Large-scale Group Decision Research Articles

An interactive consensus reaching model with updated weights of clusters in large-scale group decision making

Consensus reaching process generates a group decision approved by all experts despite their possible divergent preferences. To circumvent a calculated and nominal consensus without exchanges of views, an interactive consensus reaching strategy is necessary even though it may bring costs, especially for large-scale group decision making problems. To allow experts to make cost-effective preference modifications to reach consensus in large-scale group decision making, this study proposes a dynamic interactive consensus reaching model. Firstly, a minimum-cost-consensus model that focuses on clusters in a large-scale context is introduced, in which the unit preference adjustment cost can be determined objectively. Then, we apply the minimum-cost-consensus solution to develop a feedback mechanism to activate discussions between experts and support preference modifications. The modification degree is defined towards each expert cluster to measure the cost performance of a cluster pertaining to the modifications. On this basis, we update the weights of clusters so as to improve the cost performance. An illustrative example about the grading management of high-alert medication is presented. By comparison, the interactive consensus model only costs 10.1 percent more than an automatic consensus model but gets group consensus with the exchanges of expert views.

Minimum cost consensus model for CRP-driven preference optimization analysis in large-scale group decision making using Louvain algorithm

Large-scale group decision-making problems based on social network analysis and minimum cost consensus models (MCCMs) have recently attracted considerable attention. However, few studies have combined them to form a complete decision-making system. Accordingly, we define the satisfaction index to optimize the classical MCCM by considering the effect of the group on individuals. Similarly, we define the consistency index to optimize the consensus reaching process (CRP). Regarding the evolution of the consensus network, the Louvain algorithm is used to divide the entire group into several subgroups to ensure that each subgroup is independent but has strong cohesion. By constructing the MCCM based on the satisfaction index and the optimized consensus-reaching process, the group opinions in each subgroup are ranked to obtain the final ranking of alternatives. Finally, to verify the validity of CRP and the practical value of the proposed model, we conduct consensus network evolution and decision-making analysis in the case of a negotiation between the government and polluting companies to achieve uniform pollution emissions. Sensitivity analysis is performed to demonstrate the stability of the subgroup weights. Furthermore, a comparative analysis using existing models verifies the effectiveness of the proposed model.

Statistics-based approach for large-scale group decision-making under incomplete Pythagorean fuzzy information with risk attitude

As loss in decision sample information occurs during large-scale group decision-making (LSGDM), this paper proposes a statistical estimation approach for handling Pythagorean fuzzy information under the risk attitude of decision-makers (DMs). The DMs are partitioned by risk attitudes (hesitancy degrees) into subgroups. A five-number summary for the subgroups from the incomplete decision information given by the DMs is obtained. The Cornish–Fisher expansion is then applied to estimate the mean, standard variance, and skewness of the decision sample information from the five-number summary. The confidence interval constructed by the skewness is used to obtain the interval-valued Pythagorean fuzzy number (IVPFN) evaluation information of the subgroups. An optimization model based on minimizing the conflicts between the subgroups and the overall group is used to derive the weights of the subgroups. A sorting function of the IVPFNs is used to rank the alternatives. A case study on green credit and a comparison analysis are applied to validate the proposed method.

Information consistent degree‐based clustering method for large‐scale group decision‐making with linear uncertainty distributions information

Clustering analysis is a key technique in reducing the dimensionality of high volume irregular data containing large-scale group decision-making (LSGDM) information. Uncertainty theory is suitable for subjective estimation or situation, such as lack of historical data, and it can be employed to effectively express the uncertainty of trust and preference information in LSGDM problems. This paper studies the dimensionality reduction and subgroup optimization in LSGDM by utilizing linear uncertain variables in social networks. A clustering method is proposed to decompose the large group into several subgroups of higher consilience degrees and higher preference similarities, and lower the dimension of information for LSGDM. In the clustering process, two measurement attributes, trust relationship and preference relationship of decision-makers, are combined, and information consistent degree is utilized as the clustering indicator. This approach does not need to preset the threshold and the number of subgroups, and can be employed to obtain subgroups with similar preferences and stable trust relationship. Through the clustering reliability evaluation of subgroups, the rationality of large-scale group clustering results is verified. Subgroup consensus contribution is used to identify superior subgroups and quantify the role of subgroups in improving the consensus level. An example of emergency decision-making and comparative analysis is provided to explain the feasibility and advantages of the proposed method.

Managing minority opinions in risk evaluation by a delegation mechanism-based large-scale group decision-making with overlapping communities

Energy performance contracting (EPC) mechanism is a good choice for conducting energy-saving renovation projects of public buildings. Furthermore, risk analysis is critical to smoothly implement these EPC projects. Therefore, this paper intends to set up a large-scale group decision-making (LGDM) framework based on delegation mechanism to rank risk factors of EPC projects. Firstly, some risk factors and evaluation criteria are identified. Meanwhile, the assessment is expressed as picture fuzzy numbers (PFNs) to handle conflicting opinions and refusals. Then, a novel bidirectional projection measure that considers both distance and included angle is defined, which can better describe the difference between two PFNs. Next, this paper uses a suitable algorithm to cluster experts and presents a delegation mechanism to allocate trust weights of external experts to internal experts. Then, a new method to protect minority opinions is presented. In addition, we use preference risk coefficient to integrate the uncertainty of decision information in consensus-reaching process (CRP), which reduces the risk of LGDM. We come up with an extended MULTIMOORA method to make full use of three parts of MULTIMOORA method. Moreover, the proposed framework is successfully implemented in a case study and some risk mitigation measures and management implications are presented.

A public and large-scale expert information fusion method and its application: Mining public opinion via sentiment analysis and measuring public dynamic reliability

With the rapid development of social media, reliable information released by the public on social media can provide important decision-making support. Therefore, the consideration of the public as another decision-making body participating in large-scale group decision-making (LSGDM) problems has become an extensively researched topic. However, the participation of the public as a decision-making body with decision-making experts faces several issues, such as the acquisition of public opinion, the reliability of public opinion, the integration of public and expert opinions, etc. Given this, this paper proposes a public and large-scale expert information fusion method that considers public dynamic reliability via sentiment analysis and intuitionistic fuzzy number (IFN) expressions. First, sentiment analysis technology is used to process public social media data and obtain IFNs as the opinions of the public decision-making body. Second, the concept of public dynamic reliability is defined to measure the degree of integration of public opinion. Third, a novel information entropy measure of IFNs is proposed, and a new method is introduced to determine the criteria weights under the two different decision-making bodies. Finally, an optimization model that considers the consensus levels of expert subgroups is proposed to determine the weights of different decision-making bodies. The public and expert opinions are then aggregated to obtain collective decision-making information. A case study is proposed to illustrate the application of the proposed method, and the comparative analysis reveals the features and advantages of this model.

How to process local and global consensus? A large-scale group decision making model based on social network analysis with probabilistic linguistic information

With the rapid development of societal and technological paradigms, large-scale group decision making becomes an emerging topic. In conventional group decision making methods, it is often assumed that all experts are independent. However, with the expansion of social media, experts usually have some relationships and get together for some reasons such as the academic relationship, working relationship or common interests. In these cases, experts are no longer independent individuals. To address the issue, this study introduces a large-scale group decision making model based on the social network analysis. In this model, experts can provide trust values on other experts. Due to the scale and complexity of the large-scale group decision making problems, the dimensional reduction, which uses community detection to classify experts into local communities, is deemed essential. Based on this process, the whole group can be divided into two layers. The first layer is the global network containing all communities, and the second layer is the local network within a community. This study develops a model to address large-scale group decision-making problems considering the local and global consensus in two layers simultaneously. This model allows experts to use probabilistic linguistic preference relations to express their cognitive complex evaluation information. An illustrative example is presented to show the usefulness of the proposed model.

Nonlinear preferences in group decision‐making. Extreme values amplifications and extreme values reductions

Consensus Reaching Processes (CRPs) deal with those group decision-making situations in which conflicts among experts' opinions make difficult the reaching of an agreed solution. This situation, worsens in large-scale group decision situations, in which opinions tend to be more polarized, because in problems with extreme opinions it is harder to reach an agreement. Several studies have shown that experts' preferences may not always follow a linear scale, as it has commonly been assumed in previous CRP. Therefore, the main aim of this paper is to study the effect of modeling this nonlinear behavior of experts' preferences (expressed by fuzzy preference relations) in CRPs. To do that, the experts' preferences will be remapped by using nonlinear deformations which amplify or reduce the distance between the extreme values. We introduce such automorphisms to remap the preferences as Extreme Values Amplifications (EVAs) and Extreme Values Reductions (EVRs), study their main properties and propose several families of these EVA and EVR functions. An analysis about the behavior of EVAs and EVRs when are implemented in a generic consensus model is then developed. Finally, an illustrative experiment to study the performance of different families of EVAs in CRPs is provided.

Study of the Game Model of E-Commerce Information Sharing in an Agricultural Product Supply Chain based on fuzzy big data and LSGDM

Information asymmetry is the root of agricultural product quality problems. Generally speaking, the common problems related to agricultural products are solved by effective supply chain management. From the perspective of agricultural supply chain management, this paper analyzes the shortcomings of the traditional supply chain management process by using fuzzy big data and LSGDM (Large scale group decision making), and puts forward a new method of supply chain management. In addition, from the perspective of asymmetric information sharing regarding agricultural products, an asymmetric information sharing model for agricultural products based on the evolutionary rule theory is established. Combined with fuzzy big data and LSGDM, this paper puts forward the hypothesis of each variable in the process of the information sharing game. On this basis, a mathematical model of the "pool equilibrium" of the high and low prices in the agricultural products market is put forward. Finally, a case study of products of different quality in the sea cucumber market is carried out. The results show that high quality sea cucumber products occupy a large market share in the supply chain of agricultural products. The research of this paper is of great significance, because it can increase the reliable theoretical data available for the research of the agricultural supply chain.

A sentiment analysis-based expert weight determination method for large-scale group decision-making driven by social media data

In the big data era, it is practical and generalizable to use social media data for decision-making. Thus, determining how to effectively use this kind of data to support large-scale group decision-making (LSGDM) is a direction worth studying. In this paper, for the first time, the sentiment analysis of social media data is used to evaluate the quality of LSGDM and then to dynamically determine the weights of experts from the statistical perspective. The proposed method helps improve the objectivity, accuracy, and acceptability of LSGDM. A case application demonstrates the feasibility of this method, and the results of comparative analyses reveal its superior accuracy and stability to a certain extent.

Public transportation development decision-making under public participation: A large-scale group decision-making method based on fuzzy preference relations

As an intensive travel mode, public transportation is an essential part of a circular economy construction. Scientific decision-making in a PT development plan is a fundamental prerequisite for ensuring its prioritization. In this study, based on the large-scale group decision-making of fuzzy preference relations, we examine PT development decision-making under public participation, to promote the effective use of PT resources. First, we cluster participants in the decision-making process based on the similarity method. Second, based on the clustering, an induced orderly weighting method is used to analyze the decision-making preferences of each sub-group. Finally, the decision-making preferences of each group are prioritized according to an analysis of group heterogeneity. We found that based on the similarity clustering method, when the threshold was set to 0.68, 85 participants were divided into 4 groups, and the demographic characteristics of the sub-groups presented some agglomeration. The four groups paid little attention to improving the quality of PT services. Moreover, the work unit had a significant impact on the decision-making preferences of participants, and public officials paid more attention to society and the government. Group heterogeneity significantly affects decision-making preferences and alternative priorities.

Two-stage consensus model based on opinion dynamics and evolution of social power in large-scale group decision making

The main challenges in large scale group decision making (LSGDM) problem are how to tackle with the great number of participants and how to achieve a common solution accepted by most of participants. To address these challenges, in this paper, we propose a novel framework based on opinion evolution to study the consensus reaching process (CRP) in the LSGDM. In the proposed framework, we focus on the CRP in a dynamical social influence relationship context and the whole CRP is divided into two stages. In the first stage, we design a social power and opinion evolution iterative algorithm to estimate the final consensus opinions in each sub-group. In the second stage, the opinion leaders are selected as the representatives of each sub-group to participate in the consensus process. Subsequently, we develop a self-appraisal mechanism to evaluate the confidence degree of each opinion leader. Furthermore, an opinion leaders’ networked preference evolution mechanism is proposed to investigate the consensus formation of the second stage. Finally, we use this model on a case study and compare it with some existing models.

An efficient consensus reaching framework for large-scale social network group decision making and its application in urban resettlement

Urban resettlement projects involve a large number of stakeholders and impose tremendous cost. Developing resettlement plans and reaching an agreement amongst stakeholders about resettlement plans at a reasonable cost are some of the key issues in urban resettlement. From this perspective, urban resettlement is a typical large-scale group decision-making (GDM) problem, which is challenging because of the scale of participants and the requirement of high consensus levels. Observing that residents who are affected by a resettlement project often have tight social connections, this study proposes a framework to improve the consensus reaching and uses the minimum consensus cost to reduce the total cost for urban resettlement projects with more than 1000 participants. Firstly, we construct a network topology that consists of two layers to deal with incomplete social relationships amongst large-scale participants. An inner layer consists of participants whose preference similarities and trust relations are known. Meanwhile, an outside layer includes participants whose trust relations cannot be determined. Secondly, we develop a classification method to classify participants into small subgroups based on their preference similarities. We can then connect the participants whose trust relations are unknown (the outside layer) with the ones in the inner layer using the classification results. To facilitate effective consensus reaching in large-scale social network GDM, we develop a three-step approach to reconcile conflicting preferences and accelerate the consensus process at the minimum cost. A real-life urban resettlement example is used to validate the proposed approach. Results show that the proposed approach can reduce the total consensus cost compared with the other two practices used in the actual urban resettlement operations.

Two-sided matching based on I-BTM and LSGDM applied to high-level overseas talent and job fit problems

With the increasing number of overseas talent tasks in China, overseas talent and job fit are significant issues that aim to improve the utilization of this key human resource. Many studies based on fuzzy sets have been conducted on this topic. Among the many fuzzy set methods, intuitionistic fuzzy sets are usually utilized to express and handle the evaluation information. In recent years, various intuitionistic fuzzy decision-making methods have been rapidly developed and used to solve evaluation problems, but none of them can be used to solve the person-job fit problem with intuitionistic best-worst method (BWM) and TOPSIS methods considering large-scale group decision making (LSGDM) and evaluator social network relations (SNRs). Therefore, to solve problems of intuitionistic fuzzy information analysis and the LSGDM for high-level overseas talent and job fit, we construct a new hybrid two-sided matching method named I-BTM and an LSGDM method considering SNRs. On the one hand, to express the decision-making information more objectively and reasonably, we combine the BWM and TOPSIS in an intuitionistic environment. Additionally, we develop the LSGDM with optimized computer algorithms, where the evaluators’ attitudes are expressed by hesitant fuzzy language. Finally, we build a model of high-level overseas talent and job fit and establish a mutual criteria system that is applied to a case study to illustrate the efficiency and reasonableness of the model.

Consensus-Based Linguistic Distribution Large-Scale Group Decision Making Using Statistical Inference and Regret Theory.

Large-scale group decision-making (LSGDM) deals with complex decision- making problems which involve a large number of decision makers (DMs). Such a complex scenario leads to uncertain contexts in which DMs elicit their knowledge using linguistic information that can be modelled using different representations. However, current processes for solving LSGDM problems commonly neglect a key concept in many real-world decision-making problems, such as DMs’ regret aversion psychological behavior. Therefore, this paper introduces a novel consensus based linguistic distribution LSGDM (CLDLSGDM) approach based on a statistical inference principle that considers DMs’ regret aversion psychological characteristics using regret theory and which aims at obtaining agreed solutions. Specifically, the CLDLSGDM approach applies the statistical inference principle to the consensual information obtained in the consensus process, in order to derive the weights of DMs and attributes using the consensus matrix and adjusted decision-making matrices to solve the decision-making problem. Afterwards, by using regret theory, the comprehensive perceived utility values of alternatives are derived and their ranking determined. Finally, a performance evaluation of public hospitals in China is given as an example in order to illustrate the implementation of the designed method. The stability and advantages of the designed method are analyzed by a sensitivity and a comparative analysis.

Evaluation of renewable energy sources in China using an interval type-2 fuzzy large-scale group risk evaluation method

As one of the most effective ways to alleviate energy crisis and environmental pollution, the renewable energy sources (RESs) have received increasing attention. Different RESs enjoy different characteristics and are suitable for different scenarios, thus it is essential to evaluate them before installation. Due to the increasing complexity of reality, the RESs evaluation usually involves various risks and large-scale group decision makers. To manage these risks and decision makers, this paper proposes an interval type-2 fuzzy large-scale group risk evaluation method. First, the interval type-2 fuzzy sets (IT2FSs) are employed to encode the qualitative information provided by the decision makers. Then, a new clustering approach integrating consensus reaching model and risk measurement model is developed to manage the decision makers and enhance the evaluation efficiency. After the clustering process, the selection procedure is activated and an interval type-2 fuzzy centroid-based ranking method is presented to rank the candidate RESs. Finally, a case study in China is provided to illustrate the effectiveness of the proposed method and comparisons are also made to verify the advantages.

Large-scale group decision-making based on Pythagorean linguistic preference relations using experts clustering and consensus measure with non-cooperative behavior analysis of clusters

To represent qualitative aspect of uncertainty and imprecise information, linguistic preference relation (LPR) is a powerful tool for experts expressing their opinions in group decision-making (GDM) according to linguistic variables (LVs). Since for an LV, it generally means that membership degree is one, and non-membership and hesitation degrees of the experts cannot be expressed. Pythagorean linguistic numbers/values (PLNs/PLVs) are novel choice to address this issue. The aim of this paper which we propose a GDM problem involved a large number of the experts is called large-scale GDM (LSGDM) based on Pythagorean linguistic preference relation (PLPR) with a consensus model. Sometimes, the experts do not modify their opinions to achieve consensus. Therefore, the experts’ proper opinions’ management with their non-cooperative behaviors (NCBs) is necessary to establish a consensus model. At the same time, it is essential to ensure the proper adjustment of the credibility information. The proposed model using grey clustering method is divided with the experts’ similar evaluations into a subgroup. Then, we aggregate the experts’ evaluations in each cluster. A cluster consensus index (CCI) and a group consensus index (GCI) are presented to measure consensus level among the clusters. Then, we provide a mechanism for managing the NCBs of the clusters, which contain two parts: (1) NCB degree is defined using CCI and GCI for identifying the NCBs of the clusters; (2) implemented the weight punishment mechanism of the NCBs clusters to consensus improvement. Finally, an example is offered for usefulness of the proposed approach.

Circular supply chain management with large scale group decision making in the big data era: The macro-micro model

Today, achieving the circular economy is a common goal for many enterprises and governments all around the world. In the big data era, decision making is well-supported and enhanced by a massive amount of data. In particular, large scale group decision making (LSGDM), which refers to the case in which a lot of decision makers join the decision making process, has emerged. Social network analyses are known to be relevant to LSGDM. In this paper, we examine the literature on LSGDM and highlight the current methodological advances in the area. We review the works focusing on applications of LSGDM. We study how big data can be used in circular supply chains. Based on the reviewed studies, we further construct the three-stage LSGDM CSCM micro framework as well as the five-step LSGDM CSCM macro framework (with a feedback loop) and form the Macro-Micro Model. We discuss how the Macro-Micro Model can help to support circular supply chain management (CSCM). We propose future research directions and areas. This paper contributes by being the first study uncovering systematically how LSGDM can be applied to support CSCM in the big data era using the Macro-Micro Model.

Dynamic programming algorithm-based picture fuzzy clustering approach and its application to the large-scale group decision-making problem

Due to the rapid development of society and economy, the large-scale group decision making (LSGDM) problems are increasingly common in the real life. In this paper, a dynamic programming algorithm-based picture fuzzy clustering approach is proposed to solve the LSGDM problems. First, aimed at the limitations of the existing operation laws of picture fuzzy sets, we define some new picture fuzzy operation laws. Based on these operation laws, a new picture fuzzy weighted geometric operator is developed to aggregate the preference information provided by the decision makers. Second, a new picture fuzzy Dice similarity measure is proposed to detect the different correlations between the decision makers. Then, inspired by the dynamic programming algorithm, a new clustering approach is proposed to improve the efficiency and quality of the decision-making. After the clustering process, the picture fuzzy score function is employed to compare and rank the alternatives. Finally, an illustrative example and a comparative analysis are provided to demonstrate the effectiveness and superiority of the proposed method.

Managing manipulative and non-cooperative behaviors in large scale group decision making based on a WeChat-like interaction network

The main challenges in large scale group decision making (LSGDM) problem are how to tackle with the great number of participants and how to achieve a common solution accepted by most of group members. In LSGDM problems, some decision makers (DMs) will exhibit manipulative and non-cooperative behaviors owing to the different interests they might present. Dealing with such large group implies a need for mechanisms to detect DMs’ manipulative and non-cooperative behaviors, which might affect the overall efficiency of the consensus reaching process. This paper introduces a novel framework based on WeChat-like interaction network to analyze manipulative and non-cooperative behaviors in the LSGDM problems. In the developed framework, we first detect and manage the manipulative behaviors based on the interaction network. Afterwards, for the consensus model based on opinion evolution, we develop an approach to identify and manage non-cooperative behaviors under the WeChat-like interaction network context. As a result, both the DMs’ weights and trust network derived from it are dynamically updated in parallel. Detailed simulation experiments and comparison analysis under different input parameters are presented to demonstrate the efficiency of this novel approach for coping with manipulative and non-cooperative behaviors.