Efficiency and fairness constitute pivotal criteria for evaluating consensus mechanisms in group decision-making (GDM) systems, where both active strategy learning and dynamic weight allocation critically impact these metrics. Active strategy learning empowers decision makers (DMs/agents) to iteratively optimize consensus strategies through Q-learning-based environmental interactions, effectively balancing individual preferences with collective objectives. Concurrently, a contribution-weighted allocation mechanism ensures fairness while maintaining original opinion authenticity. To address existing research gaps in integrated learning frameworks, fairness quantification, and decision rationality verification, this study proposes an adaptive Q-learning consensus model enhancing efficiency through reward feedback mechanisms. A dual-factor reward function integrating contribution weights and opinion retention to improve fairness metrics. An algorithmic framework with complexity analysis is validated through multi-scenario simulations. Empirical results from case study and simulation analysis demonstrate the method’s superior performance in achieving efficient convergence, equitable resource distribution, and rational opinion evolution compared to conventional approaches.

Preference relation has been one of the most useful tools for experts to express their comparison information over alternatives in group decision-making (GDM) problems. Recently, a new type of preference relations called linguistic preference relations with self-confidence (LPRs-SC) has been proposed, which makes multiple self-confidence levels into consideration when experts provide their preferences. This study focuses on the consensus reaching process for GDM with LPRs-SC. To do that, some new operational laws for LPRs-SC are presented. Subsequently, an iteration-based consensus proposal for LPRs-SC is proposed. In the proposal, we aggregate the individual LPRs-SC using a self-confidence indices-based method which gives more importance to the most self-confident experts. A self-confidence score function is presented to derive the individual and collective priority vectors. Moreover, considering experts’ acceptable adjustment range of preference values, a two-step feedback adjustment mechanism is utilized to improve the consensus level, which adjusts both the preference values and the self-confidence levels. Finally, an example and some analyses are furnished to demonstrate the feasibility and effectiveness of the proposed method.

Preference relations have been widely used in group decision-making (GDM) problems. Recently, a new kind of preference relations called fuzzy preference relations with self-confidence (FPRs-SC) has been introduced, which allow experts to express multiple self-confidence levels when providing their preferences. This paper focuses on the analysis of additive consistency for FPRs-SC and its application in GDM problems. To do that, some operational laws for FPRs-SC are proposed. Subsequently, an additive consistency index that considers both the fuzzy preference values and self-confidence is presented to measure the consistency level of an FPR-SC. Moreover, an iterative algorithm that adjusts both the fuzzy preference values and self-confidence levels is proposed to repair the inconsistency of FPRs-SC. When an acceptable additive consistency level for FPRs-SC is achieved, the collective FPR-SC can be computed. We aggregate the individual FPRs-SC using a self-confidence indices-based induced ordered weighted averaging operator. The inherent rule for aggregation is to give more importance to the most self-confident experts. In addition, a self-confidence score function for FPRs-SC is designed to obtain the best alternative in GDM with FPRs-SC. Finally, the feasibility and validity of the research are demonstrated with an illustrative example and some comparative analyses.

Consensus reaching models are widely used to derive a representative solution in group decision-making problems. Current models present limitations regarding the achievement of the agreement and keeping enough consistency for achieving valid solutions. Therefore, this paper proposed a new consensus model based on the deviation degree of two fuzzy preference relations (FPRs), in which a novel consistency index (CI) is defined to measure whether an FPR is of acceptable consistency. Additionally, an interindividual similarity index (ISI) is devised to measure the consensus degree of two FPRs. In the proposed consensus reaching process, ISI is also used to guide the two most incompatible decision-makers (DMs) to modify their judgments. The proposed iterative consensus reaching algorithm is convergent, CI preservation. After that, a stationary vector method is adopted to determine DMs’ weights for the aggregation process based on DMs’ opinion transition probabilities. Finally, an illustrative example and comparative analysis is given to demonstrate the effectiveness of the proposed model.

Network information system security has become a global issue since it is related to the economic development and national security. Information system security assessment plays an important role in the development of security solutions. Aiming at this issue, a dual hesitant fuzzy (DHF) group decision-making (GDM) method was proposed in this paper to assist the assessment of network information system security. A systemic index containing four aspects was established including organization security, management security, technical security, and personnel management security. The DHF group evaluation matrix was constructed based on the individual evaluation information from each expert. Some power average operator–based DHF information aggregation operators are proposed and used to fusion the performance of each criterion for information systems. The advantage of these operators is that they can describe the relationship between the indexes quantitatively. Finally, a case study about information systems security assessment was presented to verify the effectiveness of proposed GDM methods.

This paper proposes a chi-square method (CSM) to obtain a priority vector for group decision making (GDM) problems where decision-makers’ (DMs’) assessment on alternatives is furnished as incomplete reciprocal preference relations with missing values. Relevant theorems and an iterative algorithm about CSM are proposed. Saaty’s consistency ratio concept is adapted to judge whether an incomplete reciprocal preference relation provided by a DM is of acceptable consistency. If its consistency is unacceptable, an algorithm is proposed to repair it until its consistency ratio reaches a satisfactory threshold. The repairing algorithm aims to rectify an inconsistent incomplete reciprocal preference relation to one with acceptable consistency in addition to preserving the initial preference information as much as possible. Finally, four examples are examined to illustrate the applicability and validity of the proposed method, and comparative analyses are provided to show its advantages over existing approaches.

This paper proposes a distance-based consensus model for fuzzy preference relations where the weights of fuzzy preference relations are automatically determined. Two indices, an individual to group consensus index ( ICI ) and a group consensus index ( GCI ), are introduced. An iterative consensus reaching algorithm is presented and the process terminates until both the ICI and GCI are controlled within predefined thresholds. The model and algorithm are then extended to handle multiplicative preference relations. Finally, two examples are illustrated and comparative analyses demonstrate the effectiveness of the proposed methods.