In the field of group decision-making (GDM), minimum cost consensus models (MCCMs) have been extensively studied to enhance decision-making efficiency and conserve resources. However, such models generally overlook decision makers' (DMs) demands for fairness, which can easily lead to non-cooperative behavior and thereby hinder the achievement of consensus. In light of this, this study focuses on two core issues under the minimum-cost constraint of MCCMs: first, how to comprehensively characterize individuals' perceptions of fairness; and second, how to design a consensus mechanism that balances efficiency and fairness. As individuals' reliance on social networks increases, this study utilizes fuzzy social networks to quantify DMs' importance and bargaining power, providing a bargaining foundation and weighting basis for subsequent model construction. Specifically, the study first measures the deviation between actual and expected returns based on cost differences arising from individual profit maximization and differentiated bargaining. It then classifies DMs into hierarchical levels based on their trust levels and bargaining power within a fuzzy social network, guiding horizontal fairness comparisons among entities within the same level and thereby quantifying individual perceptions of fairness. Building on this foundation, the study further calculates the maximum achievable fairness level for the group to determine whether it meets the preset fairness threshold requirement. Subsequently, two types of optimization mechanisms are constructed: a fairness-oriented model requiring additional costs, and an efficiency-oriented mechanism based on the deep deterministic policy gradient (DDPG) algorithm, designed to maximize the number of DMs meeting the fairness threshold. Finally, the Taihu Lake cross-regional water pollution control initiative serves as an empirical case study to validate the proposed method's effectiveness. Combined with sensitivity analysis and comparative experiments, its application advantages are thoroughly examined.

In group decision making (GDM) problems, fuzzy social networks (FSNs) provide a new theoretical framework for trust management among decision makers (DMs) and play a key role in weight allocation, opinion dissemination, and consensus building. However, the problem of trust risk still cannot be ignored. To this end, this study proposes an innovative GDM optimization method, TWD-FSN-A-PT, from the perspectives of optimization computation and decision-making application. The method combines the theory of three-way decision (TWD) theory and FSNs, aiming at solving the problem of trust risk and behavioral tendency in fuzzy environments. Specifically, the innovations of the method include: identifying and reducing pseudo-trust risk using the TWD theory; adopting a new mechanism to distinguish between selfish and altruistic behaviors of DMs by considering both group and individual optimization; and maximizing global stability by optimizing the model and respecting individual preferences, which ensures that the adjustment cost is minimized while reaching an efficient consensus. These innovative methods fully rely on the theory and techniques of applied mathematics and ensure the robustness of the model under different parameter settings. Finally, the TWD-FSN-A-PT method is applied to the regional electricity demand analysis, demonstrating the results of ranking the electricity demand at different time periods.

Existing multi-criteria sorting methods predominantly rely on preset classification thresholds or fixed numbers of alternatives for classification, exhibiting strong subjectivity and overlooking potential consensus correlations between classifications. In group decision-making (GDM), the consensus feedback mechanism drives the consensus reaching process (CRP) and gives rise to the problem of adjustment amount allocation among decision-makers (DMs). However, existing studies over-rely on consensus thresholds and neglect differences in DMs’ adjustment capabilities and sequences, which significantly reduces the applicability and accuracy of the methods. To address the above issues, this study proposes a novel group consensus method (NS-FPR-PM) integrating the Nash-Stackelberg game and preference maps within the framework of fuzzy preference relations (FPRs). Specifically, class probability thresholds are objectively derived through an optimization model; the classification results are then converted into preference maps based on these class probability thresholds to explore the inherent consensus relations, thereby eliminating reliance on consensus thresholds. The Nash-Stackelberg game model can characterize the differences in bargaining power among DMs, and an asynchronous adjustment mechanism is designed accordingly to achieve fair allocation of adjustment amount. Finally, we provide an example to illustrate the proposed method, the experimental results and analysis demonstrate that the method exhibits significant advantages over similar methods in terms of consensus reaching efficiency and unit adjustment conversion rate.

ABSTRACT China's Second Outline of the Action Plan to Increase Grain Production Capacity by 50 Million Metric Tons places strong emphasis on maize yield improvement; however, its implications for domestic food security and global maize markets remain unclear. This study adapted an open‐source multicountry partial equilibrium model, calibrated it to a 2023 base year, and simulated a baseline and three policy‐induced maize yield‐improvement scenarios for 2030. Relative to the baseline, the Action Plan scenarios increase China's maize production by 4.01–12.19 million metric tons, reduce net maize imports from 22.45 million metric tons to 18.51–10.46 million metric tons, and raise the maize self‐sufficiency ratio from 93.17% to 94.37%–96.82%. Lower Chinese import demand reduces the world maize price by 0.93%–2.84% and contracts global maize trade by 1.31%–3.99%. Synchronized climate shock stress tests indicate that climate‐related production volatility can generate much larger price movements than those associated with medium‐term policy effects. The Action Plan can, therefore, strengthen China's maize security and moderately reshape global trade, but it should be complemented by climate adaptation, diversified trade, and transparent stock management.

This paper examines whether policy cognition is associated with rural households’ stated willingness to participate in China’s homestead reform, which is a case of restructuring layered and incomplete property rights. Using a 2019 survey of 1,355 households in 11 provinces, we estimate probit models for compensated exits and transfers of homestead use rights. A one-point increase in the nine-item policy cognition index is associated with 2.31- and 1.97-percentage-point increases in the two predicted probabilities. The associations remain positive across most alternative estimators and alternative constructions of the policy cognition index. Conditional mixed-process estimates are treated only as sensitivity evidence because the village-peer policy cognition index may reflect shared local conditions. The potential pathway results are consistent with the roles of prior market experience and procedural acceptance of collective recovery but do not establish mediation. The findings support targeted policy communications on eligibility, transaction rules, compensation, inheritance, and postexit security.

Purpose Establishing adult-equivalent (AE) scales for rural household food consumption expenditures is crucial for policymakers to set unified benchmarks for living costs in rural China. This study aims to estimate AE scales for food expenditures, providing a standardized tool to capture structural differences in rural household consumption. Design/methodology/approach Using survey data from 49,254 rural households across China, a Poisson Pseudo-Maximum Likelihood (PPML) estimator models expenditures across major food categories. AE scales are derived by gender, age, and income groups, with rural males aged 35–40 as the benchmark group (scale = 1). Findings At the category level, staple foods have a mean scale of 0.727, edible oils 0.682, aquatic products 0.670, dairy and eggs 0.645, meat and poultry 0.564. At the product level, flour and other grains record 0.752 and 0.738, pork 0.717, eggs 0.712, and beef and mutton lowest at 0.492 and 0.491. Male scales exceed female scales, with values among males aged 40–55: aquatic products 1.607, edible oils 1.398, legumes 1.394, and staple foods 1.354. Across the life cycle, scales rise to a peak and then decline, with females showing a rebound in old age. Practical implications The estimated AE scales provide a policy-relevant tool to calibrate household needs, support nutrition interventions, and improve welfare measurement and programme evaluation in rural China. Originality/value This study applies a PPML framework to a large rural sample to quantify AE scales and reveals systematic heterogeneity by gender, age, and income, offering evidence-based guidance for equitable rural policy design.

In group decision-making processes, achieving consensus often requires decision-makers to adjust their initial preferences, which incurs adjustment costs and may be constrained by individual budget limitations. Existing consensus models mainly focus on optimizing preference adjustments, while insufficient attention has been paid to budget feasibility and compensation allocation. To bridge this gap, this study proposes a consensus compensation analysis framework that explicitly incorporates individual budget constraints and external compensation. We first develop a budget feasibility diagnostic model to evaluate whether a target consensus level can be achieved under given budget conditions and to determine the minimum required compensation. Building on this, a minimum cost consensus model incorporating individual budgets and compensation is constructed, and its feasibility conditions are derived. To address situations of budget shortfalls, two compensation allocation mechanisms are designed based on Nash bargaining and the Shapley value, respectively. An illustrative example inspired by the Taihu Lake Basin, involving eight decision-makers and four governance alternatives, demonstrates the implementation process. Sensitivity analysis and comparative experiments demonstrate the feasibility, fairness, and robustness of the proposed framework under limited budgets.

The authors would like to make the following corrections about the published paper [...]

PurposeThis paper aims to examine the asymmetric effects of price increases and decreases on the food demand and nutrient intake of rural households, especially low-income households.Design/methodology/approachWith household pooled cross-sectional data from 2018-2020 in rural China, the price elasticities of demand for food and nutrients are estimated via the almost ideal demand system (AIDS) with reference prices, and then a simulation is undertaken based on the estimated elasticities.FindingsThe price elasticities of demand for food and nutrients show significant asymmetric responses to price increases and declines. Food demand is more sensitive to price decreases than to increases, which is more obvious for other households than for the low-income group. This asymmetric pattern may be dominated by stockpiling behaviors. Stockpiling helps households amplify the benefits of reducing food prices. Moreover, nutrient elasticities indicate that nutrient intake is more sensitive to price increases due to substitution between foods. The simulation results suggest that changes in food prices increase the gap in food consumption and nutrient intake between lower- and higher-income classes in rural China.Practical implicationsThis study offers insights into preventing nutritional poverty and improving diet in terms of food prices.Originality/valueWe estimate the asymmetric price elasticity of food demand in rural China via AIDS with reference prices, which corrects the systematic error in elasticities estimated by traditional demand system models. The vulnerability of low-income households to price fluctuations and stockpiling behaviors is revealed in rural China.

Probabilistic linguistic term set (PLTS) provides a flexible and comprehensive approach to reflecting qualitative information about decision makers (DMs) by fusing linguistic terms and probability distributions. This fusion makes PLTS an important focus of fuzzy decision theory. Dealing with uncertainty and ambiguity has always been a major challenge in the group decision-making (GDM) process, and PLTS provides a versatile and effective approach to address these issues. PLTS is able to more accurately represent the preferences and opinions of the DMs, thus improving the accuracy and consistency of decision-making, thereby improving the accuracy and consistency of decision-making. Therefore, the application of PLTSs in GDM (PLTS-GDM) has attracted more and more attention and shown great potential. In this paper, we provide a comprehensive overview of the underlying theories of PLTS-GDM, the existing approaches and the challenges they face. Specifically, we explore how the PLTS utilizes fuzzy information systems to manage imprecise and ambiguous data to enhance the effectiveness of decision-making. In addition, through an extensive review and analysis of the current literature, we summarize the major advances in the field and identify important gaps in the existing research. Finally, we point out future research directions aimed at addressing these challenges and further advancing the application and development of PLTS-GDM. In summary, this paper provides a valuable resource for scholars and practitioners to help them understand and promote the practical applications of PLTS-GDM.

IntroductionWith the rise of the digital economy, e-commerce has become a significant driver of agricultural modernization, offering opportunities to increase farmers’ income by expanding sales channels, reducing transaction costs, and enhancing product value. However, despite growing empirical research, disparities remain in the research findings, and the impact and mechanisms of farmers’ involvement in e-commerce operations on their income require further investigation.MethodsThis study utilizes the 2020 China Rural Revitalization Survey to both theoretically and empirically examine the impact of farmers’ participation in e-commerce on their total household income, while also exploring the mechanisms driving this relationship.Results(1) The empirical results of the endogenous switching regression model show that farmers’ participation in e-commerce operations can increase their income. This conclusion remains robust after applying winsorization, the instrumental variable approach, and core variable substitution. (2) Heterogeneity analysis reveals that, under the counterfactual hypothesis, if non-e-commerce households were to participate in e-commerce operations, their average treatment effect in the low-income group would be greater than that in the high-income group. That is, their increase in household income would be larger than that of the corresponding high-income group, suggesting that farmers’ participation in e-commerce would reduce income disparities among farmers. (3) Mechanism analysis indicates that farmers’ participation in e-commerce operations promotes income growth primarily through three channels: enhancing information acquisition capacity, promoting social participation, and saving operating costs.DiscussionTherefore, this study recommends that the government refine policymaking to facilitate the integration of small-scale agricultural operators into emerging e-commerce models and establish a robust institutional support system. Additionally, efforts should focus on optimizing the rural e-commerce environment, enhancing farmers’ digital awareness and social participation efficiency, and supporting their engagement in e-commerce. Lastly, strengthening rural digital skills education, cultivating and retaining e-commerce talent, and fostering sustained income growth for farmers.

In contemporary industrial applications, particularly within the service sector, optimizing decision-making processes is essential for enhancing both customer satisfaction and operational efficiency. The convergence of advanced engineering information systems and social network analysis has become a pivotal strategy for improving group decision-making (GDM) across various industries. However, traditional methods often fall short in effectively balancing individual preferences with collective interests, especially when addressing non-cooperative behaviors and ensuring equitable outcomes. This paper introduces a new approach using probabilistic linguistic term sets (PLTSs), namely, PLTS-NC-UF, which significantly improves the fairness and efficiency of reaching consensus in social network-based GDM scenarios. The core innovations of this approach are: (1) A novel formula for constructing fuzzy sociometric matrices from adjacency matrices, providing a more precise depiction of the relationships among experts; (2) An in-depth analysis of non-cooperative behaviors by scrutinizing the discrepancies between individual and group optima, and the strategic incorporation of altruistic behaviors to counteract non-cooperative tendencies; (3) A fair adjustment allocation mechanism that ensures experts with comparable status and authority undertake similar adjustments. The efficacy of the proposed method is demonstrated through comprehensive experimentation, including a case study focused on the selection of tourism accommodations, a critical decision-making scenario within the service industry. The results indicate that the proposed method achieves lower adjustment costs, diminished non-cooperation, and heightened fairness compared to existing consensus models, thus holding substantial potential for refining decision-making processes in industrial applications.

In the realm of addressing consensus challenges within group decision-making (GDM) that encompass individual preferences, this article presents an innovative approach. This article introduces a three-way group consensus methodology grounded in probabilistic linguistic preference relations (PLPRs) that ensures an acceptable level of inconsistency by applying the three-way decision (TWD) principle. This methodology is referred to as the TWD-GC-AIC approach. The TWD-GC-AIC approach consists of two core components, each dedicated to distinct aspects: ensuring the internal consistency of individual expert preference relations and achieving consensus within the expert group. The first component is dedicated to enhancing the consistency of individual expert preferences. This process commences with the determination of expert weights and the development of a novel aggregation formula. Subsequently, the consistency metric is refined through the incorporation of a newly devised distance formula. Once the predefined consistency threshold is reached, this study seamlessly integrates a planning model with an iterative algorithm. This integration serves a dual purpose: minimizing adjustment costs while retaining as much of the original information provided by the experts as possible. In the consensus-reaching phase, known as the consensus reaching process (CRP) of the expert group, this study employs iterative algorithms that incorporate TWD within the feedback mechanism. This strategic approach aims to comprehensively consider the emotional attitudes of the experts when adjusting the evaluation information, ultimately leading to a more informed and rational final decision outcome. Finally, this paper empirically validates the effectiveness and efficiency of the TWD-GC-AIC method, particularly in scenarios involving probabilistic linguistic term sets (PLTSs). The method is applied to a practical example and rigorously benchmarked against various other consensus methodologies to assess its performance.

Scaling service operations is an effective way to promote modernization among small farmers. Exploring the factors influencing grain farmers’ choices in selecting services is essential to promote the strong development of the agricultural production service market and improve the efficiency of agricultural operations in China. Based on the 2019 data on corn farmers in the China Rural Revitalization Survey (CRRS) database, and using the Double-Hurdle Model, the factors influencing the service selection behavior of corn farmers are explored, and the research conclusions are as follows: (1) agricultural service prices have a negative impact on the demand for agricultural services, which varies from service to service; (2) labor prices do not influence the demand for any kind of service; (3) land circulation rents have a negative impact on the demand for agricultural services, which varies from service to service; (4) a high family net income can significantly prompt the adoption of agricultural services, which varies from service to service; (5) small-scale farmers are more sensitive to changes in service prices than large-scale farmers; (6) the four economic factors have no effect on the sowing service market. Based on the above conclusions, this paper puts forward suggestions such as improving the market price mechanism for agricultural production services, and increasing subsidies related to agricultural production services.

Agricultural mechanization services (AMS) are a key strategy for farmers to achieve mechanized production. However, farmers' access to these services is impeded by information gaps and high search costs. This study investigates the impact of internet usage on AMS accessed by farmers, based on 8,299 observations gathered from 12 Chinese provinces. The results indicate that farmers who use the internet have a 24.4% higher probability of accessing AMS than those who do not. Moreover, heterogeneity tests revealed that internet usage significantly promotes AMS access among middle- and high-education groups, younger groups, middle-scale farmers, middle- and high-income groups, and the eastern and western regions. Additionally, internet usage promotes farmers' access to AMS by expanding their information channels and strengthening their social networks.

China has implemented policies like Leading areas for Agricultural Green Development (LAGD) to mitigate livestock and poultry farming pollution while promoting industry growth. However, it remains uncertain whether LAGDs have successfully balanced emission reduction with stable development. This study examines 165 LAGDs to analyze changes in emissions, assess the decoupling of emission reduction from output value, and identify influencing factors. Findings reveal that emissions from livestock and poultry in LAGDs initially increased and then decreased between 2010 and 2019. Cattle were responsible for over 40% of fecal emissions, and pigs for more than 20%. Additionally, pigs contributed to over 61% of urine emissions. From 2010 to 2014, increases in chemical oxygen demand were mainly due to pigs and cattle. Total nitrogen levels were significantly impacted by cattle, while pigs were affected by total phosphorus. From 2014 to 2019, reductions in emissions were largely attributed to a decrease in pig-related pollutants. The decoupling status shifted from strong to weak and then back to strong between 2014 and 2019. Production efficiency played a crucial role in reducing emissions, while changes in industrial structure moved from supporting to hindering this reduction. Economic development was a primary factor in driving these changes. Standard emissions in Chinese regions showed a rising and then declining trend from 2010 to 2019. The Northeast and Northwest regions of China demonstrated emission trends that were in sync with the growth in rural income. This study offers insights into the successes and challenges of LAGDs in achieving a balance between reduced emissions and development, using quantitative analysis. The findings are instrumental in informing policies for a sustainable livestock and poultry industry. Recommendations include evaluating coordinated approaches to pollution reduction and industrial growth, setting decoupling goals, designing policies based on influential factors, conducting regional assessments of livestock and poultry demand, and implementing region-specific strategies.

This study employs panel data and a dynamic Almost Ideal Demand System (AIDS) model to investigate the habit formation effect of food consumption among Chinese rural residents and its consequential impact on nutritional intake. The dataset, spanning from 2012 to 2018, encompasses nine provinces in China and involves 5390 rural households. The findings reveal that, excluding beef, mutton, and poultry, there are significant habit formation effect on the consumption of food categories, notably grains, vegetables, and edible oils. Lower-income and younger demographics demonstrate a more pronounced reliance on established dietary habits. Influenced by the habit formation effect, there is a substantial reduction in the income elasticity differences across various food types. Overlooking the habit formation effect in food consumption would lead to an underestimation of the income elasticity of energy, fat, and carbohydrates. This suggests that, over the long term, food consumption habit formation is a pivotal factor in enabling the enhancement of residents’ dietary structures, amplifying the incremental energy intake associated with income increases, and accelerating the transition towards nutritional surplus. The conclusions drawn from this study offer valuable insights for ensuring food security and nutritional balance. Policy-makers of food and nutrition strategies should duly consider the habit formation effect on residents’ food consumption, and seek to optimize dietary patterns and promote nutritional transformation by food consumption habit intervention.

Social networks are gaining importance as an important application landscape for machine learning techniques. Currently, it is prevalent thinking to introduce social networks into group decision-making research, despite exhibiting promising performance, there remain significant challenges, including 1) trust risk is often overlooked, and 2) group opinions are excessively relied upon. In this regard, this article introduces the trust risk test for group consensus (SN-TRT-GC) by using probabilistic linguistic preference relations under probabilistic linguistic term sets. The proposed method ensures that the expert's competence matches the discourse as much as possible by virtue of the trust risk value. Moreover, opinion evolution relies on the dual attributes of similarity and trust, which promote the exchange of opinions among experts and greatly accelerate the consensus reaching process. Empirical investigations of satisfaction surveys demonstrate the validity and superiority of the presented SN-TRT-GC technique.

Intelligent decision-making collaborates with big data analytics to navigate the intricate landscape of the digital economy, orchestrating data-driven strategies to achieve the most favorable results. Through the integration of specific objectives and relevant data, intelligent decision-making involves the modeling, analysis, and realization of decisions. This comprehensive process seamlessly incorporates elements such as constraints, strategies, preferences, and uncertainty, ultimately leading to the autonomous achievement of optimal outcomes. In this context, the probabilistic linguistic preference relation (PLPR) serves as a recently introduced form of linguistic evaluations, offering adaptable expression of expert preference assessments. Within the domain of preferences, consistency emerges as a pivotal consideration. Extremes occur when calculating the additive consistency of PLPR using expectation values. To comprehensively address the trouble, this paper introduces an innovative planning model that employs deviation degrees. The establishment of a consistency threshold is approached objectively using the principle of minimum individual regret and maximum group delight. Once consistency is established, the process advances to consensus reaching process (CRP). During the consensus feedback phase, the infusion of the three-way decision (TWD) theory accounts for distinct expert modification attitudes, while ensuring consistency remains upheld throughout the modification procedure. For clarity, the proposed technique is referred to as the TWD-GC-EA method. Notably, the effectiveness of the designed approach is demonstrated through its application to a real-world scenario. Furthermore, a comparative assessment is conducted against several other consensus methods to validate its efficacy and superiority.

The planting industry is crucial in ensuring food security in China. The development of the planting industry has underpinned the country’s historic transition from merely achieving food sufficiency to enjoying high-quality diets, consequently promoting the gradual improvement of dietary quality among residents. In the new era, the development of the Chinese planting industry faces challenges from internal and external risk factors, such as resource environment pressure, extreme climate impacts, and unstable international geopolitical situations. This study predicts the food supply and demand situations in 2035 and 2050. Results show that net imports of grain in China will mainly focus on soybeans and corn, while the self-sufficiency rate of rapeseed and sugar will continue to decline, the self-sufficient rate of peanuts and fruits will rise after declining first, and the vegetables will be more than self-sufficient. Thus, this study provides an overview and summary of the challenges faced by China’s planting industry regarding food security and proposes strategic ideas and policy recommendations for ensuring food security in the new era. These recommendations include improving the planting industry’s production capacity and structure, promoting low-carbon production and the efficient use of resources , optimizing residents’ consumption structure and health concepts, encouraging agricultural technology innovation and equipment development, and innovating new business entities. Major projects regarding technology innovation, quality improvement, ecological protection, and protein substitution are also proposed. Furthermore, we suggest adhering to the overall strategy of “ensuring basic selfsufficiency of grain and absolute security of staple food”, clarifying the industry development priorities by regions, improving the agricultural infrastructure and technology shortcomings, and perfecting the strategic system for responding to major crises, thereby enhancing the level of agricultural development and effectively ensuring food security in China.