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The application of the traditional failure mode and effects analysis (FMEA) technique has been widely questioned in evaluation information, risk factor weights and robustness of results. This paper develops a novel FMEA framework with extended MULTIMOORA method under interval-valued Pythagorean fuzzy environment to solve these problems.

This paper introduces innovatively interval-value Pythagorean fuzzy weighted averaging (IVPFWA) operator, Tchebycheff metric distance and interval-value Pythagorean fuzzy weighted geometric (IVPFWG) operator into the MULTIMOORA submethods to obtain the risk ranking order for emergencies. Finally, an illustrative case is provided to demonstrate the practicality and feasibility of the novel fuzzy FMEA framework.

The feasibility and validity of the proposed method are verified by comparing with the existing methods. The calculation results indicate that the proposed method is more consistent with the actual situation of project and has more reference value.

The research results can provide supporting information for risk management decisions and offer decision-making basis for formulation of the follow-up emergency control and disposal scheme, which has certain guiding significance for the practical popularization and application of risk management strategies in the infrastructure projects.

A novel approach using FMEA with extended MULTIMOORA method is developed under IVPF environment, which considers weights of risk factors and experts. The method proposed has significantly improved the integrity of information in expert evaluation and the robustness of results.

Reasonable risk sharing is the key to the smooth implementation of infrastructure public-private partnership (PPP) projects and the optimization of benefit distribution among the participants. This study aims to explore the risk redistribution ratio between the government and the private sector under different degree of fairness concern.

Renegotiation is a mechanism to provide flexibility and make up for incompleteness of PPP contracts. However, the threshold value of risk redistribution ratio and negotiation cost are not explicitly considered in previous studies. In addition, these studies do not consider the influence of the fairness concern psychology on the negotiation process. To address these gaps, based on risk-income equilibrium analysis, this paper established the bargaining optimization model of PPP projects renegotiation considering the fairness concerns of the negotiating parties. Furthermore, this study analyzed the influence of fairness concern degree on negotiation thresholds, negotiation results, and negotiation incomes under three scenarios.

The results showed that excessive focus on the fairness of incomes may exclude the risk redistribution ratio that is most beneficial to project incomes from the negotiation threshold. Moreover, the increase in the fairness concerns of negotiating parties can reduce the negotiation success period, but the net income may not necessarily be improved.

The main contribution of this paper is to propose a new risk renegotiation methodology based on the risk-income equilibrium analysis, which is helpful to develop risk management strategies in the construction field. The research results can provide government with reference about renegotiation in decision making and provide theoretical support for the practice of PPP renegotiation.

The Public–Private Partnership (PPP) mode has been widely used in the urban water environment treatment project (UWETP). The public is the direct perceiver of urban water environment treatment PPP project (UWETP-PPP), and their satisfaction with it can reflect the project's success to some extent. The purpose of this paper is to provide operational management strategies for special-purpose vehicle (SPV) company through public satisfaction evaluation of UWETP-PPP.

A questionnaire was designed through the literature review and experts' opinions that consisted of 33 indexes to investigate public satisfaction with UWETP-PPP. Then, the exploratory factor analysis (EFA) was used to confirm the evaluation index system of public satisfaction. Next, the weights of the indexes were calculated by the normalized mean method and fuzzy synthetic evaluation (FSE) was applied to evaluate public satisfaction with UWETP-PPP. Finally, the importance-performance analysis (IPA) was used to suggest improvement strategies of public satisfaction with UWETP-PPP.

The factors affecting public satisfaction with UWETP-PPP are preliminarily determined, and an evaluation model that provides a specific basis for evaluating public satisfaction with UWETP-PPP in the future is constructed. Furthermore, some strategies and suggestions to improve the performance level of UWETP-PPP are put forward.

First, the factors influencing public satisfaction with UWETP-PPP are numerous and complex. The factors discussed in this study may be further refined to make the research more reliable and effective. Second, the sample from this study can be expanded to multiple projects, so as to make the study more general. Finally, given that the influencing factors in the paper were elicited by using scores obtained through a questionnaire survey, it would bring bias to the result to some extent. The evaluation method can be further improved, such as combining with interval intuitionistic fuzzy evaluation.

In the context of the characteristics of PPP projects in water environment treatment and the huge demand of the country to apply PPP model in the territory of water environment treatment, this study evaluated the public satisfaction with UWETP-PPP in Xuchang City, China. The result provided a beneficial reference for the private organizations to take appropriate actions to improve the public satisfaction level of UWETP-PPP, so as to improve the performance level of SPV. It also provided a system of public satisfaction evaluation with UWETP-PPP, which can be considered as the standard of public satisfaction survey, thus improving the comprehensiveness of the UWETP-PPP performance evaluation system and the government regulatory capacity, thus affecting the sustainable development of UWETP-PPP.

In addition, the research results provide a useful reference for the public organizations to issue a UWETP-PPP regulation rule, review a UWETP-PPP design plan, and conduct new similar project decision-making. In summary, the study results not only serve as a good reference for the evaluation of public satisfaction of eco-environmental PPP projects, but also have essential application value for improving the service level, performance improvement and operational management of the SPV.

The research results of this paper have certain wide-spread value, and the research framework and research method can be applied to other infrastructure section, such as transportation, stadium et al.