Managing non-cooperative behaviors is a critical challenge in the consensus reaching process of large-scale group decision-making (LSGDM). Existing studies usually rely on static social relationships and non-overlapping community structures, which cannot adequately capture the dynamic interactions and multiple community memberships of decision experts. To address this issue, this study proposes a consensus model that fuses dynamic social network relationships and overlapping community structures for non-cooperative behavior management in LSGDM. Firstly, the COPRA algorithm is used to cluster decision experts and effectively identify experts and communities with overlapping structures, thus capturing the complex social interaction patterns among decision experts. Secondly, the PageRank algorithm is used to calculate the weights of decision experts based on the social network structure. On this basis, a consensus model is constructed by fusing dynamic network relationships and overlapping communities, which guides experts to adjust their opinions through feedback mechanisms, thereby reducing the influence of non-cooperative behaviors and promoting consensus reaching. To verify the rationality of the proposed method, the model is applied to a subway line planning decision problem. Finally, simulation experiments and comparative analyses demonstrate that the proposed method is effective in managing non-cooperative behaviors and improving consensus performance compared with existing approaches.

In large-scale group decision-making (LSGDM), directly establishing trust relationships among decision-makers (DMs) is challenging due to the influence of multiple factors. Moreover, DMs typically prioritize achieving their own goals when adjusting their opinions. Existing studies fail to identify the sources of trust, tending to rely on single-factor analyses. In real-world decision-making environments, decision-making groups often adopt a certain approval proportion to determine whether consensus on a solution has been achieved, depending on the nature of the decision problem. Requiring agreement from all DMs frequently leads to excessive communication and coordination efforts, which in turn reduces decision-making efficiency. To address these limitations and better reflect real-world decision-making processes, this paper proposes a minimum adjustment consensus model (MACM) for LSGDM based on a hybrid trust network. The method consists of three stages. Firstly, to obtain more accurate trust relationships, a hybrid trust network is constructed by integrating expert collaboration and opinion similarity. Second, based on the hybrid trust network and the consistency of alternative rankings, an improved Louvain algorithm is applied to identify multiple subgroups. Finally, an MACM considering consensus proportion and rules is proposed. An example of urban public transportation system optimization is provided for application analysis and comparison. The results demonstrate that the proposed method is both feasible and effective.

With the development of the Internet, online reviews have become an indispensable reference in decision-making processes. As a prevalent social behavior, group decision-making (GDM) is widely applied across various domains. Integrating valuable information from online reviews with GDM not only bridges real-world applications through authentic data but also significantly enhances decision accuracy and reliability. However, members’ preferences in GDM are fuzzy and conflicting, making consensus achievement critical for opinion coordination. This paper proposes an online review-driven group consensus decision-making method based on sentiment analysis and an adaptive feedback model. The method transforms online reviews into attribute-level sentiment scores, uses a novel Precise-Interval Fuzzy Preference Relation (PIFPR) structure to objectively extract endo-confidence, determines influence weights by fusing subjective and objective factors, and implements an adaptive feedback mechanism with tailored adjustment strategies. Using TripAdvisor hotel selection as a case study, the method’s practical feasibility is demonstrated. Simulation experiments show that preference adjustment cost is reduced by over 9.9

In recent years, large-scale group decision-making (LSGDM) has garnered significant scholarly attention. Given that decision-makers (DMs) may come from various departments and have distinct knowledge backgrounds, they often use heterogeneous information to express their assessments. To address these challenges, this paper proposes a new decision-making model for large groups in a social network environment. Initially, the large group is divided into communities based on the trust relationships among DMs using community detection algorithm. Subsequently, a direct method is used to process DMs' heterogeneous information. Simultaneously, we integrate the weight information of DMs and communities to calculate the preferences of the group using a weighted averaging operator. Additionally, an innovative feedback mechanism is designed, which takes into account the bounded confidence of experts and the influence of community leaders, to enhance the consensus level. Finally, the feasibility and effectiveness of the proposed model are demonstrated through a specific case study.

In recent years, the issue of large-scale group decision-making (LSGDM) has garnered widespread attention. Considering that decision-makers (DMs) may come from various professional fields and possess different knowledge backgrounds, they often use heterogeneous preference structures to provide their evaluation opinions and exhibit different psychological behaviors in the decision-making process. To address this, this paper proposes a novel heterogeneous LSGDM model that integrates decision-making theory with prospect theory, taking into account the psychological behaviors of DMs. Firstly, the large group of experts is divided into different communities based on the departmental information, and opinion representatives from each community are identified based on the trust relationships among experts to reduce the complexity within the DMs. Secondly, during the individual selection phase, the heterogeneous preference information of the experts is transformed into preference orderings through a direct method, and a preference approval structure is introduced to determine the reference point in prospect theory. Subsequently, the prospect value function calculates the experts' and the group's prospect values regarding alternatives. Furthermore, this paper designs a two-stage feedback mechanism to adjust the experts' evaluation information and preference approval structure, thereby enhancing the level of group consensus. Finally, the methodology presented in this paper was applied to a specific case and successfully resulted in an optimal solution, providing a new approach to address enterprise financial investment decision-making problems.

PurposeIn large-scale group decision-making (LSGDM) situations, existing TODIM group decision-making methods often fail to account for the influence of social network relationships and the bounded rationality of decision-makers (DMs). To address this issue, a new TODIM-based group decision-making method is proposed that considers the current trust relationships among DMs in a large-scale trust relationship network.Design/methodology/approachThis method consists of two main stages. In the first stage, the large-scale group is partitioned into several sub-clusters based on trust relationships among DMs. The dominance degree matrix of each sub-cluster is then aggregated into the large-scale group dominance degree. In the second stage, after aggregating the large-scale group dominance degree, the consensus index is calculated to identify any inconsistent sub-clusters. Feedback adjustments are made based on trust relationships until a consensus is reached. The TODIM method is then applied to calculate the corresponding ranking results. Finally, an illustrative example is applied to show the feasibility of the proposed model.FindingsThe proposed method is practical and effective which is verified by the real case study. By taking into account the trust relationships among DMs in the core process of LSGDM, it indeed has an impact on the decision outcomes. We also specifically address this issue in Chapter Five. The proposed method fully incorporates the bounded rationality of DMs, namely their tendency to accept the opinions of trusted experts, which aligns more with their psychology. The two-stage consensus model proposed in this paper effectively addresses the limitations of traditional assessment-based methods.Originality/valueThis study establishes a two-stage consensus model based on trust relationships among DMs, which can assist DMs in better understanding trust issues in complex decision-making, enhancing the accuracy and efficiency of decisions, and providing more scientific decision support for organizations such as businesses and governments.

Large-scale group decision making (LSGDM) is considered when the number of experts involved in the decision exceeds 20. Due to the large number of people involved in LSGDM, its decision-making process is uncertain, complex, and time-consuming. Therefore, how to effectively help large groups reach consensus in a complex environment is a challenge for current research. Consensus reaching process (CRP) is an effective tool to eliminate group conflicts. Based on this, we propose a consensus reaching process based on the Louvain algorithm, social network, and bounded confidence (SNBC) model with interval numbers. First, we use interval numbers to express expert opinions and social network relationships among experts. Second, the experts are clustered using the Louvain algorithm. The weights of experts are obtained by social network analysis. Third, we use the SNBC model to design a feedback mechanism for tripartite opinions. In addition, we give a numerical example and simulation experiments to demonstrate the flexibility and effectiveness of the proposed approach. Finally, the comparative analysis shows the superiority of our method.

在社会网络环境下的大群体决策问题当中,决策专家之间的社会网络关系对决策过程和结果的影响至关重要.文章创新地提出一种考虑决策专家社会网络关系和非合作行为的大群体共识决策模型,有效促进大群体共识的达成.首先,根据决策专家的偏好信息和社会网络关系,改进经典Louvain社区发现算法,对大决策群体进行社区划分.其次,运用社会网络分析方法确定决策专家个体和社区的权重.随后,根据决策专家的偏离程度对决策专家非合作行为进行识别,并考虑社会网络关系的影响对非合作行为进行管理,以此构建共识决策模型.最后,通过案例分析来验证所建立共识决策模型的可行性和有效性.文章构建的共识决策模型,不仅在大群体社区划分过程中,创新性地同时考虑决策专家的偏好信息和社会网络关系的影响,并且在非合作行为管理过程中,也考虑到了社会网络关系对非合作行为决策专家偏好调整的影响,使其更适应社会网络决策环境.

针对在群体决策中如何利用专家之间的社会关系和决策专家的有限理性的问题,提出一种信任网络下的TODIM群体决策方法.首先,根据专家讨论次数,在每一次讨论中,每个专家会根据信任接受程度参考信任者的决策矩阵,并通过信息交互和协商修改决策矩阵;其次,当达到设定的专家讨论次数时,计算最终的群体决策矩阵;最后,分别运用信任网络下的TODIM群体决策方法和TODIM群体决策方法计算各方案排序.对所得结果进行对比分析,并对专家讨论次数和信任接受程度进行灵敏度分析.案例分析结果表明,信任网络下的TODIM群体决策方法能充分结合信任网络,保证了决策过程中的多阶段信息交互和反馈过程,并在对比分析和灵敏度分析上优于对比方法.

To obtain the suitable alternative(s) for the organization, this paper proposes a more practical method to solve the decision-making problems in society. That is combined with the TODIM (TOmada de decisão interativa multicrit e ´ rio). The maximizing dominance degree model to reach consensus is proposed with two following components: (1) constructing the complete trust relationships network; (2) the maximizing dominance degree feedback mechanism to reach group consensus. Therefore, firstly owing to the complexity of the trust relationships network, judging the direct and indirect trust propagation paths among the decision makers (DMs) to construct the complete trust relationships network and identifying the highest value of Trust Score (TS) as the leader is possible. Then identify the inconsistent DM based on the established consensus index. During the feedback process, inconsistent DMs adopt the feedback mechanism based on the dominance degree of the leader until the group consensus is reached. Later, the corresponding ranking result is calculated by the TODIM method. Finally, a numerical example is applied to illustrate the effectiveness and feasibility of the optimal model.

针对现有多属性群体决策方法较少考虑社会网络和决策者有限理性因素的影响,考虑到社会网络中的信任关系,提出了基于信任关系的TODIM(TOmada de decis?o interativa multicritério)群体多属性决策方法.根据决策专家之间的信任关系,计算出信任网络中的领导者、信任关系矩阵以及评价矩阵等.专家根据自身的自信程度来参考领导者的评价矩阵,调整备选方案的优势度.运用TODIM方法计算各方案最终的排序结果,并与未考虑信任关系时得出的排序结果进行比较,并对自信程度进行灵敏度分析.算例结果说明了该方法的可行性和有效性.结合信任网络和TODIM决策方法的性质和研究现状,对未来的研究发展方向进行了展望.

随着社会化媒体的快速发展,社会化因素己经成为影响群体决策过程及其结果的重要因素.针对群体决策者的判断信息以残缺判断矩阵形式给出,且考虑群体决策者社会网络邻接关系的群体决策问题,提出可行的解决方法.首先,提出一种基于决策者相似性程度和社会网络距离的残缺判断矩阵补全方法;然后,提出考虑决策者社会网络影响力的群体共识交互决策模型,该交互模型不仅考虑群体决策者之间的社会邻接关系,而且可以在较大程度上保存决策者给定的原始判断信息;最后,通过一个物流企业选择存储仓库的算例验证所提出算法的可行性和优势.

There are plenty of researches on group decision making (GDM) problem and most of them assume that all the experts are independent. However, the social network connection is an important characteristic among experts, and should been taken into account in the GDM decision process. The social network analysis (SNA) is a rapidly developing technology to deal with the problem about social network connections. In this paper, we address GDM problem with fuzzy preference relations where the experts have directed social network connections. And we use in-degree and out-degree centrality indices in SNA to build the social characteristics of the experts. Then we utilize the importance induced ordered weighted averaging (I-IOWA) operator to aggregate all the individual fuzzy preference relations with social indices. Furthermore,we investigate the reciprocity, additive consistency and acceptable consistency properties about the obtained group fuzzy preference relations. A procedure of addressing GDM problem with fuzzy preference relations where the experts are within directed social network connections is developed. Moreover, we compare the results of the case where all the experts are independent and the case where all the experts are within directed social network connections. Some useful tips that affect final outranking result in the directed graphical social network connection are obtained. In the end, we summarize the main results of this paper and point out some research directions for future research.

With the development of social media, the social relationships among group decision makers should be taken into consideration when addressing group decision making problems. As an extension of the fuzzy set, the Pythagorean fuzzy set has recently been applied to depict the uncertainty in practical group decision problems. The purpose of this paper is to propose a multi-criteria Pythagorean fuzzy group decision approach considering social relations. In this paper, the similarity degree and the paths between any two experts in a social network are combined to construct a connection strength matrix to detect the leader among all the experts. A leader-following consensus reaching algorithm is proposed to adjust the multi-criteria Pythagorean fuzzy decision making matrix. Moreover, a procedure for the multi-criteria Pythagorean fuzzy group decision approach based on social network analysis is proposed. We use an example to illustrate the feasibility and advantages of the proposed method.

Dempster-Shafer theory (DST) of evidence has wide application prospect in the fields of information aggregation and decision analysis. To solve the issues of interval evidence combination and normalization, we have reinvestigated the methods provided for interval evidence combination within the fra meworks of DST and evidential reasoning (ER) approach, respectively, and pointed out the shortcomings of existing methods. A more general interval evidence combination approach based on the ER rule is constructed. Numerical examples are provided to indicate that the proposed method not only suitable to the conflict-free interval evidence combination, but also to the conflicting interval evidence combination, and interval evidence specificity can be kept intact in the interval evidence combination process. Moreover, the interval evidence combination methods based on DST or ER are special cases of the proposed method in some cases.

Because of the complexity of interval-valued intuitionistic fuzzy set, there are few literatures investigating the additive consistency of the interval-valued intuitionistic preference relation. This paper proposes a group decision making approach with interval-valued intuitionistic preference relations. Firstly, two additive reciprocal fuzzy preference relations and two fuzzy non-preferred relations are obtained by dividing an interval-valued intuitionistic preference relation in order to avoid the operations of interval-valued intuitionistic fuzzy numbers. Here, the fuzzy non-preferred relation is interpreted as the non-preferred intensity of one alternative over another one. Moreover, the rational concept of additive consistency of interval-valued intuitionistic preference relation is defined. Secondly, optimizing models to derive priority weight vector from interval-valued intuitionistic preference relation are constructed. In particular, the priority weight vector is in terms of interval-valued intuitionistic fuzzy numbers, which is rational under the interval-valued intuitionistic fuzzy environment. Thirdly, an extended approach to address group decision making (GDM) problems is proposed. Each individual expert’s consistency index is applied to measure his/her degree of importance. Finally, an illustrative example of supplier selection is provided to illustrate the proposed approach addressing GDM problems. The feasibility to derive priority weight vector in terms of interval-valued intuitionistic fuzzy numbers using the developed approach is verified. And the proposed approach is compared with the other conventional existing ones to show its advantages.

The determination of evidence weights is an important step in evidence combination, which significantly influences final results. Taking into account the assumption of "psychology of economic man", decision-makers may tend to seek similar pieces of evidence to support their own evidence in the process of negotiation and thereby forming an alliance of benefit. In the process of negotiation, decision-makers are concerned about the fairness of negotiation. To achieve the aim of fairness, in this paper, we extend the concept of evidential reasoning (ER) to evidential reasoning based on Gini coefficient (ERBGC) to obtain the weights of evidence. The main concept of the ERBGC approach is that the decision-maker is willing to engage negotiation with others only when the negotiation process is fair, that means the gap between maximum and minimum distributed interests among all decision-makers is less than that without negotiation. It shows that negotiation can make interests distribution fairer among decision-makers. In this study, the optimization model was developed to generate the relative weights based on Gini coefficient and enable weighted evidence to be combined using the ER rule. The approach is then applied to a case study and compared with other related approaches to demonstrate the effectiveness and applicability.

The decision maker’s attitudinal character towards risk and the psychological aspects are critical factors of the multiple attribute decision making (MADM) problems. In this paper, we consider the attitudinal character during the whole decision making procedure. The reference points associated with prospect theory are in the form of interval-valued intuitionistic fuzzy number (IVIFN) and we assume the membership degree and non-membership degree of the IVIFN obey normal distribution according to the central limit theorem. We combine the properties of normal distribution and the attitudinal character associated with the ordered weighted averaging (OWA) operator to convert all the reference points into crisp numbers. We construct one feasible multiple objective optimization programming to obtain the optimal weight vector of the attributes by minimizing the deviation between the alternative and the reference point corresponding to each alternative. The hybrid weighted averaging (HWA) operator is applied to aggregate the prospect values for each alternative. Especially, we directly reorder the weighted prospect values considering their plus or minus, which reflects the decision-maker’s attitudinal character towards risk as well. Finally, an illustrative example about group-buying is provided to show the feasibility of the proposed method.

Group decision making with intuitionistic fuzzy preference information involves three steps: the consistency checking process, the consensus checking process and the selection process. In this paper, we investigate the above three steps with respect to additive intuitionistic fuzzy preference relation (IFPR). Firstly, a consistency index is introduced to measure the additive consistency level of IFPR and an automated approach is developed to improve the consistency level with respect to IFPR to an acceptable level. Meanwhile, the group consensus index of IFPR is defined and one algorithm for reaching acceptable level of consensus is developed. Secondly, after implementing this modified algorithm, consistency index and group consensus index are investigated. And we prove that they can hold on, even receive better levels. Thirdly, a framework for group decision making is developed based on IFPR with additive consistency and group consensus. Finally, an illustrative example is presented to demonstrate the effectiveness and applicability of the proposed approach.

In this paper, we introduce the concept called fuzzy non-preferred relation where the elements are interpreted as the non-preferred intensity of one alternative over another one. We divide an intuitionistic preference relation into the fuzzy preference relation part and the fuzzy non-preferred relation part . Based on this division, we propose a new definition of additive consistency of intuitionistic preference relation based on the traditional one. Then, we construct an optimization model for deriving intuitionistic fuzzy weights which can be ranked easily in individual decision making environment. And we develop an optimization model for deriving the collective intuitionistic fuzzy weights to address group decision making problems. Finally, two numerical examples are provided to illustrate the developed approaches.