be in the first place when ranked based on \(S\) or \(R\); Only when both of the above two conditions are met can a unique compromise solution be obtained. However, in many cases, due to the insufficient difference between risk factors, the above two conditions cannot be met simultaneously. In this case, a set of compromise solutions will be generated and output as the result. The calculation method is as follows: If only Condition 2 cannot be met, the set of compromise solutions is \(\{F', F''\}\); If condition 1 cannot be satisfied either, then the set is {F′, F″,... F (M)}, where M is the maximum value for which can hold.

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