Elsevier

Information Sciences

Volume 547, 8 February 2021, Pages 689-709
Information Sciences

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

https://doi.org/10.1016/j.ins.2020.08.042Get rights and content

Abstract

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.

Introduction

Group decision making (GDM) is a type of participatory procedure involving a certain number of experts or decision makers. Typically, individuals are required to provide their opinions regarding several alternatives. Final scores are obtained via opinion collection, communication, evolution and aggregation [25]. In most real-life scenarios, experts engage in the discussion process with others, and through such iterations, their individual opinions may change. Thus, the influence of social relationships has received increasing attention in recent years [17], [1]. We make the essential assumption that experts are more willing to accept the opinions of colleagues with whom they have better working relationships [18]. In this context, a type of social network group decision-making (SNGDM) problem has emerged and become a research hotspot; in this problem, a series of techniques for modeling influence, such as social network analysis (SNA) [30] and the social influence network (SIN) [4], [7], play vital roles. In [17], SNA metrics are used to estimate the influence between experts, and global opinions are obtained over several iterations. Furthermore, the representation of the uncertainty contained in opinions has also developed through the use of several related tools, such as evidence theory [20] and rough set theory [39].

However, with the development of modern decision science, situations now occur involving a large number of experts or decision makers who have been employed to select from among alternatives. Hence, a common form of decision problem, called large-scale group decision making (LSGDM), has recently begun attracting widespread interest [24]. In such scenarios, the traditional GDM models may not be effective. For instance, when the opinions of too many experts are considered, it is difficult to analyze each person’s opinions individually. Moreover, as mentioned above, when applying SIN techniques, there is a correlation between the speed and complexity of opinion convergence and the number of experts. Furthermore, as the number of iterations increases, the sensitivity of the preference evolution process to noise also increases, and the accuracy and reliability of the convergence results decrease. Take [1] for instance; Capuano et al. introduced an advanced fuzzy GDM model that considers the interpersonal trust among experts. Experts are required to provide a fuzzy ranking of the other experts and the alternatives, and by means of a series of transitional steps, global opinions can be obtained after several iterations. However, when the number of experts increases too rapidly, the preference evolution processes are difficult to complete.

Several scholars have developed advanced models to address such issues [19], [33], [47], [43]. For example, Liu et al. [19] illustrates a novel LSGDM method based on the evaluation results of an identifier set, whereas Wu et al. [33] developed an interval type-2 fuzzy technique that determines order of preference by similarity to an ideal solution (TOPSIS) model that considers social network information. Zhang et al. used multigranular linguistic distribution assessment to preserve the maximum amount of information during the initial LSGDM stages [47] via an optimization procedure. Zahir proposed a clustering method to classify LSGDM participants into several homogeneous organizations [43]. One effective framework for addressing such LSGDM problems among participants divides the experts into several organizations, an approach that implements the concept of granular computing [6], [9]. Related approaches achieve good performance in solving LSGDM problems, which demonstrates the effectiveness of the framework. Nevertheless, several aspects of the existing models still remain to be optimized. These aspects can be organized as follows.

  • Analysis of individual-based social features: Most existing partition models are based on the topological relationships within the global social network [48]. In the field of complex networks, for the community structure, the connections between vertices within a group are dense, while the connections between vertices belonging to different groups are sparse [23]. However, in a real-life LSGDM environment, nodes located closely together in the network may not always be similar. Hence, the features of individual-based social relationships (social circles) are also highly important.

  • Employment of advanced division method: Most traditional clustering-based community detection methods are based on two-way decisions (hard clustering in many cases) in which an acceptance or rejection decision is made based on current information, despite the potential for such information to be incomplete or insufficient [33], [30]. However, situations in which individuals possess features of multiple organizations commonly occur (within overlapping regions) in the LSGDM process. Hence, the optimization of more advanced techniques deserves exploration.

  • Evaluation of reasonable organizational importance: The importance (influence) of organizations in most existing literature is extracted as the number of individuals within each organization during the aggregation process (for instance, in [44]). However, this measure of importance is unreasonable considering the limitations of the clustering process, especially in situations in which many individuals have multiple organizational features. In other words, the individuals within overlapping regions should be carefully considered when generating an organizational importance measure.

Clearly, it is critical to advance the framework for handling such issues, especially modeling the uncertainty contained in overlapping regions. An effective alternative is the three-way theoretic framework [41]. In detail, the three-way decision is a human cognition-based decision-making framework based on a belief that people can make quick judgments on items when they have a full grasp of acceptance or rejection; and when they cannot make an immediate decision on the item in the decision-making process, they often postpone the judgment of the event, that is, they defer the decision. Considering its advantages in lowering decision-making risk during the analysis procedure, such a theoretic framework has been widely explored. For instance, the trisecting-acting-outcome (TAO) model was well developed in [40] with a discussion on the two fields of three-way decisions and granular computing. Zhang et al. investigated game-theoretic shadowed sets, which can well determine the thresholds of three-way approximations based on a tradeoff principle with games [46]. A decision model involving decision-theoretic rough sets with multiple decision makers under the linguistic evaluation information-based three-way decision framework was also well presented [29]. In addition, a GDM-based three-way decision model was also discussed in [16], which proves its potential for application to more complex decision environments. In [45], the interval-valued scenario was also discussed considering the aggregating inclusion measures. Recently, this advanced framework has been the subject of widespread interest and applied in many fields. For instance, Chen et al. found support for three-way decisions in diagnosing focal liver lesions [3]. Yao et al. discussed web-based medical decision support system applications [38]. In [15], Liang et al. investigated a novel risk decision-making methodology that considered hesitant fuzzy information. In [11], Gao et al. applied such a framework in the target threat assessment field. In [50], three-way decision-based research into optimizing the industry research on new-energy vehicles was discussed. The core idea behind three-way decision making is adding a deferment decision to avoid high risk when the currently available information is insufficient. With regard to clustering-based community detection, a three-way representation of a community (cluster) can be formulated using an interval set that divides a community into three regions: a core region, a fringe region and a trivial region [39], which is an effective application of three-way decision theory. Compared with hard clustering approaches, three-way clustering has shown its potential for use in other more complex applications. In [41], the detection of overlapping regions based on a three-way decision framework was well developed. Furthermore, Zhao et al. introduced the general definition of a three-way fuzzy partition with the introduction of two sets of properties, and it can be applied to dealing with clustering tasks more effectively [49].

In this study, we propose an evidential three-way theoretic LSGDM model based on ego networks. Based on the actual social phenomenon, the assumption that experts or decision makers with similar personal social circles are more likely to provide identical opinions is reasonable. Specifically, personal social circle information is extracted by generating ego networks, which have been widely used to discover and model social circles [21]. Given a social network containing decision makers and experts, we first generate all the possible ego networks and construct a similarity matrix. Rough detection is then implemented to perform an initial organizational division. Furthermore, the mass function, one of the main concepts in Dempster-Shafer evidence theory, is introduced to model the overlapping areas. Then, the proposed organization influence degrees (OIDs) can be calculated through the measure-based Shapley value. A designed smooth detection process is employed to classify fringe nodes. In addition, a fuzzy adjacency matrix of the SIN for each organization can be constructed via the initial opinion collection. After preference evolution, the opinions of each organization are obtained. Eventually, the final scores of all the alternatives are obtained via several advanced aggregation methods.

Below, we highlight the main contributions of this study:

  • 1) We propose an evidential three-way theoretic decision framework based on the network structure to effectively address LSGDM problems;

  • 2) The individual-centric social relationships of large-scale experts are analyzed based on the proposed similarity degree through the introduction of ego networks;

  • 3) We investigate both rough and smooth detection procedures to partition organizations when applying the three-way decision analysis framework;

  • 4) The proposed label-matching algorithm and the reliability degree can be utilized to make reasonable judgments on the optimal partition results;

  • 5) An OID is effectively modeled by extracting the measure-based Shapley value after the BPA generation process.

The remainder of this article is organized as follows. In Section 2, the background and basic concepts are introduced. In Section 3, which is divided into eleven parts, the proposed methodology is illustrated in detail to demonstrate the complete procedure. In Section 4, we report the results of a simulation experiment of the proposed methodology applied to large-scale group decision analysis. A comparative analysis and discussion are also presented. Finally, conclusions are briefly summarized in Section 5.

Section snippets

Preliminaries

In this section we briefly introduce several basic concepts, including the SIN, the ego network, the three-way decision framework, and evidence theory.

The proposed evidential three-way theoretic LSGDM methodology

In real-life scenarios, such as leader election, a large number of experts may need to participate in the decision-making process; thus, the process of unifying rational opinions plays a vital role in such scenarios. In this study, we propose a novel three-way theoretic LSGDM approach based on ego networks. Specifically, multiple random clustering processes are utilized to extract uncertain information to complete the rough detection of organizations that contain several individuals. Then, DSET

Experimental Evaluation

In this section, a simulation experiment is conducted to demonstrate the proposed methodology, and a comparison is presented between the approaches in several related works and the proposed methodology. In addition, we provide an analysis of the proposed methodology.

Conclusion

Social relationships are a crucial factor in solving LSGDM problems. In this paper, we investigated a network-based evidential three-way theoretical LSGDM framework. Social relationships are modeled through a similarity degree analysis based on pairwise ego networks. We defined rough and smooth detection procedures to partition organizations by applying a three-way decision analysis framework. Additionally, we utilize the measure-based Shapley value and the BPA generation process to extract the

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Zeyi Liu is currently pursuing the bachelor’s degree with the School of Computer and Information Science, Southwest University, China. He is also serving as a research assistant of University of Electronic Science and Technology of China and Tsinghua University . His research interests include social network analysis, information fusion, decision making, safety assessment and fuzzy logic. His research results have been published in refereed journals, including IEEE TRANSACTIONS ON SYSTEMS, MAN,

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    Zeyi Liu is currently pursuing the bachelor’s degree with the School of Computer and Information Science, Southwest University, China. He is also serving as a research assistant of University of Electronic Science and Technology of China and Tsinghua University . His research interests include social network analysis, information fusion, decision making, safety assessment and fuzzy logic. His research results have been published in refereed journals, including IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS: SYSTEMS, Information Sciences, International Journal of Intelligent Systems, Applied Intelligence, Entropy, among others.

    Xiao He received the B.E. degree in information technology from the Beijing Institute of Technology, Beijing, China, in 2004, and the Ph.D. degree in control science and engineering from Tsinghua University, Beijing, China, in 2010. Currently, he is a tenured Associate Professor with the Department of Automation, Tsinghua University. He has authored more than 60 papers in refereed international journals. His research interests include fault diagnosis and fault tolerant control, networked systems, Cyber-Physical Systems, as well as their application. Dr. He is now a Full Member of Sigma Xi, the Scientific Research Society, and a Senior Member of Chinese Association of Automation. He is an Associate Editor of the Control Engineering Practice.

    Yong Deng received the Ph.D. degree in precise instrumentation from Shanghai Jiao Tong University, Shanghai, China, in 2003. From 2005 to 2011, he was an Associate Professor with the Department of Instrument Science and Technology, Shanghai Jiao Tong University. Since 2010, he has been a Professor with the School of Computer and Information Science, Southwest University, Chongqing, China. Since 2012, he has been a Visiting Professor with Vanderbilt University, Nashville, TN, USA. Since 2016, he has been a Professor with the School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an, China. Since 2017, he has been a Full Professor with the Institute of Fundamental and Frontier Science, University of Electronic Science and Technology of China, Chengdu, China, and also an Adjunct Professor with the Medical Center, Vanderbilt University. He has published more than 100 articles in refereed journals. His research interests include evidence theory, decision making, information fusion, and complex system modeling. He served as the Program Member of many conferences, such as the International Conference on Belief Functions. He served many editorial board member positions, such as Editorial Board Member of Applied Intelligence and Journal of Organizational and End User Computing. He served as a Guest Editor, such as International Journal of Approximate Reasoning, Mathematical Problems in Engineering, and Sustainability. He served as the Reviewer for more than 30 journals. Since 2014, he has received numerous honors and awards, including the Elsevier Highly Cited Scientist, in China.

    The authors greatly appreciate the reviewers’ suggestions and the editor’s encouragement. This work was supported by National Key Research and Development Program of China under Grant 2017YFA0700300, National Natural Science Foundation of China under Grants 61733009, 61973332 and Key Project from Natural Sciences Foundation of Guangdong Province under Grant 2018B030311054.

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