During the consensus reaching process (CRP), decision makers (DMs) typically achieve the desired consensus through discussion and persuasion. In this process, the moderator invests time and resources to persuade the DMs to change their opinions. Consequently, various interaction behaviors occur during the CRP, encompassing interactions between the moderator and DMs, as well as interactions among DMs. This article aims to develop a minimum cost-based consensus model by considering these interaction behaviors during the CRP. We utilize a network game to model the interplay among the behaviors of DMs and employ the Stackelberg game architecture to design an interactive mechanism between the DMs and the moderator. In the proposed model, the moderator provides compensation strategies and feedback suggestions to guide the DMs toward achieving the desired consensus level with minimal consensus cost. Meanwhile, the DMs adjust their opinions with the aim of maximizing their satisfaction. We then present an equilibrium analysis for the proposed model. Finally, we conduct an example application to illustrate and justify the performance of the proposed model.

With the rapid advancement of information and network technologies, the landscape of art communication has undergone significant transformation. Among various platforms, WeChat stands out for its robust social features, emerging as a central hub for professional artists to connect and collaborate. Leveraging WeChat’s unique capabilities for group interactions, this paper explores a consensus adjustment mechanism specifically designed for group decision-making in online art evaluations. The approach begins by segmenting decision-makers into subgroups based on their social network connections within WeChat, followed by an analysis of interpersonal tie strength within each subgroup. To enhance collaboration, the mechanism incorporates strategies to identify and address non-cooperative behaviors, ensuring effective management of such challenges. A case study on art evaluation demonstrates the practical value and efficacy of the proposed mechanism, highlighting its potential to enrich decision-making processes in digital art communities.

The multiple criteria decision-making (MCDM) problem is a significant issue in various aspects of social life. In many practical cases, decision makers (DMs) care not only about the ranking results but also the sorting results, and they may provide holistic estimations for decision-making problems. To leverage these holistic estimations effectively and address both the sorting and ranking results, in this paper, we design three novel case-based distance sorting (CBDS) methods for ranking alternatives and clustering them into predefined categories using probabilistic linguistic information within the MCDM framework. First, to determine the optimal alternative, we propose a new method based on the comparison rules for probabilistic linguistic term sets (PLTSs). Then, we introduce a method of checking the consistency of DMs' preferences and establish a mathematical programming model to identify the consistent preference subsets, thereby maintaining the consistency. Furthermore, we develop an algorithm to identify all consistent preference subsets of a DM and establish three novel CBDS methods that explicitly account for DMs' preference inconsistencies and the number of alternatives. Finally, we apply our methods in a case study that clusters disabled elders into three categories to demonstrate both the effectiveness and practicability of the proposed approaches. A robust test shows that the framework preserves the best and worst alternatives while yielding highly consistent rankings.

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.

In linguistic group decision-making (GDM), achieving consistency and consensus is crucial and has attracted significant academic interest. This paper explores GDM scenarios in which decision-makers (DMs) evaluate alternatives based on objective information on criteria, utilizing incomplete linguistic preference relations (ILPRs) to express their preferences. We propose an innovative multi-criteria consensus model that integrates personalized individual semantics (PIS) with preference analysis to uncover the dynamic evaluation strategies of DMs within multi-criteria GDM contexts. Our method effectively manages incomplete preference data without requiring the imputation of missing values, focusing instead on revealing the intrinsic preferences embedded in the available information. This approach integrates attribute weight vectors, derived from each DM's ILPRs and objective information on criteria, as decision variables within the preference analysis model, enabling nuanced interpretations of linguistic terms. We begin by enhancing the consistency of individual ILPRs through the PIS method, accommodating the diverse perspectives of DMs. Next, an optimization model translates ILPRs and objective information on criteria into criteria-specific preferences represented by weight vectors, revealing underlying preference patterns. Subsequently, a feedback mechanism is constructed based on the mined preference information to progressively enhance group consensus. The effectiveness of the proposed model and algorithm is validated through numerical results and simulation analyses, demonstrating their accuracy, resilience, and practical applicability.

Nowadays, social networks and mobile internet have become prominent features of daily life, leading to increasingly interconnected relationships among decision-makers (DMs). The social network group decision- making (SNGDM) method uses social network analysis technology to consider the impact of social trust relationships among DMs on decision results during the decision-making process. The Utilites Additives (UTA) method can infer the DMs' preference structure based on the partial preference information. This method effectively resolves the consensus problem in SNGDM by utilizing the DMs' preference structure. This paper proposes a novel SNGDM method based on the UTA method that considers the consistency of preference information provided by DMs in the form of pairwise comparisons. Firstly, since the trust relationship between DMs is asymmetric and DM's opinions are usually different, a new preference conflict degree between DMs in SNGDM is defined. Then, to consider the opinion differences and social trust relationship between DMs in the clustering process, a clustering method based on the preference conflict degree is proposed. Furthermore, to obtain the maximal subsets of consistent pairwise comparisons for each DM, we designed a simulation algorithm involving an optimization model to examine the pairwise comparisons provided by the DMs and to obtain the maximal subsets of consistent pairwise comparisons. Moreover, since using only preference information in the form of pairwise comparisons in the consensus reaching process (CRP) leads to a limited space for changes in DMs' opinions, a method for converting the opinions of DMs based on maximal subsets of consistent pairwise comparisons is proposed. This method transforms pairwise comparisons provided by DMs into fuzzy preference relations (FPRs). In addition, in the CRP, a method for adjusting the FPRs of DMs is proposed. Finally, a case study is conducted using real data on new energy vehicles from Autohome to illustrate the effectiveness of the proposed method.

Social network group decision-making (SNGDM) provides support for obtaining consistent decision results based on social trust relationships between individuals. However, excessive internal conflict level within clustered subgroups may affect the consensus reaching process (CRP). To solve this problem, it may be necessary to assign some decision-makers (DMs) to two or more subgroups simultaneously during the clustering process. This paper investigates the CRP in the context of SNGDM problems with overlapping DMs. Firstly, taking into account the trust degree and evaluation conflict degree between DMs, we propose a definition of comprehensive evaluation conflict network in SNGDM. Then, we introduce a DM overlapping clustering method based on the FloydWarshall algorithm. The method takes into account the comprehensive evaluation conflict degrees among DMs and is capable of identifying overlapping DMs belonging to multiple clustered subgroups. Furthermore, we propose a two-stage opinion adjustment process that takes into account overlapping DMs. This process provides an opinion adjustment strategy for DMs when the consensus states across the multiple subgroups they belong to differ. Moreover, we design a consensus determination mechanism based on stochastic multi-criteria acceptability analysis method, which can reduce the impact of subjectively given criteria weights on the accuracy of SNGDM results. Finally, we use an elderly care service provider evaluation case to illustrate the effectiveness of our proposed method. Results indicate that the proposed method can effectively identify overlapping subgroups and overlapping DMs, and the proposed method can solve the SNGDM problems when DMs can not provide preferences for criteria weights.

Interaction behaviors play a core role in the process of reaching a consensus. In this article, a network game is employed to model the interplay between the behaviors of decision makers (DMs) and Stackelberg game architecture is used to design an interactive mechanism between the DMs and the moderator. An optimization model based on these two games results in a consensus model with maximum linear-quadratic payoffs and minimum adjustment (MPMACM). In the proposed MPMACM, the moderator provides compensation strategies and feedback suggestions to guide the DMs to reach the desired consensus level with minimum adjustment, while the DMs adjust their opinions aiming to obtain their maximum payoffs. We present the equilibrium analysis for the MPMACM, and an adaptive differential evolution algorithm is offered to enact this optimization model. Finally, an example application is conducted to illustrate and justify the performance of the MPMACM.

Spent lithium-ion battery (LIB) recycling can create great pollution to the environment. Understanding the safety, environment, technique, and regulation factors’ impact on the recycling process is crucial. Due to the complexity of the relevant factors, and there is a certain degree of correlation and dependence between the factors, the Decision Making Trial and Evaluation Laboratory (DEMATEL) method is used to analyze the factors’ degree of impact in this study. As the experts are ambiguous about some relations between the factors, it is impossible to conduct integrated evaluation. The improved DEMATEL method is proposed in this study to make up the missing relations. Further, the weights of the factors will be calculated. In the improved DEMATEL method, the numerical scale of a linguistic term set is introduced. Therefore, the numerical scale used by experts can not only be uniform and symmetrical, but can also be non-uniform symmetric, non-uniform asymmetric, etc. Finally, both reusing and recycling companies are included in this study and their factors’ importance weights were analyzed with the fuzzy comprehensive evaluation method.

Trust network analysis has been widely applied in various fields, such as group recommendation, group decision-making and other related areas. In this paper, we focus on obtaining the complete trust network in which experts express their trust relationships for another with a single linguistic term or distribution assessments of a linguistic term set. We first discuss the conditions of obtaining the complete trust network, and the propagation and aggregation of the trust relationships with a single linguistic term. Since the linguistic term set may be symmetric and uniform, symmetric and non-uniform, or asymmetric and non-uniform, we translate linguistic terms into numerical indexes and define the propagation operator based on the semantics of the linguistic term and the Archimedean t-norm. The propagation result is translated to 2−tuple linguistic model because it may not exist in the initial linguistic term set. Some properties are proposed to verify that the proposed operator is compatible with human thought. Then the 2−tuple distribution assessments on a linguistic term set are defined, and the other aggregation operator is proposed to propagate linguistic distribution assessment trust relationships. The second aggregation operator focuses on both the aggregation of linguistic terms and symbolic proportions of linguistic terms and is a generalization of the first operator. Finally, a numerical example of CouchSurfing comparative analyses further demonstrates that the proposed operators are effective and reasonable, and can consider the different semantics of a linguistic term in practical application.

In social network group decision-making (SNGDM) problems, decision-makers (DMs) often express their opinions or preferences using probabilistic linguistic term sets (PLTSs). In this paper, a novel SNGDM method for probabilistic linguistic information is proposed. Firstly, to obtain the prioritization of DMs in the clustering process, a DM clustering method for SNGDM is developed considering the influence of trust relationships and opinions similarity among DMs. Then, to satisfy the requirements of the consensus reaching process in SNGDM, a dynamic consensus threshold calculation method based on an optimization model is introduced. Furthermore, in the consensus measure stage, a novel consensus measure method for both DMs and subgroups is proposed, using a stochastic multi-criteria acceptability analysis (SMAA) method. Based on the consensus measure method, a novel SNGDM method based on SMAA for PLTSs is proposed. Finally, a case study of service quality evaluation in institutional pensions is used to illustrate the effectiveness of the proposed method. The results of case show that the proposed method can adjust consensus thresholds dynamically based on each round of collective opinions, and can solve the SNGDM problems when DMs can not provide their preferences for criteria weights.

In the contemporary business landscape, the demand for robust big data capabilities within enterprises has surged, facilitating in-depth analysis and extraction of crucial insights from supply chains to bolster data-driven dynamic decision-making. This study endeavors to develop a meticulous evaluation system tailored for assessing big data capabilities within manufacturing supply chains. Initially, the internal logic of big data capability evaluation criteria is refined by leveraging the Technology-Organization-Environment framework. Subsequently, an advanced Multi-Attribute Group Decision Making model is proposed, seamlessly integrating the Defining Interrelationships between Ranking Criteria (DIBR) method with the Evaluation based on Distance from Average Solution (EDAS) method under Pythagorean fuzzy set theory. To harness expert insights, COWA-Dombi aggregation operators are proposed. The determination of indicator weights is achieved through Pythagorean fuzzy DIBR, followed by employing Pythagorean fuzzy EDAS to compare Big Data Capabilities across various enterprises. This methodological framework is empirically validated through a case study involving six prominent manufacturing companies, offering actionable insights for organizations to leverage strengths and mitigate risks associated with big data implementation in real-world settings. The results underscore the efficacy of the proposed method in effectively assessing big data capabilities within manufacturing supply chains, further validated through comparative and sensitivity analyses.

This paper studies the propagation of social influence and the evolution of opinions for a group of decision makers (DMs) who communicate and collaborate to make decisions. Given the DMs' decision matrices and their social network, a social influence propagation model, which combines the rule of PageRank and the primacy effect phenomenon in psychology to show the evolution of individual's social influence, is proposed. Afterwards, an opinion evolution model considering the dynamic social influence evolution is proposed to model the opinion formation process. Furthermore, we establish the convergence properties of this nonlinear dynamical model for the settings of irreducible and reducible social influence network, where the reducible one is discussed in two scenarios, respectively, the reducible influence network with globally reachable nodes and without globally reachable nodes. With this proposal it is feasible to predict the evolution of individuals' decision information along the discussion process.

Due to the urgent nature of emergency decision making, it is necessary to reach the consensus requirement quickly. Ordinal consensus measure explores the relation between the rankings and helps to intuitively know which alternative needs to be adjusted to accelerate the improvement of consensus. Moreover, decision makers (DMs) in the decision making problem are often connected through trust relationships which affect the DMs’ judgments in the process of DMs’ interaction. Therefore, this paper explores trust network-based group decision-making in which the consensus level is estimated by an ordinal consensus measure. We first focus on the supplementation of an incomplete trust network. One of the most common methods is to design the trust propagation operator, whereas the intensity of information propagation may be different in various scenarios. Therefore, considering the different numerical scale of the linguistic term set, a trust propagation operator with different intensity of trust propagation is designed to obtain the indirect trust relationship. In the process of supplementing the incomplete trust network, the contribution of DMs to propagating information is concerned, which can be described by the betweenness centrality, and the importance weights of DMs are determined by combining the betweenness centrality and trust in-degree. In the consensus reaching process, we first propose an improved ordinal consensus measure, which takes into account the consistency of orders of the same alternative in different rankings as well as the importance of positions of alternatives. Then, we design the identification rule and the feedback mechanism for those with low consensus levels. The identification rule is used to select the DMs which first few alternatives in the ranking are different with those in the ranking of group. And in the feedback mechanism, the referenced preference relation (FPR) obtained by the trust network is provided for the identified DMs. Afterwards, combining the referenced FPR, an optimization model is designed to give the adjustment opinion. Finally, a numerical example elaborates on the feasibility of the trust propagation operator and consensus model. The comparative analysis demonstrates the rationality and effectiveness of the proposed model.

Internet of Things (IoT) technology now has a new purpose and relevance as a result of the digitalization wave. In this setting, businesses start to plan how they will use IoT technology. But some critical factors can prevent the successful deployment of IoT, and businesses must get beyond these critical factors if they want to do so. The literature review, system literature review, and Delphi technique are used to identify 15 critical factors. These critical factors are then divided into four categories: organization, technology, process, and environment. The PFN-weighted power harmonic operator is proposed with the aim of more effectively obtaining assessment data from experts and lessening the inaccuracy of outcomes caused by information loss. The best and worst method (BWM) is used to determine the ideal weight of critical factors. Results indicate that the primary critical factors to the effective adoption of the Internet of Things are talent, resource limitations, integration complexity, technical operations, equipment power consumption, technical dependability, and data governance. This research will benefit corporate managers in recognizing the significance of the effective deployment of the Internet of Things, identifying major critical factors to this achievement, and making decisions to remove these factors. Thus, an organization may support the effective adoption of the animal Internet of Things.

The worsening of environmental pollution has compelled industrial organizations to implement improvements across the board and work to inspire staff to engage in active green behavior. However, the majority of recent studies are restricted to a certain perspective, and there is a dearth of study on the variables influencing employees' green behavior in general. This research is grounded in a comprehensive viewpoint. Experts evaluate the relevant aspects using fuzzy language, and they combine their individual judgements using the central ordered weighted operator to get a more scientific conclusion. The outcomes of expert judgment are then examined using a variety of analytical techniques, including decision-making trail and evaluation laboratory method, interpretative structural model, and MICMAC Matrix, to identify the critical variables that influence employees' adoption of environmentally friendly behavior. The findings indicate that the most important variables impacting workers' green behavior are employee motivation, values, and responsible leadership. The attitudes, practices, and leadership philosophies of leaders regarding green conduct have an impact on employee motivation and values. The enterprise's sustainable development idea is also shown to be impacted by leaders' attitudes toward green conduct in a number of other areas, including the organizational environment, organizational and human resource management, and other areas. All of these elements have an impact on employees' values and drive to adopt green practices, either internally or outside. This research can assist businesses in identifying the critical influencing elements that impact workers' green behavior and provide focused recommendations to enhance employee green behavior.

In group decision-making problems, decision-makers typically use probabilistic linguistic term sets (PLTSs) to express their evaluation opinions. This paper focuses on the social network group decision-making method for probabilistic linguistic information. First, we propose a new consensus judgment mechanism by computing the absolute grey relation degree between the most probable optimal vectors of individual decision makers and collective opinion. Furthermore, in order to reduce the calculated amount in the decision-making process, we propose a model to transform the score value into a PLTS. This technique uses stochastic multicriteria acceptability analysis to determine the criteria weights. The preferences of the decision-makers can be accurately portrayed by this approach. In addition, we put forward a model to transform the score value into a PLTS and propose a new way to obtain the criteria weights using stochastic multicriteria acceptability analysis. Moreover, we develop an advice generation method with two steps for the PLTS in a feedback adjustment process. Finally, we use a case study and comparative analysis to illustrate the effectiveness of our method. Our proposed method can be applied to address many group decision-making problems involving multiple interest groups, such as social policy, facility placement, and other issues.

Multi-criteria social network group decision making (SNGDM) that allows decision makers (DMs) to interact with each other has attracted increasing attention in the field of decision analysis. In this paper, we take stochastic multicriteria acceptability analysis (SMAA) into account to study consensus reaching processes in multi-criteria SNGDM problems with manipulative behaviors. First, we propose a SMAA-based method to transform decision matrices into fuzzy preference relations to detect manipulators in multi-criteria SNGDM. Then, we design a new consensus determining mechanism using the weight stability interval and SMAA methods, which does not require a consensus threshold to be determined in advance. Based on this, we propose a two-stage feedback process to help DMs reach consensus. Then, we propose an algorithm to summarize the main steps of the proposed method. Finally, we use a case study of nursing home location selection to illustrate the effectiveness of the proposed method.