Large-scale Group Decision-making Problems Research Articles

Managing noncooperative behaviors in large-scale group decision-making with linguistic preference orderings: The application in Internet Venture Capital

In Internet venture capital (VC), it is very important to fully analyze and evaluate the influential factors. Because this activity usually involves amounts of experts, it makes sense to incorporate it into large-scale group decision-making (LSGDM). In this process, how to deal with the noncooperative behaviors and express the preference information are two important issues that need to be addressed. Given this, this paper is committed to evaluating the influential factors of Internet VC by managing noncooperative behaviors in LSGDM. Firstly, the preference information can be expressed by linguistic preference orderings (LPOs) which can be used to express unbalanced relationship between any two adjacent alternatives. Then, three kinds of noncooperative behaviors are taken into consideration, and we can identify the group who belongs to one of the three noncooperative behaviors, and then develop methods to manage them respectively. Furthermore, a consensus reaching model is established to manage these noncooperative behaviors. Moreover, we apply the proposed model to solve a practical LSGDM problem involving the evaluations of the influential factors in Internet VC. Finally, comparative analyses between the proposed model and some existing methods are made to show the validity and applicability of the proposed consensus reaching model.

An overlap graph model for large‐scale group decision making with social trust information considering the multiple roles of experts

AbstractSocial network analysis is an efficient tool to investigate the relationships of decision‐makers in large‐scale group decision making (LSGDM). Existing social network‐based LSGDM studies generally assumed that each decision‐maker has a single role or belongs to only one subgroup. The assumption that a decision‐maker has multiple roles or belongs to multiple subgroups is rarely taken into consideration. In this regard, this study proposes an overlap graph model (OGM) in which decision‐makers can participate in the decision‐making process in multiple roles to solve LSGDM problems with social trust information. In the OGM, decision‐makers are firstly divided into two types: multiple‐role decision‐makers and single‐role decision‐makers. Since it is unpractical for a decision‐maker to evaluate all others in a LSGDM problem, we then investigate how to construct a complete social trust network based on an Agent mechanism. A two‐stage consensus reaching process is proposed to reduce the discrepancies among decision‐makers: The first stage is for single‐role decision‐makers within a subgroup while the second stage is for Agents and multiple‐role decision‐makers. Finally, an illustrative example regarding selecting treatment plans for critical patients in COVID‐19 is provided to test the applicability and rationality of the proposed model.

Consensus Model Handling Minority Opinions and Noncooperative Behaviors in Large-Scale Group Decision-Making Under Double Hierarchy Linguistic Preference Relations.

With the rapid development of society and continual progress of science and technology, large-scale group decision-making (LSGDM) problems are very commonly encountered in real-life situations. Considering that the information required for decision-making and people's cognition processes is becoming more and more complex, double hierarchy linguistic preference relation (DHLPR) can be used to express complex linguistic information reasonably and intuitively. Sometimes experts in LSGDM unwillingly modify their preferences or even modify them on purpose in a contrary way to the other experts. Thus, differing opinions or minority preferences are often referred to as obstacles to decision-making. This article develops a consensus model to manage minority opinions and noncooperative behaviors in LSGDM with DHLPRs. In addition, to establish the consensus model, some basic tools, such as the clustering method, weights-determining method, and adjustment coefficients-determining method, are developed. Finally, a practical LSGDM problem is set up to prove that the proposed consensus model is feasible and effective, and some comparative analyses are made to highlight the advantages of these methods and models, as well as to analyze current deficiencies.

A k-core decomposition-based opinion leaders identifying method and clustering-based consensus model for large-scale group decision making

Due to the development of network technology, large-scale group decision making (LSGDM) has become increasingly concerned. In this paper, a k-core decomposition-based opinion leaders identifying method and clustering-based consensus model are developed for LSGDM problems. Firstly, a clustering method based on similarity degree is provided for dividing decision makers (DMs) into several clusters. Then, sub-clusters are presented for social networks (SNs) construction process, which are consist of DMs with same alternative ranking information. Furthermore, a novel k-core decomposition-based opinion leaders identifying method is proposed for selecting opinion leaders of these SNs. Finally, the opinion leaders identified are applied to the following clustering-based consensus model in LSGDM. The weights of DMs are distributed appropriately and the group can efficiently reach a consensus based on the proposed social network analysis (SNA) methods and consensus reaching process (CRP). A case study on flood disaster management shows that the proposed methods are feasible for LSGDM problems.

Network-based evidential three-way theoretic model for large-scale group decision analysis

Social relationships are critical to the group decision-making (GDM) process, especially for large-scale scenarios. Conventional GDM models have several drawbacks when applied to large-scale GDM problems. In this paper, we propose an evidential three-way theoretic model for large-scale group decision analysis based on the introduction of ego networks. A similarity matrix of all individuals is obtained after ego network generation via social network feature extraction. Rough and smooth detection are then conducted in the framework of three-way decisions. Specifically, the degree of organizational influence is analyzed based on the generated basic probability assignments (BPAs), and the individuals are divided into several organizations. After an opinion collection process, preference evolution is implemented via a social influence network (SIN) technique and a fuzzy preference relation (FPR) model. Then, the global final scores of all the alternatives are obtained using an aggregation process. Finally, we conduct a simulation experiment to illustrate the entire procedure. Based on a comparison of related methods, we believe that the proposed method can reasonably solve real-world large-scale group decision-making (LSGDM) problems and has good practicability and effectiveness.

A PSO-algorithm-based consensus model with the application to large-scale group decision-making

Group decision-making (GDM) implies a process of extracting wisdom from a group of experts. In this study, a novel GDM model is proposed by applying the particle swarm optimization (PSO) algorithm to simulate the consensus process within a group of experts. It is assumed that the initial positions of decision-makers (DMs) are characterized by pairwise comparison matrices (PCMs). The minimum and maximum of the entries in the same locations of individual PCMs are supposed to be the constraints of DMs’ opinions. The novelty comes with the construction of the optimization problem by considering the group consensus and the consistency degree of the collective PCM. The former is to minimize the distance between the collective PCM and each individual one. The latter is to make the collective PCM be acceptably consistent in virtue of the geometric consistency index. The fitness function used in the PSO algorithm is the linear combination of the two objectives. The proposed model is applied to solve a large-scale GDM problem arising in emergency management. Some comparisons with the existing methods reveal that the developed model has the advantages to decrease the order of an optimization problem and reach a fast yet effective solution.

Dynamic subgroup-quality-based consensus in managing consistency, nearness, and evenness quality indices for large-scale group decision making under hesitant environment

With the increasing complexity of decision-making environment and the development of societal demands, large-scale group decision making (LSGDM) has become a hot topic in recent years. Due to the demand of the current decision-making environment, up to now, studies regarding LSGDM methods focussing on different approaches have been published. However, there are few studies that focus on evaluating the results of LSGDM problems. This study proposes three subgroup quality indices, namely, consistency degree, nearness degree and evenness degree, to measure the effectiveness of LSGDM methods. These three quality indices not only can evaluate the effect of a subgroup on the global group, but also can measure the effect of final decision results. Furthermore, the consistency measure is used to design the weights of subgroups, based on which an adaptive dynamic consensus reaching process is introduced. An illustrative example is given to verify the applicability and effectiveness of our proposed model.

Social network community analysis based large-scale group decision making approach with incomplete fuzzy preference relations

Large-scale group decision making (LSGDM) is characterized by a large number of participators, multiple groups and a mass of decision data provided by the participators. With the development of social media and e-democracy technologies, the social relationships among group decision makers should be taken into consideration when we address LSGDM problems with incomplete fuzzy preference relations. In this paper, a social network community detection approach of social networks based on the fuzzy clustering method is proposed. Then, a method of repairing incomplete fuzzy preference relations based on the divided communities is proposed. Moreover, we have proposed a two-stage consensus reaching method to balance the number of iterations and modification range of original decision information, in which the group closeness centrality of community is applied to measure its importance. Also, the procedure for LSGDM with fuzzy preference relations based on social network community analysis is established. The feasibility and advantages of the proposed method for LSGDM based on social network community analysis are illustrated by an illustrative example of a flexible manufacturing system.

Managing Multigranular Unbalanced Hesitant Fuzzy Linguistic Information in Multiattribute Large-Scale Group Decision Making: A Linguistic Distribution-Based Approach

With the increase of technological and societal demands, more and more decision makers are involved in the process of group decision making, which is called large-scale group decision making (LGDM). For an LGDM problem with linguistic information, it is common that different decision makers tend to provide linguistic assessments defined on multigranular linguistic term sets due to the difference in knowledge and culture background, and that hesitant fuzzy linguistic term sets (HFLTSs) are used by decision makers to model the hesitancy of their assessments. This article proposes first an algorithm to represent a linguistic distribution assessment (LDA) using a hesitant linguistic distribution (HLD). Two other algorithms are then proposed to transform an unbalanced HFLTS into a balanced LDA and to transform a balanced LDA into an unbalanced LDA, respectively. An approach is then proposed to deal with multiattribute LGDM problems with multigranular unbalanced hesitant fuzzy linguistic information based on these algorithms. In the proposed approach, all unbalanced hesitant fuzzy linguistic information is transformed into LDAs defined on a balanced linguistic term set, and then an LDA-based clustering algorithm is devised to cluster decision makers. Based on the clustering result, decision makers’ linguistic distribution decision matrices are further fused to obtain collective assessments of alternatives. In order to provide easy-to-understand linguistic results for decision makers, all LDAs of alternatives are represented by HLDs defined on each decision maker's initial linguistic term set. Finally, an example for the selection of subway lines is used to demonstrate the proposed approach.

Social Recommendation With Large-Scale Group Decision-Making for Cyber-Enabled Online Service

Along with the development of several emerging computing paradigms and information communication technologies, it is said that cyber computing technology is playing an increasingly important role across cyber-related systems and applications. In this article, we focus on cyber–social computing and propose a computational model that integrates large-scale group decision-making (LSGDM) into social recommendations for cyber-enabled online services. As a concrete application example, a graph model is built to describe the LSGDM problem among researchers in scholarly big data environments. Following the basic profiling to describe decision-makers within scholarly networks, measures are defined to evaluate one researcher’s academic performance and research outcome and further quantify correlations between them based on their collaboration relationships in a constructed network model. A two-stage large-scale decision-making solution is then proposed for social recommendations: A network partition algorithm is developed based on the identification of experts along with their influence extending to a group of researchers, and a random walk with the restart-based algorithm is improved to calculate the weighted decisions for group decision aggregation and alternative ranking. Experiments using the real-world data demonstrate the usefulness and effectiveness of our proposed model and method, which can provide the target researcher with more reliable recommendations.

Social network analysis-based consensus-supporting framework for large-scale group decision-making with incomplete interval type-2 fuzzy information

Experts are assumed to be mutually independent and incomplete decision matrices are used, in traditional large-scale group decision-making (LSGDM). Social network analysis (SNA) methods are useful for managing LSGDM problems considering the social relationships among experts. This study develops a novel SNA-based decision framework for addressing LSGDM problems with incomplete interval type-2 fuzzy information. First, a community detection algorithm is designed to classify experts, and a trust propagation and aggregation mechanism is developed to obtained experts’ indirect trust values and weights based on the social trust network. Second, a multi-objective programming model integrated with trust relationships among experts is constructed to estimate the missing values in incomplete interval type-2 fuzzy decision matrices. The proposed estimation approach is robust and effectively estimates missing values while maintaining high discrimination levels. Subsequently, an SNA-based consensus-reaching model is designed for achieving a group consensus based on a twofold feedback adjustment mechanism, namely, adaptive judgment and weight feedback. Finally, an illustrative example is presented to demonstrate the applicability of the proposed approach. A simulation and comparison study is conducted to verify the efficiency and advantages of the SNA-based consensus-supporting framework for LSGDM.

Large-scale group decision making with multiple stakeholders based on probabilistic linguistic preference relation

A large number of stakeholders take part in the process of decision making, namely, large-scale group decision making (LGDM) problems. Every stakeholder utilises a linguistic preference relation (LPR) to represent her/his preference information for alternatives. Then, a probabilistic LPR (PLPR) is established to represent the group preference. However, some stakeholders may only provide partial preference information about the alternatives. Thus, a PLPR with incomplete probabilities can be used to manage LGDM problems in complex environments. Based on the defined expected multiplicative consistency of PLPR, a probability computation model is established by mathematical programming to derive the missing probabilities of PLPR. In addition, an iterative algorithm to improve the consistency is proposed to obtain the PLPR with satisfactory consistency. Finally, a real-world investment decision-making problem with multiple stakeholders is solved to demonstrate the effectiveness of the proposed method.

Linguistic Distribution-Based Optimization Approach for Large-Scale GDM With Comparative Linguistic Information: An Application on the Selection of Wastewater Disinfection Technology

Managing comparative linguistic expressions (CLEs) information is a key issue in group decision-making (GDM). A transformation approach has been previously defined to convert CLEs into hesitant fuzzy linguistic terms sets (HFLTSs). However, it is noted that the occurring possibilities of the linguistic terms in the HFLTSs are assumed equal. This assumption might sometimes not capture the real opinions of the decision makers. Linguistic distribution assessments (LDAs) are an effective way to deal with this issue. This paper develops a linguistic distribution-based optimization approach for converting CLEs into LDAs, in which we assume that decision makers provide their opinions using preference relations with CLEs. Particularly, the proposed optimization approach is based on the use of a consistency-driven methodology, which seeks to minimize the inconsistency level of LDA preference relations obtained by transforming the original CLE preference relations elicited from decision makers. The linguistic distribution-based optimization approach is further developed to transform CLEs into interval LDAs to increase their flexibility. Moreover, society and technology trends make it possible to involve and manage large groups of decision makers in GDM environment. Therefore, a large-scale GDM framework with CLE information is designed based on the linguistic distribution-based optimization approach. To justify the effectiveness and applicability of the proposed methodology, it is applied to solve a real large-scale GDM problem, pertaining the selection of the best sustainable disinfection technique for wastewater reuse projects. A comparison against a baseline method is likewise provided to highlight the advantages and innovations of our proposal.

A clustering method for large-scale group decision-making with multi-stage hesitant fuzzy linguistic terms

A large-scale group decision-making (LGDM) problem is studied from the perspective of multi-stage hesitant fuzzy linguistic term sets (MHFLTSs). Solving an LGDM problem requires two processes: a clustering process is helpful for breaking down the larger problem into smaller pieces for simplification purposes, and a selection process is utilized for obtaining a final solution. Along with the MHFLTSs, the decision-making process should include consideration of the distinctiveness of the term sets. With this idea in mind, we propose a clustering method and a selection method based on consideration of multiple reference points derived from the MHFLTSs. First, taking into account the HFLTS characteristics, an expert similarity measurement is proposed based on both the expectation distance and hesitancy similarity between two HFLTSs. Second, multiple reference points are examined: a positive ideal reference point and a development reference point. Reference similarity is then measured by combining these two points. With the goal of maximizing the reference similarity of the alternatives, the third element is the establishment of an optimization model for determining the stage and attribute weights based on consideration of the sensitivity of these two weights to the problem. In the fourth step, a fuzzy clustering method is applied in order to create expert clusters based on expert similarity as well as on the stage and attribute weights. An additional feature is a selection analysis based on the reference similarity between the cluster centers, which entails consideration of the degree of certainty of each cluster as a measure of cluster weighting. The final phase of the research is the application of the proposed method to two cases as a means of illustrating the applicability and feasibility of the new method.

Alternative Ranking-Based Clustering and Reliability Index-Based Consensus Reaching Process for Hesitant Fuzzy Large Scale Group Decision Making

Recently, large scale group decision making (LSGDM) problems have become a hotspot. This paper focuses on hesitant fuzzy LSGDM problems where decision makers (DMs) use hesitant fuzzy preference relations (HFPRs) to express their assessment information. HFPRs can represent the fuzziness and hesitancy of DM assessment information well. To improve the efficiency of hesitant fuzzy LSGDM problems, we first propose a reliability index-based consensus reaching process (RI-CRP). By assessing the ordinal consistency of DM's assessment information and measuring the deviation from collective opinion, the DM's opinion reliability index is given. To avoid unreliable information, we propose an unreliable DM management method to be used in the RI-CRP, based on the computation of DM's opinion reliability index. Moreover, an alternative ranking-based clustering (ARC) method with HFPRs is proposed to improve the efficiency of the RI-CRP. The similarity index between two DMs’ opinions is provided to ensure the ARC method can be effectively implemented. Compared with those clustering methods which need to preset several correlated parameters, the presented ARC method is more objective with a different approach based on the alternative ranking. A numerical example shows that the proposed ARC method and the RI-CRP are feasible and effective for hesitant fuzzy LSGDM problems.

A two-stage social trust network partition model for large-scale group decision-making problems

With the development of big data and social computing, large-scale group decision making (LGDM) problems attract much attention and become merging with social networks or behavioral factors. In this paper, by considering the trust of social behavioral factor, a two-stage trust network partition algorithm is proposed to reduce the complex of LGDM problems. The large-scale decision makers (DMs) are classified into some leader–follower sub-networks through a network partition algorithm. And a solution method based on trust relationship is proposed to keep the independency of the sub-networks when one follower belongs to more than one leader. Next, weights of independent sub-networks and their individual members are computed, and are further used to aggregate the comprehensive decision information. Finally, alternatives of LGDM problems are sorted with the comprehensive decision information. An experiment with MovieLens data is given to illustrate the proposed LGDM algorithm. And a comparison analysis with general clustering method is provided to verify the effectiveness and feasibility of the proposed method.

An interval type-2 fuzzy TOPSIS model for large scale group decision making problems with social network information

Large scale group decision making (LGDM) problems and social network analysis (SNA) methods are both attracting increasing attention, and SNA methods are useful for addressing LGDM problems. By considering social network information, a new interval type-2 fuzzy TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) model is proposed to solve LGDM problems in complex and uncertain environments. First, a SNA community detection method is applied to reduce the complexity of large scale decision makers (DMs) according to the social connections among them. Then, interval type-2 fuzzy sets (IT2 FSs) and linguistic variables are employed to handle the uncertainties, and the TOPSIS method is improved using IT2 FSs to obtain an optimal alternative for a LGDM problem. Next, decision weights are computed based on the centrality of the SNA, and the decision information is aggregated by the interval type-2 fuzzy weighted average method. The procedure for solving LGDM problems is presented. Finally, an illustrative example is investigated to demonstrate the feasibility of the proposed solution for LGDM problems, and the results are compared with those of an existing method to verify the validity of the new proposed method.

An improved consensus-based group decision making model with heterogeneous information

In group decision making (GDM) problems, it is natural for decision makers (DMs) to provide different preferences and evaluations owing to varying domain knowledge and cultural values. When the number of DMs is large, a higher degree of heterogeneity is expected, and it is difficult to translate heterogeneous information into one unified preference without loss of context. In this aspect, the current GDM models face two main challenges, i.e., handling the complexity pertaining to the unification of heterogeneous information from a large number of DMs, and providing optimal solutions based on unification methods. This paper presents a new consensus-based GDM model to manage heterogeneous information. In the new GDM model, an aggregation of individual priority (AIP)-based aggregation mechanism, which is able to employ flexible methods for deriving each DM's individual priority and to avoid information loss caused by unifying heterogeneous information, is utilized to aggregate the individual preferences. To reach a consensus more efficiently, different revision schemes are employed to reward/penalize the cooperative/non-cooperative DMs, respectively. The temporary collective opinion used to guide the revision process is derived by aggregating only those non-conflicting opinions at each round of revision. In order to measure the consensus in a robust manner, a position-based dissimilarity measure is developed. Compared with the existing GDM models, the proposed GDM model is more effective and flexible in processing heterogeneous information. It can be used to handle different types of information with different degrees of granularity. Six types of information are exemplified in this paper, i.e., ordinal, interval, fuzzy number, linguistic, intuitionistic fuzzy set, and real number. The results indicate that the position-based consensus measure is able to overcome possible distortions of the results in large-scale GDM problems.

A two-stage dynamic group decision making method for processing ordinal information

In group decision making (GDM) problems, ordinal data provide a convenient way of articulating preferences from decision makers (DMs). A number of GDM models have been proposed to aggregate such kind of preferences in the literature. However, most of the GDM models that handle ordinal preferences suffer from two drawbacks: (1) it is difficult for the GDM models to manage conflicting opinions, especially with a large number of DMs; and (2) the relationships between the preferences provided by the DMs are neglected, and all DMs are assumed to be of equal importance, therefore causing the aggregated collective preference not an ideal representative of the group’s decision. In order to overcome these problems, a two-stage dynamic group decision making method for aggregating ordinal preferences is proposed in this paper. The method consists of two main processes: (i) a data cleansing process, which aims to reduce the influence of conflicting opinions pertaining to the collective decision prior to the aggregation process; as such an effective solution for undertaking large-scale GDM problems is formulated; and (ii) a support degree oriented consensus-reaching process, where the collective preference is aggregated by using the Power Average (PA) operator; as such, the relationships of the arguments being aggregated are taken into consideration (i.e., allowing the values being aggregated to support each other). A new support function for the PA operator to deal with ordinal information is defined based on the dominance-based rough set approach. The proposed GDM model is compared with the models presented by Herrera-Viedma et al. An application related to controlling the degradation of the hydrographic basin of a river in Brazil is evaluated. The results demonstrate the usefulness of the proposed method in handling GDM problems with ordinal information.