Traditional BP neural networks frequently encounter local optima during carbon price forecasts. This study adopts a hybrid approach, combining a genetic algorithm and particle swarm optimization (GA-PSO) to improve the BP neural network, resulting in the creation of a GA-PSO-BP neural network model. Seven critical factors were identified affecting carbon prices, and we utilized data on carbon emission trading prices from China for the analysis. Compared to traditional BP neural network models, including GA-BP neural network models optimized solely with genetic algorithms and PSO-BP neural network models enhanced through particle swarm optimization, the findings reveal that the GA-PSO-BP neural network model demonstrates superior performance in terms of precision and robustness. Furthermore, it demonstrates advancements across various error evaluation metrics, thus delivering more accurate forecasts. Offering precise carbon price predictions, the enhanced GA-PSO-BP neural network model proves to be a valuable tool for analyzing the market and making decisions in the carbon pricing sector.

Improving transparency of food safety supervision information can reduce the occurrence of information asymmetry, decrease food safety incidents, and promote socially joint regulation for food safety. In this study, an index system of food safety supervision information transparency (FSSIT) is constructed using the fuzzy-ANP comprehensive evaluation model. Using this system, the FSSIT in China is evaluated. A total of 1651 questionnaires containing 139525 data are collected from food and drug administration (FDA), consumer association (CA), and media at the central, provincial, prefectural, and county levels. Empirical results indicate that the FSSIT achieves a qualified level; however, the works of FDA, CA, and media still present deficiencies. The information transparency in the entirety presents deficiencies and gradually declines when that in the administrative level decreases. The economic development level indirectly determines the transparency level, and the transparency level does not conform to China’s current economic development level.

In order to prevent and control risk factors which harm the quality and safety of the food supply chain effectively and reduce the probability of food safety incidents, this paper investigated on some problems of the upstream and downstream enterprises of the food supply chain under the three different forms of cooperation based on the neoclassic economics and game theory method. These problems include the effectiveness of the quality and safety efforts, the profits, the effect of the losses that the food safety incidents caused on the quality efforts’ efficacy, and the social welfare comparison. Meanwhile, we constructed evolutionary game model to analyze the macro and micro factors that influenced the cooperation strategy and demonstrated the effect of diversity of decision-making parameters on evolution results based on numerical simulation. By the theoretical and simulation analysis, we found that (1) the quality efforts’ efficacy, the profits, the sensitivity coefficient of the quality efforts efficiency to the losses, and the social welfare without thinking about the externality all met their maximum under the full cooperation situation; (2) strengthening supervision over the source of the food supply chain can reduce the probability of food safety incidents; (3) macro and micro environment will be the important basis for companies’ decision-making on cooperation strategy in the food supply chain.

This study constructs the network diffusion model of food safety scare behavior under the effect of information transparency and examines the network topology and evolution characteristics of food safety scare behavior in a numerical simulation. The main conclusions of this study are as follows. (1) Under the effect of information transparency, the network degree distribution of food safety scare behavior diffusion demonstrates the decreasing characteristics of diminishing margins. (2) Food safety scare behavior diffusion increases with the information dissemination rate and consumer concern about food safety incidents and shows the characteristics of monotone increasing. And with the increasing of the government food safety supervision information transparency and media food safety supervision information transparency, the whole is declining characteristic of diminishing marginal. In addition, the extinction of food safety scare behavior cannot be achieved gradually given a single regulation of government food safety supervision information transparency and media food safety supervision information transparency. (3) The interaction effects between improving government food safety supervision information transparency or media food safety supervision information transparency and declining consumer concerns about food safety incidents or information transmission rate can engender the suppression of food safety scare behavior diffusion.

This study employed the dynamic conditional correlation algorithm and incorporated the temporal dynamics of spillover effect to enhance the Multivariate Stochastic Volatility (MSV) model. Consequently, a DGC-t-MSV model (multiple stochastic volatility model of dynamic correlation coefficient with Granger causality test) was constructed to simulate and examine the volatility spillover effects between China’s carbon market and the traditional energy market. The findings reveal the following: (1) A significant spillover effect in price volatility exists between China’s carbon and traditional energy markets, with a notably fluctuating spillover index. The traditional energy market in China exerts a stronger unidirectional volatility spillover effect on the carbon market. Price fluctuations in the traditional energy market impact carbon market prices through mechanisms such as cost transmission and market expectations. (2) In the initial stages, the dynamic correlation between China’s carbon and traditional energy markets showed an overall downward trend, underscoring the positive influence of policy incentives and technological advancements on the growth of alternative energy. A mutual weakening effect exists between the carbon and traditional energy markets. (3) Price fluctuations in China’s carbon and traditional energy markets display a high degree of interdependence and short-term persistence, with evidence of a long memory and significant inertia in these price movements. Integration of the DGC-t-MSV model with the Bayesian approach and the Markov Chain Monte Carlo (MCMC) method and the introduction of a time-varying factor enabled the efficient measurement of the volatility spillover effect between China’s carbon and traditional energy markets.