Large-scale Group Decision Research Articles

Large-Scale Group Decision Making with Dual Feedback from Community Residents Based on the Organizational Invisible Field

In China, communities function as grassroots self-governing bodies, and the enhancement of public participation in community governance has remained a central focus of study. This paper applies the Large-Scale Group Decision-Making (LSGDM) method to the process of community self-governance and proposes a dual feedback group consensus decision-making model that takes into account the unique social relations among residents. Firstly, the concept of the Organizational Invisible Field—formed in communities by intangible social capital such as positional power and interpersonal relationships within the organization—is introduced. The definition of Invisible Field Force is utilized to measure the influence of these forms of capital on social relationships. Subsequently, drawing on field dynamic theory, the process by which residents’ preferences within the organization are shaped by the action of Invisible Field Force is explored. Secondly, acknowledging that invisible relationships can be affected by dynamic interactions during the decision-making process, the Invisible Field Force change model is constructed. Building on this, a dual feedback consensus coordination mechanism—encompassing both in-organization members and all residents—is designed. Finally, the validity and utility of the model are verified through case studies and sensitivity analyses.

A minimum cost and maximum fairness-driven multi-objective optimization consensus model for large-scale group decision-making

A minimum cost and maximum fairness-driven multi-objective optimization consensus model for large-scale group decision-making

Dynamic clustering-based consensus model for large-scale group decision-making considering overlapping communities

Consensus-reaching strategy is crucial in large-scale group decision-making (LSGDM) as it serves as an effective approach to reducing group conflicts. Meanwhile, the common social network relationships in large groups can affect information exchange, thereby influencing the consensus-reaching process (CRP) and decision results. Therefore, how to leverage social network information in LSGDM to obtain an agreed solution has received widespread attention. However, most existing research assumes relative independence between communities in the dimension reduction process of LSGDM and neglects the possibility of different overlaps between them. Moreover, the impact of overlapping communities on CRP has not been adequately explored. Besides, the dynamic variations in clusters and their weights caused by evaluation updates need to be further studied. To address these issues, this paper proposes a dynamic clustering-based consensus-reaching method for LSGDM considering the impact of overlapping communities. First, the LINE-based label propagation algorithm is designed to cluster decision makers (DMs) and detect overlapping communities with social network information. An overlapping community-driven feedback mechanism is then developed to enhance group consensus by utilizing the bridging role of overlapping DMs. During CRP, clusters and their weights are dynamically updated with trust evolution due to the evaluation iteration. Finally, a case study using the Film Trust dataset is conducted to verify the effectiveness of the proposed method. Simulation experiments and comparative analysis demonstrate the capability of our method in modeling practical scenarios and addressing LSGDM problems under social network contexts.

A hierarchical consensus reaching model based on trust and uncertain degree for heterogeneous large-scale group decision making and application to product design

Nowadays, due to the fierce market competition, companies in many industries needs to constantly introduce new products. How to select an optimal product design has become a widespread problem. Due to complexity and a large number of decision makers (DMs) participating in decision-making, this paper formulates the product design selection as a type of large-scale group decision making (LSGDM). Because of the differences in occupation, purpose, and personality of DMs in LSGDM, they prefer to provide evaluations by heterogeneous representation formats. A hierarchical consensus reaching model is developed based on trust and uncertain degree for heterogeneous LSGDM. Firstly, the heterogeneous evaluations of DMs are transformed into fuzzy preference relations (FPRs) through possibility degrees. According to trust relationships and original evaluations of DMs, the trust and uncertain degrees of DMs are extracted considering the inherent personalities and psychological traits implied in the heterogeneous evaluations. Thereby, this paper (1) constructs an optimization model to determine the weights of DMs and (2) divides the feedback mechanism into four cases. Case study of product design selection is provided to illustrate the applicability of the proposed model. Several comparisons validate the advantages of the proposed model.

Consensus methods with Nash and Kalai-Smorodinsky bargaining game for large-scale group decision-making

With the significant advancements in communication technology, group decision-making (GDM) can now be implemented online, allowing a large number of decision-makers (DMs) to participate concurrently. However, current methods for large-scale group decision-making (LSGDM) are primarily suitable for 20 to 50 DMs, and their effectiveness in scenarios involving thousands or even tens of thousands of participants has yet to be fully validated. Furthermore, as the number of participants increases, the evaluation information becomes increasingly diverse and complex. At the same time, the social networks associated with the DMs typically become sparse, making information sharing and consensus building more challenging. In light of these challenges, we develop two new methods based on cooperative games to effectively address the challenges in super LSGDM. First, we propose a two-stage semi-supervised fuzzy C-means (FCM) clustering method with trust constraints, which aims to address the issue of sparsity in relationships within large-scale social networks. This method utilizes trust relationships as reliable resources and prior knowledge to guide and supervise the clustering process. On this basis, we discuss three scenarios from the perspective of cooperative games: (i) subgroup optimal consensus adjustments in non-cooperative situations, (ii) group optimal consensus adjustments in cooperative situations, and (iii) subgroup optimal consensus adjustments in cooperative situations. Subsequently, we view the consensus adjustment allocation as a cost cooperative game problem and propose two new LSGDM consensus methods based on Nash Bargaining (NB) and Kalai-Smorodinsky Bargaining (KSB). Finally, experiments on real datasets demonstrate the superiority and reliability of our proposed LSGDM methods.

An interactive iteration consensus based social network large-scale group decision making method and its application in zero-waste city evaluation

The construction of zero-waste (ZW) cities receives increasing attention from the Chinese government. The evaluation is essential to make policy variations according to the actual situation in each place. Previous assessments of ZW cities have primarily relied on historical data, which fails to account for the subjective preferences of various stakeholders. For example, it is challenging to capture residents' subjective opinions about the development of a ZW city. This paper presents a social network large-scale group decision-making method for evaluating the construction of ZW city. First, experts' evaluation opinions and trust relations are used to develop an improved clustering method. The weights of the clusters are then determined using internal-external cohesion indices and the number of experts, with experts' weights defined by their similarity-trust degree. An optimization model based on interactive iteration consensus is formulated, considering the fairness and rationality of allocation schemes. Additionally, a new social network large-scale group decision-making method is presented. Finally, the proposed method is illustrated with a case study of selecting a national-level ZW city in Jiangsu Province.

Reliability-based ordinal consensus adjustment model for large scale group decision making

In large scale group decision-making (LSGDM), there are the substantial number of decision makers (DMs) with diverse knowledge, backgrounds, and interests related to the decision-making problem, and it is not possible to assure that all DMs are completely reliable. Thus, in order to enhance the quality of decision-making, it is necessary to analyze the reliabilities of DMs in LSGDM. This paper proposes the method to evaluate the reliabilities of DMs, sorts these DMs according to their degree of reliability, and investigates the consensus reaching process based on categories and an ordinal consensus measure. Considering the DMs' trust network, the uncertainty of a DM's evaluation information represented by a fuzzy preference relation (FPR), the deviation between a DM's FPR and those of the other DMs, and additive consistency of FPRs, the reliability of a DM is assessed using four criteria: PageRank centrality, professional competence, collaborative competence, and additive consistency. Following these reliability assessment criteria, ELECTRE-TRI is employed to sort DMs into three ordered categories according to DMs' different levels of reliability under the four assessment criteria. Furthermore, an improved ordinal consensus measure is designed to consider both the importance weights of positions and the deviation of Borda counts of the same alternative in two rankings. As for the consensus reaching process, due to the varied reliabilities of DMs in different categories, we propose a multiple strategies feedback mechanism for DMs in different categories. Finally, a numerical example is provided to illustrate the rationality and validity of the proposed model.

An ordinal-cardinal consensus adjustment allocation mechanism for large-scale group decision making based on the consistency of distributed preference relations under fuzzy uncertainty

Large-scale group decision making (LSGDM) problem is common in real life. With the increase in the number of alternatives and the limited rationality of human beings, consistency problem is inevitable when pairwise comparison method is used. We propose an improved consistency calculation approach to generate consistent distributed preference relations (DPRs), which adopts adjacent score intervals to calculate the score intervals of non-adjacent alternative pairs. By using optimization model, the initial DPR is preserved as much as possible on the premise of order consistency. As for the consensus analysis, the concept of relationship-possibility degree is defined to capture the ignorance and fuzzy uncertainty in assessments. An ordinal consensus measure method considering absolute position difference and relative position dissimilarity with relationship-possibility degree is proposed. Ordinal-cardinal consensus adjustment model based on DPR is then constructed to obtain the minimum consensus adjustment of decision makers or subgroups coalition which are considered as coalition payoff. In addition, to distribute the ordinal-cardinal minimum consensus adjustment reasonably, we construct a two-stage consensus adjustment allocation mechanism adopting the improved multi-weighted Shapley function in the cooperative game. Several optimization models are constructed to obtain the adjusted DPRs of decision makers or subgroups. Finally, an illustrative example is presented to demonstrate the validity of the proposed method in dealing with the decision problems of product development engineering. It is expected to make the LSGDM procedure in a more intelligent way.

Correction to: A Large-Scale Group Decision-Making Model Considering Expert Authority Degree and Relationship Evolution Under Social Network

Correction to: A Large-Scale Group Decision-Making Model Considering Expert Authority Degree and Relationship Evolution Under Social Network

Large-Scale Group Decision-Making Method with Public Participation and Its Application in Urban Management

Large-Scale Group Decision-Making Method with Public Participation and Its Application in Urban Management

An ordinal–cardinal consensus model for three-way large-scale group decision-making considering co-opetition relations

In large-scale group decision-making (LSGDM), the complexity of the decision-making environment highlights the significance of co-opetition in reaching a consensus among decision-makers (DMs) with diverse knowledge. Thus, this paper proposes an ordinal–cardinal consensus model for three-way LSGDM that considers co-opetition relationships among DMs. Specifically, we first improve the ordinal consensus measure and propose the ordinal–cardinal consensus measure by analyzing the co-opetition relationships. Then, utilizing the constructed trust consensus network, DMs are categorized into subgroups, and spokespersons are selected from each subgroup. Further, we establish the consensus identification rule using the three-way decision (TWD) theory and design a personalized feedback regulation mechanism for distinct relationships among subgroup representatives based on ordinal consensus. Also, an example of economic revitalization is employed to illustrate the feasibility of the proposed approach. Finally, the benefits and values of the proposed method are highlighted by simulation and comparative analysis.

Minimum cost consensus model with variable cost for multi-criteria large-scale group decision-making considering the tolerance of decision-makers

The objective of multicriteria large-scale group decision-making (LSGDM) is to obtain a decision result that gains acceptance from the majority of decision-makers (DMs). The consensus reaching process (CRP) plays a crucial role in guiding DMs to continuously adjust their opinions through feedback adjustment mechanisms to form a widely accepted decision result. In practical decision-making, adjusting opinions incurs costs and involves limited resources. Simultaneously, DMs have tolerance for modifying their opinions. To this end, this paper proposes a minimum cost consensus model (MCCM) with variable cost to reach consensus efficiently within limited resources and DMs’ tolerance. Firstly, a method to measure the combined similarity among DMs is proposed. Then, an extended local fitness maximization (ELFM) algorithm suitable for multicriteria LSGDM problems is proposed for clustering. Furthermore, an objective method of determining the unit adjustment costs for DMs in the MCCM is provided. For the CRP that considers the tolerance of DMs, this paper introduces the MCCM with variable cost to obtain the adjustment opinions of DMs. During the selection process, we utilize the stochastic multicriteria acceptability analysis (SMAA) method to evaluate alternatives and selection. Finally, the feasibility of the proposed method is verified through an illustrative example, and its advantages are emphasized through comparative analysis.

A Consensus Model with Non-Cooperative Behavior Adaptive Management Based on Cognitive Psychological State Computation in Large-Scale Group Decision

A Consensus Model with Non-Cooperative Behavior Adaptive Management Based on Cognitive Psychological State Computation in Large-Scale Group Decision

Overlapping community-driven dynamic consensus reaching model of large-scale group decision making in social network

Large-scale group decision-making (LSGDM) serves as a pivotal tool for facilitating consistent decision results through intricate interactions among individuals within the network. However, the impact of complex trust relationships within overlapping communities on consensus is often overlooked in many studies. Moreover, the dynamic interaction between overlapping communities and the consensus reaching process (CRP) is seldom taken into account. This paper aims to build an overlapping community-driven consensus reaching model for addressing LSGDM challenges in social network. Given the advantages of intuitionistic fuzzy numbers (IFNs) in uncertain information representation, IFNs are used to express evaluation information and trust information. Firstly, a novel overlapping community detection method is developed to divide subgroups and detect overlapping communities. Secondly, to determine reliable subgroup weights, this paper constructs a weight determination model that considers multiple factors and their internal correlations. Then, an overlapping community-driven dynamic consensus model is proposed, which provides a new way to resolve the opinion conflicts, considering the dynamic change of CRP. Simultaneously, the reverse effect of opinion adjustment on the social trust network is considered. Finally, the practicality of the proposed model is demonstrated through illustrative cases. Furthermore, through a comparative analysis, the superiority of the proposed model is demonstrated and the efficiency improvement for CRP is verified.

Biobjective Optimization Method for Large-Scale Group Decision Making Based on Hesitant Fuzzy Linguistic Preference Relations With Granularity Levels

Biobjective Optimization Method for Large-Scale Group Decision Making Based on Hesitant Fuzzy Linguistic Preference Relations With Granularity Levels

A dual-level consensus model for large-scale group decision-making driven by trust relationships in social networks

In large-scale group decision-making, obtaining reasonable and reliable decision results is the research focus. To this end, a dual-level consensus model for large-scale group decision-making is constructed. In the model, we first presented a method for measuring the two-dimensional similarity between decision-makers. The method considered the opinion similarity at evaluation scales and ranking results level, which provided a more comprehensive measure of the opinion differences between decision-makers. A hierarchical clustering algorithm based on the two-dimensional similarity-trust matrix is proposed. By considering the two-dimensional similarity and trust relationships among decision-makers, the method contributed to the formation of subgroups with excellent cooperative and communicative atmospheres. Furthermore, we introduced a dual-level consensus measures method to comprehensively and accurately assess the group consensus level. To increase the efficiency of decision-making and the satisfaction of decision-makers, we proposed a personalized feedback adjustment mechanism for decision-makers. Additionally, for the subgroups that have not reached consensus, a social networks DeGroot model is constructed to adjust the opinion of subgroups. Finally, a case study of low-carbon supplier selection verified the feasibility and applicability of the model. The effectiveness and superiority of the model are demonstrated by comparative and simulation analysis. The analysis results show that the model is conducive to promoting cooperation and coordination among decision-makers and obtaining highly acceptable and quality decision results.

A Large-Scale Group Decision-Making Model Considering Expert Authority Degree and Relationship Evolution Under Social Network

In Large-Scale Group Decision-Making (LSGDM), effectively implementing consensus models is pivotal for managing decision complexity. While trust-based LSGDM has garnered attention, there remains a need for deeper insights into the dynamics of interexpert trust and the impact of authority effects on the decision-making process. This study introduces a sophisticated model for large-scale group decision-making, incorporating considerations of expert “trustworthiness-authority.” Initially, the study assesses the trustworthiness of experts based on social network relationships and opinion similarity while using background information and consensus levels to establish their authority. Subsequently, experts are categorized into four distinct regions based on their trustworthiness and authority assessments. Furthermore, tailored consensus adjustment methods are proposed for each region based on social contagion theory to facilitate consensus achievement. Additionally, a case study is conducted to demonstrate the rationality and effectiveness of the proposed LSGDM model, considering expert “trustworthiness-authority.” Finally, the necessity and superiority of the proposed model are further verified through comparison analysis and sensitivity analysis.

An Online Review Data-Driven Fuzzy Large-Scale Group Decision-Making Method Based on Dual Fine-Tuning

Large-scale group decision-making (LSGDM) involves aggregating the opinions of participating decision-makers into collective opinions and selecting optimal solutions, addressing challenges such as a large number of participants, significant scale, and a low consensus. In real-world scenarios of LSGDM, various challenges are often encountered due to factors such as fuzzy uncertainties in decision information, the large size of decision groups, and the diverse backgrounds of participants. This paper introduces a dual fine-tuning-based LSGDM method using an online review. Initially, the sentiment analysis is conducted on online review data, and the identified sentiment words are graded and quantified into a fuzzy data set to understand the emotional tendencies of the text. Then, the Louvain algorithm is used to cluster the decision-makers. Meanwhile, a method combining Euclidean distances with Wasserstein distances is introduced to accurately measure data similarities and improve clustering performances. During the consensus-reaching process (CRP), a two-stage approach is employed to adjust the scores: to begin with, by refining the scores of the decision representatives via minor-scale group adjustments to generate a score matrix. Then, by identifying the scores corresponding to the minimum consensus level in the matrix for adjustment. Subsequently, the final adjusted score matrix is integrated with the prospect–regret theory to derive the comprehensive brand scores and rankings. Ultimately, the practicality and efficiency of the proposed model are demonstrated using a case study focused on the purchase of solar lamps. In summary, not only does the model effectively extract the online review data and enhance decision efficiency via clustering, but the dual fine-tuning mechanism in the model to improve consensus attainment also reduces the number of adjustment rounds and avoids multiple cycles without achieving the consensus.

Consensus reaching in LSGDM: Overlapping community detection and bounded confidence-driven feedback mechanism

The surge of social media has made large-scale group decision-making (LSGDM) crucial in real-world decision-making. The intricacies of trust relationships within social networks that emerged from relations in social media affect both the clustering and the consensus of large groups. However, existing research often neglects the impact of overlapping social trust networks on group consensus. To fill this gap, this study introduces a novel consensus-reaching process (CRP) that integrates overlapping community detection and ELICIT-based optimization models under bounded confidence. Initially, the Lancichinetti-Fortunato method (LFM) is employed to identify overlapping community structures within social trust networks, delineating several subgroups and identifying corresponding non-overlapping and overlapping decision-makers (DMs). Subsequently, the PageRank (PR) algorithm is utilized to compute both global and local weights for individuals, facilitating a rational aggregation of collective and subgroup opinions. Next, two-stage Extended Comparative Linguistic Expressions With Symbolic Translation (ELICIT)-based optimization consensus models under bounded confidence are designed, aiming to provide optimal feedback for guiding DMs' preference adjustments. Since overlapping DMs may belong to multiple subgroups, a weighted influence feedback mechanism is introduced to mitigate conflicting guidance from these multiple affiliations. Finally, we demonstrate the effectiveness and superiority of our proposed method through numerical validation and comparative analysis against existing approaches.

A PSO-algorithm-based dual consensus method for large-scale group decision making and its application in medical imaging equipment purchasing

The increasing complexity of social activities requires an expanding number of people to be involved in decision-making, so that the large-scale multi-attribute group decision-making problems have gained widespread attention. After overviewing the researches of large-scale multi-attribute group decision-making methods, we have found that: The existing methods only consider consensus based on evaluation information of alternatives, while ignoring the consensus on importance of attributes. Thus, in order to tackle the issues and describe the hesitancy of decision makers in the decision-making process, this paper proposes a novel dual consensus method in large-scale multi-attribute group decision making under hesitant fuzzy linguistic environment. In the consensus reaching process, the method considers not only the consensus on the evaluation information of alternatives, but also the consensus on the importance of attributes, where both consensus reaching processes are implemented by the particle swarm optimization algorithm. The subjective weights of attributes are derived from the consensus reaching process of preference matrices, and the objective weights of attributes are obtained from the consensus reaching process of decision matrices, so as to acquire the comprehensive weights. After that, the overall ranking of alternatives can be obtained by TODIM. Finally, the proposed method is applied to a case study of medical imaging equipment purchasing decision-making, and the comprehensive analysis is provided to clarify advantages of the proposed method.