In multidimensional uncertainty environments, group decision-making faces challenges such as the complex expression of individual preferences and significant behavioral differences. This paper proposes a multidimensional preference modeling method based on complex variables, utilizing the modulus of complex numbers to represent preference intensity and the phase angle to reflect emotional tendencies in preference judgments, thereby achieving a unified expression of preference information in the rational-emotional dual dimension. Furthermore, the multiplicative and additive consistency of complex fuzzy preference relations is defined, and a two-stage group consensus decision-making method that considers risk perception is constructed. In the first stage, a complex fuzzy preference completion model based on multiplicative consistency is proposed for incomplete information, and a particle swarm optimization algorithm based on the complex domain is designed to solve the model, enhancing information completeness and consistency analysis capabilities. In the second stage, prospect theory is introduced to model individual risk perception behavior, and a criterion weight group decision model capable of characterizing behavioral features such as risk-seeking, risk-averse, and risk-neutral is developed. Numerical experiments and sensitivity analysis validate the effectiveness and adaptability of the proposed method in multidimensional fuzzy information processing, consistency optimization, and behavioral modeling.

As a dominant mode of maritime transportation with unique risk characteristics, container shipping requires accurate and applicable risk assessment. However, conventional risk matrices oversimplify complex interactions, while pure data-driven models lack operational utility. To address this, a hybrid method for container ship risk assessment is proposed. This method integrates CatBoost-based predictive method, FAHP-grid search optimized risk matrix, and GIS-supported risk mapping. A comprehensive study of maritime casualties and piracy accidents is conducted, utilizing historical incident data sets collected from the Global Integrated Shipping Information System (GISIS). The global maritime accident risk of container ships is then evaluated and mapped. The sensitivity analysis confirms the robustness of the method under varying linguistic distance parameters, while expert weights have a moderate impact on the assessment results. Finally, the effectiveness of the proposed method is validated through comparative analyses on predictive performance, risk discrimination capability, and risk assessment accuracy. CatBoost algorithm outperforms XGBoost, LightGBM, and Random Forest algorithms in predictive metrics. The designed risk matrix shows strong discriminatory ability for container ship risk levels. In historical accident data validation, the proposed method also achieves higher accuracy than combinations involving XGBoost, LightGBM, or Random Forest with the designed risk matrix.

Consensus-reaching processes (CRPs) inherently demand compromise, requiring each decision maker (DM) to adjust their initial opinions-a process that often entails both tangible cost and disutility. Traditional optimisation-based mechanisms in CRPs focus primarily on minimising adjustment cost while overlooking DMs' discontent. However, repeated and excessive discontent can threaten the sustainability of CRPs, especially when certain DMs are consistently disadvantaged (i.e., required to make significant adjustments) compared to others, leading to envy and disengagement. To address this, we develop a new optimisation-based mechanism in CRPs that balances minimising both cost and envy. Incorporating an envy objective introduces significant computational challenges, as envy is captured by a non-convex function, even when the disutility is convex. Fortunately, many non-convex optimisation problems, such as bilinear and mixed-integer linear programs, can now be solved efficiently using off-the-shelf solvers. Leveraging this capability, we enhance the generalisability of our cost-sensitive, envy-resistant mechanism for consensus by assuming that cost and disutility are representable as polyhedral loss functions, allowing us to reformulate the proposed model as a bilinear program or approximate it with a priori error bound. We demonstrate our model using real data from RateMyProfessors.com, which includes student ratings on the quality and difficulty of courses taught by professors.

The integration of artificial intelligence (AI) into healthcare systems offers substantial clinical and operational benefits, yet it also introduces critical social risks-including algorithmic bias, data privacy violations, and accountability gaps-that may undermine institutional trust and ethical governance. Addressing these challenges requires structured decision-support mechanisms capable of reconciling divergent expert judgments under uncertainty. This study proposes an optimization-oriented group decision-making (GDM) framework that explicitly integrates consistency preservation and consensus enhancement for medical AI social risk management. The framework comprises four sequential stages. First, structural disagreement among experts is quantified using evidence correlation coefficients derived from belief function theory. Second, risk mitigation strategies are classified via an enhanced K-means++ clustering approach to accommodate practical resource constraints. Third, expert preference structures are optimized through a modified genetic algorithm that jointly balances individual consistency and collective consensus with minimal opinion adjustment. Finally, potential consensus bottlenecks are identified using a two-dimensional consistency-consensus clustering mapping method. A case study focusing on the prioritization of social risk mitigation strategies for an AI-assisted breast cancer diagnostic system demonstrates the feasibility, robustness, and interpretability of the proposed framework. The results indicate that the approach effectively harmonizes interdisciplinary expert perspectives while maintaining decision rationality. Overall, the framework provides a systematic decision-support tool for hospital ethics committees and AI regulatory bodies, facilitating the translation of ethical principles into operational risk governance strategies and supporting the trustworthy deployment of medical AI systems.

Analyzing human errors' interrelationships is one of the most important assignments for human reliability improvement in sociotechnical systems. Human factor analysis and classification system (HFACS) is effective in human error analysis due to its taxonomy and systematical perspective. It reveals interrelationships among human errors emerging in a multi-hierarchy of systems. However, the conventional HFACS method is incapable of quantifying their interrelationship. Especially, due to the nature of human errors, their objective data is limited. Experts' opinions are important resources to facilitate human error analysis. However, limited improved HFACS considers experts' consensus on interrelationships analysis results, especially in linguistic environments. Accordingly, this paper aims to address HFACS-based interrelationships analysis problems utilizing linguistic decision-making trial and evaluation laboratory (DEMATEL) with consensus reaching process (CRP). First, probabilistic linguistic terms are utilized to represent experts' opinions on human errors' interrelationships. Second, CRP is introduced to derive consensual opinions on human errors' interrelationships, shifting the focus to identifying human errors with low consensus levels rather than experts. Then, a hybrid weighting method is introduced to determine the weight of experts' opinions in the information fusion phase, which reflects inherent uncertainty and inter-recognition of experts’ opinions. Furthermore, DEMATEL is introduced to model direct and indirect interrelationships among human errors. Finally, a case study of a drug administration process is conducted to validate the efficiency of the proposed method. The case study indicates that neglect of safety culture development and limited financial and human resources are the top two human errors, with importance degree 0.148 and 0.107.

Individual interactions and conformity play a crucial role in shaping group opinions and influencing the decision-making process. This article introduces a novel opinion evolution model to simulate the impact of conformity on group opinion formation, focusing on weight allocation, relationship propagation, and evolution analysis. In the weight allocation phase, individual weights are evaluated using network structure and the PageRank algorithm. For relationship propagation, indirect trust relationships are computed via a weighted average method, leading to a more precise social network model. In the evolution analysis, an improved Hegselmann-Krause (HK) model demonstrates evolutionary stability. Two types of conformity behavior are simulated: active conformity behavior within clusters and passive conformity behavior via opinion leaders across clusters. Experimental studies on public health policy validate the effectiveness of the proposed model. The results show that this model more accurately captures the complex behavioral patterns of individuals in large-scale social networks and exhibits strong evolutionary stability.

Partner selection is one of the important problems in international engineering project implementation process. And the financial risk situation of cooperative companies is particularly important for partner selection. In this paper, we propose a dynamic financial risk assessment method considering the expert psychological state based on the technique for order preference by similarity to ideal solution (TOPSIS) and drift diffusion model, and determine the best and worst partner with the dynamic financial risk assessment result. First, consider that the financial risk assessment indexes include the benefit and cost type, which is a remarkable feature of TOPSIS method, and further use TOPSIS method to get the company’s financial risk assessment results of single psychological states. Second, consider that the interaction between the expert psychological states in company’s dynamic financial risk assessment process, and the drift diffusion model can better describe this feature, we apply the drift diffusion model and introduce its relative properties to aggregate the company’s financial risk assessment result at different psychological states. Then, we propose a dynamic financial risk assessment with TOPSIS and drift diffusion model considering the expert psychology based on the above mentioned steps. Finally, we apply our proposed dynamic method in the partner selection of the Chinese French Saint Louis new terminal development project. The results show that the best and worst partners change with the partner’s dynamic financial risk evaluation result accordingly.

In the credit risk evaluation process, considering that the decision maker's irrational behavior may cause the interference effect between evaluation information, and further decrease the reliability of evaluation results. To solve this problem, the best evaluation sequence method and its application in credit risk evaluation based on quantum cognitive theory is proposed in this paper. First, the quantum cognition theory and the evaluation information given by the decision maker are used to get the interference degree between evaluation information. Second, the interference degree between evaluation information is aggregated to obtain the comprehensive interference degree of each alternative. Third, according to the idea that the greater the comprehensive interference degree of the alternative, the more backward the evaluation sequence of the alternative is, we determine the best evaluation sequence of alternatives. Finally, our proposed method is applied to obtain the best evaluation sequence of commercial bank credit risk.

Human error is one of the major contributors to adverse events in a socio-technical system. Human factor analysis and classification system (HFACS), a qualitative method, is widely recognized for analyzing human errors from a systematic perspective. To overcome its limitation in quantitative analysis of the risk of human error, many multi-criteria decision making (MCDM) techniques are combined with HFACS. However, most existing MCDM technique-based HFACS methods ignore the uncertainty of experts’ opinions, the consensus among experts, and the interference effect between experts. To this end, a consensus reaching process (CRP)-based linguistic MCDM integrating the gained and lost dominance score (GLDS) method and quantum probability theory (QPT) is proposed to rank human errors’ risk under the HFACS framework. First 2-tuple linguistic variables are utilized to represent experts’ opinions on human errors’ risk which can handle experts’ linguistic opinions in an interpretable, accurate, and simple way. Second, a two-stage feedback mechanism-based CRP shifts to identify the human errors whose risk evaluation information is with low consensus degree and improve their consensus, which contributes to high consensus on human errors’ risk prioritization results. Then, GLDS and QPT are combined to derive human errors’ collective risk value, where GLDS considers both the comprehensive and worst performances of human errors and QPT considers the interference effect among experts. Finally, a case study of risk analysis for human errors involved in hospital care is conducted to show the efficiency of the proposed method.

Since the development of the best–worst method (BWM) in 2015, it has become a popular research focus in multi-criteria decision-making. The original optimization problem of the BWM is a nonlinear min–max model that can lead to multiple optimal solutions, while the linear model of the BWM produces a unique solution. The two models need to be solved by optimization software packages. In addition, although the linear model of the BWM can obtain a unique solution, it produces different feasible regions than the nonlinear model of the BWM, and it changes the objective function. This study aims to solve the nonlinear model of the BWM mathematically to obtain the analytical forms of the optimal solutions. First, we transform the original nonlinear model of BWM into an equivalent optimization model driven by the optimally modified comparison vectors. The equivalent BWM provides a solid basis for computing the analytical solutions. Second, for not-fully consistent pairwise comparison systems, we strictly prove that there is only one unique optimal solution with three criteria, and there might be multiple optimal solutions with more than three criteria. We further develop the analytical forms of these unique and multiple optimal solutions and the optimal interval weights. Third, we develop a secondary objective function to select a unique solution for the BWM. The secondary objective function retains all the characteristics of the original nonlinear model of the BWM, and we find the unique solution analytically. Finally, some numerical examples are examined, and a comparative analysis is performed to demonstrate the effectiveness of our analytical solution approach.

Occupational health and safety (OHS) risk analysis serves as a foundation for identifying, preventing, and controlling OHS hazards to reduce occupational accidents. As a representative risk analysis approach, Fine-Kinney has been commonly applied to control hazards. However, current Fine-Kinney studies ranked hazards without considering the consensus reaching process (CRP) with incomplete information, insufficient to tackle decision makers’ (DMs’) dissatisfaction. Besides, risk analysis mainly relies on DMs’ subjective assessments, where opinion interactions inevitably exist because of DMs’ communication during the assessment process. This paper aims to develop a hybrid generalized TODIM (an acronym in Portuguese for Interactive Multi-criteria Decision Making) approach in the Fine-Kinney framework, integrating CRP with dynamic social influence network (SIN), and probabilistic linguistic terms (PLTSs). The PLTSs are used to cope with the complex and incomplete DMs’ opinions. The dynamic SIN is proposed to calculate the weights of DMs and describe the opinion interactions considering the psychological behaviors of DMs. Then, a new CRP is developed including a two-fold personalized feedback mechanism based on the dynamic SIN. The generalized TODIM method is introduced to rank all identified potential occupational hazards based on the collective opinions after CRP. Finally, a numerical example is conducted to verify the efficiency of the proposed approach. Comparison and sensitivity studies are also carried out to test the rationality and efficiency of the proposed approach.

Social network group decision making generally involves experts who have complex social relationships to influence each other. Order effect arises from the order of opinion representation among decision makers. Nowadays, quantum theory has become an efficient instrument for simulating and quantifying the complex behavior among the decision makers. This paper proposes a quantum framework for modelling order effect in social network group decision making process. Firstly, we integrate the opinion similarity into social connections. Then, the Louvain Algorithm is used to cluster experts into different subsets. The weights of individuals and clusters are obtained by using a constructed sociability-similarity centrality index. And we fuse individual opinions into a collective one within each cluster. Next, the path probability method in quantum framework is used to aggregate opinions of all clusters, which interprets order effect by converting a state vector with different sequences of operators to represent different orders of opinion representation. Then, we introduce an algorithm to determine a local optimal order of opinion representation to minimize order effect among clusters. In the end, we apply the proposed model to a numerical example and demonstrate its effectiveness and stability through detailed sensitivity analysis and comparative analysis.

One of the most significant goals that must be guaranteed for high-speed railway systems is safety. A new model is constructed for high-speed railway accident analysis with interval type-2 fuzzy DEMATEL method based on the 24Model. Specifically, the 24Model is introduced to identify the accident factors from four stages at the individual and organizational levels. The DEMATEL method is combined with interval type-2 fuzzy sets to analyze the key causations of the accident considering the interrelationships between factors under an uncertain environment. A specific case of the "7.23" Yong-Tai-Wen railway accident is employed to validate the proposed model. The analysis results show that poor management of the ministry of railways, imperfect rules and standards and little supervision or inspection are core organizational factors that lead to accidents. Besides, unsafe material conditions and unsafe human conditions are the direct causes of the accident which are easily influenced by other accident factors. The relevant managers need to strengthen the inspection to ensure the safe operation of the high-speed railway.

Cross-efficiency evaluation with the data envelopment analysis (DEA) model is an effective way to assess performance and provide a complete ranking of decision-making units. However, it is generally assumed that decision makers are perfectly rational in the cross-efficiency model, which fails to consider the subjective preferences of decision-makers. Moreover, the arithmetic average method is usually adopted to aggregate efficiency scores in traditional cross-efficiency methods, which underestimates the importance of self-evaluation. To address these issues, we extend cross-efficiency with the DEA model by incorporating prospect theory and the distance entropy function. First, we calculate the prospect values of decision-making units to describe the non-rational subjective preferences under the risk of decision-makers. Second, based on prospect cross-efficiency, a new distance entropy function is developed to aggregate the ultimate prospect cross-efficiency values. More specifically, some traditional cross-efficiency evaluation models can be considered special cases of prospect cross-efficiency models with appropriate adjustments to the parameters. Finally, an empirical example is used to evaluate the prospect cross-efficiency results with the high-tech industries of 29 provinces in China to illustrate the applicability and effectiveness of the proposed model in ranking observations.

Recent increases in climate-induced natural disasters have amplified the risk of Natech (natural hazard-triggered technological) accidents, particularly in the chemical industry. These emergencies, characterized by their urgency and resource constraints, pose significant challenges for emergency planning. The Functional Resonance Analysis Method (FRAM) offers a systematic approach to enhance emergency response strategies. This study introduces a FRAM-based methodology specifically designed for fuel storage tank farms, structured into four critical stages: understanding, designing, analyzing, and enhancing the response process. It promotes a cycle of continuous improvement. A case study on a seismic Natech incident at a fuel storage facility demonstrates the methodology's effectiveness and its potential to boost the resilience of emergency response systems against Natech challenges.

The human error factor is one of the leading causes of medical errors. Among risk analysis techniques for human error factors, HFACS (Human Factor Analysis and Classification System) method has been regarded as one of the most valuable approaches due to its advantage in potential failure classification. However, the conventional HFACS method is insufficient to handle the risk analysis problem for human error factors considering the interactive relationship among these factors. Moreover, the current fuzzy HFACS frameworks cannot address quantitative risk analysis issues, including imprecision and reliability of information. Thus, this paper constructs an integrated linguistic Z-number-based HFACS framework for analyzing the risk of human error factors. This framework can capture the uncertainty and reliability of the risk evaluation information and the interactive relationships among factors. First, the linguistic Z-number-DEMATEL (Decision Making Trial and Evaluation Laboratory) method is used to generate the comprehensive risk matrix of human error factors identified by the HFACS method. Then, an extended linguistic Z-number-ORESTE method based on the score function is presented to prioritize the risk of human error factors, which can show the preference, indifference, and incomparability relationship among human error factors. Finally, a case study of a healthcare system is conducted to illustrate the reliability of the proposed method. The result of this case indicates that inadequate resources are the most severe risk. Sensitivity analysis and comparative analysis indicate the necessity of considering the effect of the semantics of language terms and the interrelationships between human error factors on risk analysis results. These results show that the proposed hybrid framework is a reliable means to analyze the risk of human error factors within the HFACS method.

The high-tech industry plays an important role in promoting the upgrading of industrial structures. Its innovation activities show an obvious two-system structure. To promote co-development and improve industrial competitiveness, it is essential to examine the efficiency and measure the coupling coordination degree between two systems. With this regard, we first measure the relative efficiency using nonparametric technologies under different specifications of each system. Second, the coupling degree and coupling coordination degree between two systems have been calculated. Finally, comparative analyses of efficiency and coupling coordination degrees have been analysed from the perspective of the regional high-tech industry. Empirical results indicate the low overall technical efficiency in the regional high-tech industry is caused by low-scale efficiency under nonconvex. However, it is caused by low pure technical efficiency under convex. Moreover, the average efficiency of technology development in regional high-tech industry is higher than that of technology transformation for convex and nonconvex cases. Furthermore, the degree of coupling coordination of the two systems of the high-tech industry in all regions is moderate and above coordination. The empirical results can provide useful suggestions for policymakers to create an environment conducive to industrial development.

The social network structure can intuitively show the degree of correlation and the trend of change among DMs, and social network analysis techniques can provide powerful tools for complex relationship analysis. Inspired by the techniques of social network analysis, this chapter provides the concept of consensus evolution networks (CENs) that can help us explore the nature of CRP. More importantly, this chapter studies the interaction between opinions evolution and trust relationships development in GDM based on CENs.

With the rapid development of social media, traditional E-commerce has gradually transitioned to S-commerce. In other words, there is a social relationship between large groups of users in social commerce. This chapter introduces the application of LSGDM methods in social recommendation.