The idea of spherical fuzzy soft set (SFSS) is a new hybrid model of a soft set (SS) and spherical fuzzy set (SFS). An SFSS is a new approach for information analysis and information fusion, and fuzzy modeling. We define the concepts of spherical-fuzzy-soft-set topology (SFSS-topology) and spherical-fuzzy-soft-set separation axioms. Several characteristics of SFSS-topology are investigated and related results are derived. We developed an extended choice value method (CVM) and the AHP-TOPSIS (analytical hierarchy process and technique for the order preference by similarity to ideal solution) for SFSSs, and presented their applications in multiple-criteria group decision making (MCGDM). Moreover, an application of the CVM is presented in a stock market investment problem and another application of the AHP-TOPSIS is presented for an environmental mitigation system. The suggested methods are efficiently applied to investigate MCGDM through case studies.

This paper analyses the correlation between automobile exhaust, PM2.5, and air pollution to explore the rate of contribution of automobile exhaust to PM2.5 pollution and the effect of government regulation on automobile exhaust gas. The results show that the atmosphere is hazy and that car exhaust is the main cause of PM2.5 pollution. This paper divides the governance strategy into two methods: reducing the number of motor vehicles and reducing the emissions capacity of motor vehicles. It also analyses the effects of congestion control on public car travel and establishes a dynamic game model. To strengthen the influence of supervision on enterprises with regard to purifying devices and restrictions, this study also creates a “prisoner’s dilemma” model. The final results of the study show that restriction measures can effectively relieve road pressure. Additionally, congestion costs can alleviate environmental pressure, but it is difficult to determine the costs, and the difficulty of implementation increases. Increasing enterprises’ installation of purifying devices is not advisable or desirable in the short term. Finally, the paper offers some suggestions for the maintenance of the atmospheric environment and the management of automobile exhaust: (1) improve the national green transport system and environmental protection awareness; (2) advocate public transport as a mode of travel; and (3) reduce the use of buses and popularize new energy vehicles.

Air pollution control as the background of a cost allocation method is based on the Shapley value to determine the core stakeholder, so fair pollution control projects and the establishment of the atmospheric pollution of governance cost allocation model are put forward for the solution of air pollution coordinated by the government supervision and the atmospheric pollution control collaborative group. The results show that the cost allocation model of air pollution control based on Shapley value is more reasonable, and the cost of stakeholders is reduced to a certain extent, and the risk of the participants is reduced so that it maximizes social benefits.