Consensus formation is pivotal in large-scale group decision-making, significantly influenced by the structure of social networks, thereby drawing substantial attention to large-scale consensus-reaching in social networks (LSC-SN). However, existing clustering methodologies for organizing decision-making experts often encounter challenges when applied to extensive networks and frequently overlook the inherent social network structures. To address these limitations, this study first introduces an evaluation similarity factor to enhance modularity. Then, we propose an improved Louvain algorithm to increase the efficiency and adaptability of network segmentation. In the consensus-reaching process (CRP), a novel Collaborative Similarity Index (CSI) is developed to regulate the cooperative behavior of decision-makers and prevent over-adaptation. Building upon this, a novel approach is introduced to simultaneously determine both decision-maker weights and community weights, while also considering the degrees of consensus within and between communities. Additionally, a dual-domain reference consensus feedback model based on CSI is constructed, integrating individual opinions, inter-domain references, and inter-domain opinion references to promote fairness. Finally, the validity and feasibility of the proposed methodology are substantiated through empirical research and comprehensive analysis.

With the rapid development of social media, social network group decision-making (SNGDM) has gained significant attention for its ability to integrate decision-makers’ (DMs) social relationships. However, existing consensus models face challenges in dynamic trust evolution, single-dimensional consensus evaluation, and information integrity, making it difficult to address decision-making needs in complex uncertain environments effectively. To overcome these limitations, this study proposes a consensus model based on Correlative-Z-numbers (Cor-Z-numbers) and a dual-feedback mechanism to enhance the reliability and adaptability of group decision-making. First, Cor-Z-number is introduced, integrating Set Pair Analysis (SPA) to incorporate fuzziness and reliability information. A complete trust network and a dynamic trust network are constructed to simulate trust evolution and opinion interaction, leading to the development of an Intrinsic Adaptive Regulation Mechanism (IARM). Second, a dual-layer consensus framework is established, combining ordinal and cardinal consensus rules to improve consensus assessment. To optimize opinion adjustments, an Extrinsic Triggered Modified Mechanism (ETMM) is proposed, consisting of a minimal adjustment model and a minimum-cost adjustment increment model, ensuring a balance between consensus optimization and information preservation. Finally, a case study validates the effectiveness and superiority of the proposed model. In the Hengshui environmental governance case, the model effectively optimized consensus while preserving decision information, highlighting its practical value for complex environmental management.

Time-series forecasting models of influenza cases have consistently been a focal point of disease prevention efforts. However, existing influenza forecasting models fail to accurately capture the dynamic transmission of influenza across multiple cities. This limitation hinders precise epidemic prediction. Similarly, traditional compartmental models also struggle to capture the influenza information from various cities effectively. By embedding domain-specific epidemiological knowledge into neural networks, there is potential for significantly improving predictive accuracy. Therefore, in order to enhance the accuracy of influenza prediction across cities, we introduce a novel dynamics-informed model named SIS-GCN-SRTCN-XLinear (SGT-XLinear). This framework integrates epidemic ordinary differential equations (ODEs), spatiotemporal prediction models and multi-scale linear modules, specifically designed to capture and forecast the spatiotemporal variations of influenza outbreaks. By combining graph convolutional networks (GCN) and temporal convolutional networks (TCN), the model efficiently extracts intricate spatiotemporal features. Additionally, the incorporation of epidemic ODEs strengthens its capacity to model influenza dynamics. A multi-scale linear module further enhances prediction accuracy by learning linear correlations present in influenza data. Extensive experiments conducted on four representative datasets of varying time spans demonstrate that our proposed model outperforms mainstream influenza prediction models, offering superior accuracy.

Contemporary urban development is a multifaceted system that includes economic, social, and environmental factors. A reasonable assessment approach is essential to accurately represent the present condition of urban development and to inform future growth trajectories. Multi-criteria group decision-making (MCGDM) integrates evaluative information from numerous experts across diverse criteria to provide rational solutions, making it common in practical decision-making and assessment contexts. This study initially presents a flexible extended prioritized average (EPA) operator in a multi-parameter format to address the restrictions inherent in the form-conservative character of the prioritized average (PA) operator. Besides, the complex fuzzy Z-number (CFZN) can delineate the reliability and periodicity of the evaluated object. Thus, within the CFZN framework, this paper develops four aggregation operators (AOs) for information fusion based on Frank T-norms and T-conorms and verifies their fundamental properties: idempotence, monotonicity, and boundedness. To ascertain the objective weights of experts and criteria, a divergence measure is developed to quantify discrepancies between CFZNs. Moreover, this study makes use of the stepwise weight assessment ratio analysis (SWARA) approach to methodically assess the subjective weights of the criteria. In the end, the proposed operators are incorporated with the combined compromise solution (CoCoSo) approach to establish an innovative MCGDM framework and apply it in a comprehensive evaluation of urban development over multiple dimensions. Furthermore, sensitivity and comparative analyses confirm the robustness and efficacy of our strategy, indicating its better performance.

The Z-number framework represents a significant advantage in fuzzy set theory since it encapsulates the reliability levels and ambiguity restrictions, and Complex Fuzzy Sets (CFSs) can describe the time-varying nature of information. Therefore, this study introduces the novel concept of Linguistic Complex Fuzzy Z-number (LCFZN), which is more adaptable and practical than numerical assessment and allows for the simultaneous representation of reliability measures and phase information. Then, this paper develops two aggregation operators, denoted as the LCFZN Sugeno–Weber Weighted Hamy Mean (LCFZNSWWHM(k)) operator and the LCFZN Sugeno–Weber Weighted Dual Hamy Mean (LCFZNSWWDHM(k)) operator, and offers unique properties of these operators, namely idempotence, monotonicity, and boundedness. Subsequently, an automobile purchase decision approach under the role of online reviews is proposed, which involves a construction process of the LCFZN evaluation environment that can effectively capture multidimensional consumer perceptions based on online review information features. As a Large Language Model (LLM), the General Language Model-4-Air (GLM-4-Air) is employed in the process of sentiment analysis of online reviews to obtain the emotional level. Finally, the proposed strategy is implemented for the purchase decision of New Energy Vehicles (NEVs), and through sensitivity analysis with various parameter configurations and comparative analysis with conventional methods, the approach demonstrates superior adaptability and decision consistency.

Linguistic preference relations with self-confidence (LPRs-SC) are the preference relation that can reflect the decision maker’s (DM) confidence psychology and has received widespread attention for their simple form and multiple information. Currently, arithmetic studies of LPRs-SC are conducted separately for preference relations and self-confidence. In addition, personalized individual semantics (PIS) is an important tool in large-scale decision-making to reflect the differences in the semantic understanding of DMs. However, the confidence level in LPRs-SC limits the preference relation to a certain extent and the linguistic representations of these two components are usually different. This means that it is not only necessary to propose an arithmetic rule that can express the restrictive relationship between the two but also to construct a model that can extract the PIS of preference relation and confidence respectively. Besides, we constructed a two-stage consensus reaching process (CRP) based on the specificity of the LPRs-SC structure when enhancing group harmony. The process takes self-confidence as an independent source of information, delineates the adjusted categories in detail, and builds an adjustment model accordingly. Finally, the example and comparative analyses verify the merits of the proposed PIS in terms of consistency enhancement and CRP in terms of speed and accuracy harmonization.

Persistent PM2.5 pollution poses a serious threat to human health. Developing an accurate urban regional PM2.5 forecasting is of practical significance for environmental protection. However, previous studies have mostly focused on individual monitoring stations, neglecting the influence of neighboring stations, which limits forecasting accuracy. Additionally, the PM2.5 of a single monitoring station cannot reflect the overall situation of a region. Therefore, this paper develops a novel PM2.5 spatiotemporal forecasting framework that combines graph convolutional module, temporal convolutional module, linear module. It enables the forecasting of PM2.5 concentrations at multiple stations and multiple time steps in the future. Concretely, we utilize a mixed graph convolutional network to extract the spatial features of PM2.5. Then, an improved temporal convolutional network, the second-order residual temporal convolutional network, is developed to capture complex temporal features. Following the classical “linear and non-linear” modeling strategy, a linear module is added to the forecasting framework. Experiments on the real air pollution dataset from Beijing demonstrate that our framework outperforms the state-of-the-art baselines.

Personalized individual semantics (PIS) is an important factor reflecting the personal habits of decision makers (DMs) and has been widely studied by scholars. Using criteria as a non-negligible information source in multi-criteria group decision making (MCGDM), how to extract PIS from it is a research gap to be solved. In addition, existing measurements of consensus are insufficiently sensitive to differences between individuals, while the current direction rules use a matrix as the unit of measurement, which is not detailed and precise enough. Therefore, this paper first constructs a PIS extraction model according to the principle that similar criteria have similar descriptions and mutually exclusive criteria have dissimilar descriptions. Secondly, the preference information of PIS is mingled with uncertainty and reliability of improved basic uncertain linguistic information (IBULI) as the data of the consensus reaching algorithm. The proposed consensus algorithm not only fully considers the dispersion of DMs in the consensus measurement stage, but also improves the objectivity of the consensus process through an adaptive feedback stage. Finally, the validity of the proposed model is verified by an example and comparative analysis of the selection of sustainable building materials.

In an increasingly complex decision-making environment, the decision information we obtain contains the decision makers’ professional cognition, psychological preference, risk attitude and other hidden uncertainty factors. These hidden inherent factors may cause evaluations being better or worse than their actual level. In order to reduce the bias brought by these factors, they should be identified and eliminated prior to decision making. Hence, a preference determination model is proposed and a risk model is established to eliminate these factors by analyzing the possible impact. Moreover, a more practical probabilistic linguistic model–2-tuple probabilistic linguistic term set is proposed and its related concepts are defined. Furthermore, an integrated decision-making method is provided. Finally, considering the application background of double carbon economy, an example by selecting the best design of electric vehicles charging station is conducted to illustrate the proposed method, and the feasibility and effectiveness are verified.

As an effective way of expressing information,Z-number can well describe the natural language with uncertain information. But most research on Z-number relies on evenly distributed linguistic term sets,and the aggregation operators used to aggregate Z-number information rarely take into account the relationships between attributes.Therefore,a non-uniform distribution language scale function was proposed,then the situation of the probability language Z-number under unbalanced semantics was discussed,and a new type of defined operator was used to aggregate the probability language Z-number.At the same time,the relevant operations and score function was defined.Then,a multi-objective linear optimization model was build to determine the optimal investment ratio.Finally,the feasibility and effectiveness of the proposed method are illustrated by examples,and sensitivity analysis is performed.

针对属性权重未知的多属性决策问题,在Z概率语言术语集(ZPLTS)环境下,提出了一种改进的PROMETHEE Ⅱ(preference ranking organization method for enrichment evaluations Ⅱ)方法.在该方法中,各评价信息的综合可靠度由评价本身的可靠度和决策者给出的可靠度来确定,并由此进一步确定属性的权重;距离测度采用扩展的欧式距离,该方法在ZPLTS环境下能够克服不同Z概率语言值(ZPLVs)之间的距离均为0所带来的决策偏差.实例研究表明,该方法在反映原始数据信息和确定未知属性权重方面显著优于TOPSIS方法和传统的PROMETHEE Ⅱ方法,因此该方法可应用于多属性决策问题中.

针对语义分布不平衡环境下的语义偏好和决策信息的复杂性问题,为提高决策的准确性,提出了一个新型不平衡语言尺度函数.它可通过改变语义偏好参数来调节相邻语义之间的偏差,适用于不同的决策环境,并对相关性质进行了证明.在犹豫不确定语言型Z-numbers(hesitant uncertain linguistic Z-numbers,简称HULZNs)的环境下,定义了两个 HULZNs之间的距离以及部分运算,建立了优先加权平均运算算子和一种新型多准则群决策模型.最后,对提出的新模型利用实例进行了分析,验证了方法的有效性和可行性.

针对准则权重未知的多准则群决策问题,提出了一种新的基于随机优势得到的优先度,在概率不确定语言术语集(Probabilistic Uncertain Linguistic Term Sets,PULTS)环境下,通过充分考虑决策者基于个人偏好对各个准则之间重要性给出的评价来确定准则权重,基于一致准则法提出的一个新的决策方法,综合考虑了专家在进行决策时的犹豫程度和所给评价本身蕴含的信息,在一定程度上减少了决策过程中的信息丢失.首先,在P ULTS环境下,定义了不确定度和得分函数,实现了由语言集到数字的转化,并且利用得分函数确定了专家权重,进而得出综合得分矩阵;其次,将随机优势的定义规则应用到概率不确定语言集优先度的定义中,根据各个准则之间的优先度确定了准则的权重;最后,在一致准则决策法的基础上做了相关改进,并将其应用到了P ULTS环境中,通过数值算例验证了新的决策方法的可行性和有效性.

针对多准则群决策问题,提出了一种新的关于专家评价组内优势关系,在概率语言型Z-number(Probabilistic Linguistic Z-number)环境中应用TODIM、PROMETHEE决策方法结合起来的一个新的决策方法,不仅避免了TODIM方法的补偿问题,也有效地反映了准则的权重;首先通过引入新定义的影响因子、敏感因子和附加因子确定了组内优势关系,其中敏感因子具有举足轻重的作用;随后根据新的优势关系定义了组内偏离度,据此将同一评价可信度的PLZN融合;其次,根据各组专家评价的可信度,将不同可信度的评价融合,由此新定义了综合偏离度;进一步利用新的决策方法:TODIM-PROMETHEE,先后得到了准则的权重以及综合优势度,根据净流判断方案的先后顺序;最后通过一个实例的应用与分析说明新决策方式的有效性与可行性.

The group decision-making problem usually involves decision makers (DMs) from different professional backgrounds, which leads to a considerable point, that it is the fact that there will be a certain difference in the professional cognition, risk preference and other hidden inherent factors of these DMs to the objective things that need to be evaluated. To improve the reasonability of decision-making, these hidden inherent preference (HIP) of DMs should be determined and eliminated prior to decision making. As a special form of fuzzy set, q-rung orthopair fuzzy numbers (q-ROFNs) is a useful tool to process uncertain information in decision making problems. Hence, under the environment of q-ROFNs, the determination of HIP based on distance from average score is proposed and a risk model is established to eliminate the HIP by analyzing the possible impact. Meanwhile, a dominant function is proposed, which extends the comparison method between q-ROFNs and an integrated decision-making method is provided. Finally, considering the application background of double carbon economy, an example by selecting the best design of electric vehicles charging station (EVCS) is conducted to illustrate the proposed method, and the feasibility and efficiency are verified.

Z+-numbers, which carry more information than Z-numbers, are studied in this paper. Based on existed models, two more scientific and reasonable probability models of Z+-numbers are developed. In order to utilize Z+-numbers to solve practical problems, the α-cut set of Z+-numbers and corresponding utility function are proposed. Meanwhile, according to the structure of Z+-numbers, the entropy, cross-entropy and comprehensive cross-entropy are introduced to measure the uncertainty and fuzziness of Z+-numbers information. Furthermore, a linear programming model based on proposed three kinds of entropy is designed to obtain the weight vector of criteria in decision-making problems. Finally, we provide an example by selecting an optimal design of electricity vehicles charge station(DEVCS) combined the PROMETHEE method with Z+-numbers, and the feasibility of the proposed method are verified.

针对属性权重未知,属性值为语言型Z-number的多属性决策问题,提出了一种基于云模型与丰富度评估的偏好排序组织方法(Preference ranking organization method for enrichment evaluation,PROMETHEE)的决策方法.首先,引入语言尺度函数,然后利用其建立转化模型完成语言型Z-number向云模型的转化.此外,通过定义云可能度函数,建立属性权重求解公式及构建正弦偏好函数,进而计算方案的优先指数,通过计算方案的正负方向优序级别值得到备选方案综合优序级别值,进而得到方案排序.最后通过算例及比较分析验证本方法的有效性和可行性.

Z-number that proposed by Zadeh is an effective tool to describe the information with uncertainty in decision-making problems. However, most of the researches on Z-numbers employed linguistic cardinalities with uniformly distributed scales. In fact, unbalance situation is much common in terms of the psychology of experts. In this paper, we propose a new computational method based on Probabilistic Linguistic Z-number with Unbalanced semantics(UPLZ), which can represent the linguistic evaluations of experts precisely combined with individual risk appetite. A new score function of UPLZs is provided based on hesitant degree and linguistic scale function to reduce the computational complexity. Afterward, a linear programming is constructed to determine weights of criteria by considering cross entropy maximization. The robust decision result can be obtained by applying MULTIMOORA method since it is specific with peculiarities of three subordinate models. Finally, a case study concerning medicine selection for the patients with mild symptoms of the COVID-19 is provided to illustrate the feasibility and effectiveness of the proposed method. The advantages of it are highlighted by sensitivity analysis and comparative analysis with two outstanding multi-criteria decision-making methods.