Traditional project evaluation methods mainly include: net present value, internal rate of return, investment payback period, equal annual value, etc. However, because the project has attributes such as one-off, the risk of the project is based on itself, and the risk cannot be excluded from the project. In order to consider the impact of project risk on project evaluation, sensitivity analysis and probability analysis are introduced. Due to the difficulty of data collection, the ignorance of the relevance of risk factors, the inability to deal with qualitative issues, and the neglect of risk connotations, both have shortcomings.

Yang, Q [20] In the process of risk analysis of highway projects, in order to avoid the subjective one-sided identification weight and the measurement of fuzzy factors, the fuzzy comprehensive evaluation method and the analytic hierarchy process are combined to construct the fuzzy analytic hierarchy process model. Through the establishment of a highway engineering risk factor analysis index set, qualitative analysis and quantitative analysis are combined to make subjective evaluation objective and solve the problem of measuring fuzzy factors.

Post-project evaluation generally uses methods such as statistical prediction and comparison, but it can only be used as a qualitative evaluation, not a quantitative evaluation. Zhu, H. [21] In order to achieve quantitative evaluation in the post-project evaluation, fuzzy mathematics was introduced into the post-project evaluation, and the difficulty of quantitative evaluation was solved by establishing a fuzzy comprehensive evaluation model and using the fuzzy mathematics evaluation model.

Xie Xiaohong [22] established an evaluation model by introducing fuzzy mathematics membership function: decomposing the project, identifying risk factors, determining the probability distribution or membership function of each factor and standardizing it, and synthesizing monetary factors or non-monetary factors according to their weights. Synthesize the total joint distribution of each evaluation plan. Taking fuzzy mathematics evaluation method as the core, by simplifying the evaluation process, using expert method to evaluate unquantified factors, it provides a multi-objective evaluation method for project evaluation. It solves the problems of risk factors that are difficult to accurately describe and quantify in the risk evaluation of the traditional probabilistic consequence model.

Project risk management can be divided into four steps: identification, estimation, evaluation, control and management. As the first step of risk management, risk identification is that the basis of risk management is the premise of risk estimation. Commonly used risk identification methods include: brainstorming method, Delphi method, etc., which mainly rely on human subjective judgment in qualitative analysis, and lack objectivity. However, quantitative analysis is lacking in traditional methods.

Zhong, Y. [23] combines fuzzy mathematics with system dynamics, and proposes a fuzzy system dynamics method with theoretical innovation and practicality, which quantitatively analyzes the uncertainty of the project. Analyze the uncertainty in the construction project from an overall perspective, so as to provide a more systematic management strategy. Wang, X. [24] established a calculation model based on interval numbers by using analytic hierarchy process and fuzzy mathematics theory. The interval membership function and the weight of each factor are quantified, and the relative advantage of the interval matrix is analyzed. A risk assessment method for water gushing and water gushing intervals in karst tunnels is proposed. On this basis, the concept and calculation form of the risk assessment model are introduced, and the risk environment, construction factors and feedback information are analyzed. Meng, G. [25] Based on the evaluation method of analytic hierarchy process and fuzzy mathematics, the risk assessment of deep foundation pit construction was studied. The results show that it is a very good risk level assessment method. Xu, S. [26] used Monte Carlo method and fuzzy mathematics to study the risk management of construction projects, combined qualitative analysis and quantitative research, and proposed a new solution.

Geng, D. [27] combines fuzzy mathematics with analytic hierarchy process, uses fuzzy risk judgment matrix to realize the risk occurrence probability and risk loss of risk factors, and comprehensively considers the risk occurrence probability and the importance of risk loss. It avoids the disadvantages of too many factors and the difficulty in assigning weights, and avoids the one-sidedness of single-factor decision-making and decision-making errors caused by human subjective consciousness. It can make scientific and accurate judgments for the selection of the construction plan. Chang Fei [28] uses fuzzy mathematics and analytic hierarchy process to establish a model that can more accurately determine the risk weights, and rank all risks as a whole, and can make a more reasonable and accurate evaluation of the risks of international projects. It solves the problem that the analytic hierarchy process is too general and the monte Carlo conditions are too strict, and the risks of international projects cannot be comprehensively analyzed.

Zheng Zhanfei [29] used fuzzy mathematics to construct a fuzzy comprehensive evaluation model of risk influencing factors: setting the domain of theory, determining the fuzzy matrix, and determining the weight vector. Through the iterative algorithm of the analytic hierarchy process, the importance of each factor is determined, and the subjective judgment of experts is used to determine. Using fuzzy comprehensive evaluation, combining subjective judgment with objective quantitative analysis, improves the problem of single and transitional dependence on expert judgment in risk identification.

Wang Yuan et al. [30] - [36] used fuzzy comprehensive evaluation method, fuzzy gray theory comprehensive evaluation method, fuzzy analytic hierarchy process and other methods to analyze and evaluate each risk factor of the project, and better considered the uncertainty in risk evaluation. And ambiguity, realizing quantitative analysis and determining the degree of risk impact, providing effective measures for project risk management. At the same time, Xie Meng [37] and Feng Guangyi [38] also conducted risk analysis in construction project management for agent construction units and auditing units, and provided references for different entities to reduce the losses caused by risks in the process of construction project management.

In the bidding process, there are many factors that affect bidding. Only by mastering the correctness and predictability of the bidding quotation strategy and method can it be possible to win the bid. Fuzzy mathematics provides mathematical language and quantitative methods for fuzzy quantity problems, and provides a powerful tool for bidding decision-making.

Wang, W. [47] uses the fuzzy evaluation method of fuzzy theory set to comprehensively evaluate the engineering bidding system, selects the best plan from multiple alternatives, and provides decision support for the company’s bidding. Li, D. [48] through the analysis of representative factors in the decision-making of bidding opportunities, proposed a quantitative method between the objects and factors in the bidding of engineering projects. Applying fuzzy mathematics to bid evaluation provides a basis for contractors to make reasonable decisions.

Li Dan [49] used fuzzy mathematics to construct a fuzzy evaluation model with a comprehensive evaluation method: the determination of the bid price factor set, the determination of the weight of each factor, the establishment of the comment set, the establishment of the membership relationship, the establishment of the fuzzy evaluation matrix, the fuzzy comprehensive evaluation, the determination of the evaluation level and Bidding quotation decision, quantitative analysis of the target and multiple influencing factors through the model. Under the premise of analyzing the cost, profit and other factors of the agent construction unit, conduct induction, deduction and reasoning to obtain the pros and cons of the agent construction unit’s bidding, so as to obtain reasonable profits and provide decision-making for the bidding unit’s bidding.

Liu Erlie, Wang Zhenxian and others [50] [51] [52] [53] used fuzzy mathematics, fuzzy logic, fuzzy comprehensive evaluation and other methods to comprehensively and scientifically evaluate bidding conditions, and use all influencing factors as a system to study and make qualitative indicators more objective and reasonable. Make the bid quotation more reasonable and more efficient and increase the bid winning rate.

The bidding not only regulates the construction market and promotes market competition, but also improves investment efficiency and saves investment for owners. The reasonable low price evaluation method, the lowest price evaluation method, and the comprehensive evaluation method used in traditional bid evaluation are expert scoring methods, and the highest score is the first winning bidder. The above methods have their own advantages and disadvantages, because scoring is artificially highly subjective.

Peng Hong [54] and others adopted fuzzy analytic hierarchy process by introducing fuzzy mathematics, and clearly reflected the relationship between various related factors through the hierarchical structure, so that decision makers could logicalize complex issues. Through the improvement of the comprehensive bid evaluation method, reasonable index weights are determined, and the scores of the candidate units are ranked by establishing the mathematical model of AHP and fuzzy mathematics, and the winning unit is finally determined.

Li Xuwei [66] put forward the theory of applying fuzzy mathematics to the rapid prediction of engineering claims by systematically analyzing the process of engineering claims and the relationship between the related parties of the claims, and constructed the corresponding prediction models. This model mainly applies the basic principles of fuzzy mathematics to the prediction of engineering claims, makes full use of the evaluation information of characteristic factors of typical engineering events, establishes an engineering claim prediction model, and proposes a calculation method of closeness to better reflect the number of engineering events. The similarity between the project to be constructed and the project to be constructed are quantitatively studied and compared, so as to quickly predict the project claim and the value of the claim value that the project to be constructed may encounter. This model can quickly analyze and identify the claim risk before the implementation of the project, and can improve the claim risk identification ability and prevention awareness of the construction parties during the project implementation process, and reduce the occurrence of claim incidents.

Bian Yanbin [67] used the risk breakdown structure method to identify the risk of project settlement disputes, and proposed a risk evaluation method based on the combination of analytic hierarchy process and fuzzy mathematics theory, established a set of risk factors and comment sets for project settlement disputes, and determined The weight of each factor and the evaluation matrix construct a fuzzy evaluation model. Realize the combination of sexual analysis and quantitative analysis, make subjective estimation objective, and provide reference for actual project settlement dispute risk evaluation decision.

Xu Fangzhou [68] uses the multi-attribute utility function decision theory to obtain the maximum utility of the three goals at a certain risk level, and introduces the principle of fuzzy mathematics to give a fuzzy representation of the duration and direct cost of each process to establish an optimization Model, and use genetic algorithm to simulate and analyze the two stages to provide decision makers with ideal planning arrangements.

Wu Peng [69] introduced the theory of multi-attribute utility function into engineering quality control and established a quality control model that considers the cost of construction period. On the basis of network planning technology, using genetic algorithm to solve the model can get the most satisfactory decision plan and multiple approximately satisfactory alternatives have practical value to solve the contradiction between construction period cost and quality control. At the same time, a fuzzy comprehensive evaluation method of engineering quality is established on the basis of fuzzy set theory. This method can meet the requirements of multi-factor and multi-level evaluation. It not only considers all influencing factors, but also uses different weight coefficients for each factor in the calculation to highlight the important ones. The evaluation project retains all the evaluation information at all levels, and the quantitative results can well reflect the actual situation.

Deng Dexue [70] used fuzzy causality analysis to establish an optimization model for engineering quality improvement to improve the quality of construction projects. The fuzzy causality analysis model can objectively and quantitatively improve the quality of the project, find out the content to be improved comprehensively, and scientifically improve the quality of the project. Through the use of quantitative analysis of causality analysis to ensure the scientific nature of quality improvement, the method of quality improvement is more scientific and objective. Reduce non-specific and non-objective problems arising from qualitative improvement of quality. It solves the problems of qualitative analysis and quantitative analysis in my country’s current construction engineering quality improvement.

Song Yang [71] systematically conducted theoretical research on residential project construction quality management, quality control, and quality management assurance system by comparing the status quo of residential project quality management at home and abroad. The basic knowledge of fuzzy mathematics is applied to the quality management of residential projects, and a mathematical model of fuzzy evaluation of residential project quality is established to comprehensively evaluate the quality of the project. The results show that it can objectively and quantitatively reflect the quality of the project to provide a more scientific and objective basis for the completion and acceptance of residential projects.

Liu Ze [72] used fuzzy mathematics to study the uncertainty of construction period of construction projects. Taking the satisfaction and reliability of the construction unit for the optimized construction period as the optimization goal, a mathematical optimization model of the construction schedule under resource-constrained conditions is established, and the construction schedule is optimized using evolutionary algorithms. Results TableThis method has high effectiveness and feasibility when dealing with fuzzy resource-constrained construction projects. It can not only meet the construction unit’s requirements for the project duration, but also provide greater flexibility for the arrangement of various procedures. It can effectively deal with the impact of weather, resources and other factors on the construction plan.

Wang Lina [73] used fuzzy recognition and fuzzy comprehensive evaluation methods to calculate the target cost and function coefficients by establishing a green building investment decision-making model based on value engineering, and then obtained the value coefficients of each plan. Compared with the traditional decision-making method that simply evaluates economic effects, the decision-making method based on value engineering can evaluate the design and implementation of green buildings more comprehensively and objectively. The results show that the combination of value engineering principles and fuzzy mathematics tools can better reflect the objective facts of things and make simple and feasible quantitative decisions. It solves the problem of considering only direct economic benefits but insufficient consideration of improving building functions and life-span economic benefits.

An Yuhua [74] uses value engineering and fuzzy comprehensive evaluation model to quantitatively evaluate the functions of each primary selection scheme of green buildings and estimate the additional cost, and finally determine the value function coefficient of each scheme to select the optimal scheme. The results show that this method can make green buildings have optimal choices at the beginning of the whole life cycle, analyze the value of green buildings from a macro perspective, and play a good role in paving the way for later construction and operation.