Local Interpretable Model-agnostic Explanations (LIME) is an interpretable method used to explain the predictions of machine learning models. It generates perturbed samples around an instance and fits a simple surrogate model, such as linear regression, to approximate the local behavior of the black-box model. This paper introduces Additive Local Interpretable Model (ALIME), a LIME variant based on generalized additive models (GAMs), where feature effects are modeled by penalized splines (P-splines), providing flexibility for capturing nonlinear relationships. Experimental results show that ALIME outperforms the original LIME method in terms of local fidelity. In addition, the shape functions generated by ALIME can clearly capture local feature contributions, providing insight into the relationship between features and model outputs, and enhancing overall interpretability.

The uncertainty of the trust relationships between decision makers (DMs) or the uncertainty of individual weights will lead to the uncertainty of fairness and consensus management in group. To provide a solid solution, we propose a robust maximum fairness consensus model with limited cost under the uncertain trust relationships and individual weights (RTRMFCM). Specifically, this article constructs an uncertainty set to more precisely describe the uncertainty of the trust relationship between DMs. Based on individual fair preference considerations from the trust network, we adopt a robust optimization method to reduce the risk of DMs feeling unfair. Furthermore, a robust approach based on the combination of uncertain individual weights has been developed to reduce the risk of consensus being destroyed. Then, some theoretical analyzes are presented. We also provide a numerical analysis to validate the applicability of the RTRMFCM. Finally, the simulation analyses have revealed the characteristics of the RTRMFCM, and show that the RTRMFCM is more effective than the maximum fairness consensus model with limited cost under trust relationship (TRMFCM).

In the large-scale group decision making (LSGDM) problems, some experts may adopt strategic manipulation behaviors which can be reflected in trust and preference values. These behaviors can bias or hinder the large-scale consensus reaching process (LCRP). This paper proposes a novel consensus framework to deal with these strategic manipulation behaviors from the perspective of historical data of trust and preference values in LSGDM. In the proposed consensus framework, the experts are classified into several clusters using the historical data of trust and preference values. Next, the strategic manipulation behaviors of trust and preference values of clusters are identified respectively. Then, we take the penalty strategy against experts in clusters with two kinds of strategic manipulation behaviors by updating experts' weights. Simulation and comparison studies are employed to show the validity of the proposed consensus framework against traditional frameworks for managing strategic manipulation behaviors in LSGDM.

Opinion and action have important roles in human society, but few studies have considered the interactive evolution of opinion and action. Inspired by the social network DeGroot (SNDG) model and the social network opinions and actions evolution (SNOAE) model, an opinion and action interactive evolution (OAIE) model based on social network leadership and opinion estimation of action is proposed, and the stable state and consensus of agents’ opinions and actions are investigated. The results show that in the interactive evolution of opinion and action, when each agent can accurately estimate the opinions of other agents based on their actions in the final stage, all agents are stable agents. If the opinion leader exists, a consensus and unified action can be formed by all agents; otherwise, all agents can reach a consensus and unified action in the subnetwork. In addition, if each agent is always unable to estimate the true opinions of other agents, then all agents are oscillatory agents.

Existing consensus models focus on improving the group consensus level, but ignore whether a higher group consensus level means higher mutual acceptance of decision makers. In the field of opinion dynamics, the bounded confidence model asserts that the decision makers will accept the preferences of others within a neighborhood of theirs with width a certain confidence level. Inspired by this research methodology, this article develops a consensus model to address the acceptance issue based on individual bounded confidences. Specifically, a bounded confidence-based consensus measure is designed to measure the level of group mutual acceptance, and a multi-stage optimization feedback mechanism based on individual bounded confidences is proposed to maximize the group mutual acceptance and minimize the amount of preference adjustment. A numerical example and a simulation analysis are included to illustrate the use of the model and to justify its effectiveness, respectively.

To date, a large number of consensus reaching processes (CRPs) have been reported in group decision making (GDM). Trust relationships should be an essential element in interactions among a group of individuals, leading to the evolution of individuals’ preferences. Therefore, in this article, we present a trust relationships CRP with a feedback mechanism which consists of two approaches of facilitating consensus reaching: 1) the leader-based preference adjustment and 2) the trust relationships improvement. In the trust relationships CRP, we build a bridge between opinion dynamics and GDM to highlight the role of the leaders and trust relationships improvements in the GDM problems. Furthermore, we present a new strategic manipulation issue, called trust relationship manipulation, and discuss some clique-based strategies to manipulate trust relationships to obtain the desired ranking of the alternatives in the GDM problems. Finally, the detailed simulation experiments are proposed to justify our proposal.

Different feedback mechanisms have been reported in consensus reaching models to provide advices for preference adjustment to assist decision makers to improve their consensus levels. However, most feedback mechanisms do not consider the willingness of decision makers to accept these advices. In the opinion dynamics discipline, the bounded confidence model justifies well that in the process of interaction a decision maker only considers the preferences that do not exceed a certain confidence level compared to his own preference. Inspired by this idea, this article proposes a new consensus reaching model with personalized feedback mechanism to help decision makers with bounded confidences in achieving consensus. Specifically, the personalized feedback mechanism produces more acceptable advices in the two cases where bounded confidences are known or unknown, and the unknown ones are estimated by a learning algorithm. Finally, numerical example and simulation analysis are presented to explore the effectiveness of the proposed model in reaching consensus.

Pursuing a consensus-based solution in group decision making has been widely studied. However, most of the existing consensus models have overlooked one important issue, that is, the decision makers' willingness to accept these suggestions in a consensus reaching process. This issue is explained by the bounded confidence model in the field of opinion dynamics. In this line, this study develops an optimization-based consensus model that considers individual bounded confidences and provides decision makers with more acceptable suggestions based on their bounded confidences. Finally, a numerical example is presented to show the use of the model.

Different feedback mechanisms have been developed in large-scale group decision-making (GDM) to provide the decision-makers with advices for preference adjustment with the aim of improving the group consensus level. However, the willingness of the decision-makers to accept these advices is rarely considered in the extant feedback mechanisms. In the field of opinion dynamics, this issue is studied by the bounded confidence model, which shows that the decision-makers only consider the preferences that differ from their own preferences not more than a certain confidence level. Following this idea, this article proposes a large-scale consensus model with a bounded confidence-based feedback mechanism to promote the consensus level among decision-makers with bounded confidences. Specifically, this feedback mechanism classifies the decision-makers into different clusters and provides the corresponding clusters with more acceptable advices based on a bounded confidence-based optimization approach. Finally, through the numerical example and the simulation analysis, the use of the model is introduced, and the effectiveness of the model is justified.

In social network group decision making (SNGDM), the consensus reaching process (CRP) is used to help decision makers with social relationships reach consensus. Many CRP studies have been conducted in SNGDM until now. This paper provides a review of CRPs in SNGDM, and as a result it classifies them into two paradigms: (i) the CRP paradigm based on trust relationships, and (ii) the CRP paradigm based on opinion evolution. Furthermore, identified research challenges are put forward to advance this area of research.