PM Cooperative Control with Fuzzy Cost and Fuzzy Coalitions.

Haze control cost is hard to value by a crisp number because it is often affected by various factors such as regional uncertain meteorological conditions and topographical features. Furthermore, regions may be involved in different coalitions for haze control with different levels of effort. In this paper, we propose a PM cooperative control model with fuzzy cost and crisp coalitions or fuzzy coalitions based on the uncertain cross-border transmission factor. We focus on the Beijing–Tianjin–Hebei regions of China and obtain the following major findings. In the case of haze control in the Beijing–Tianjin–Hebei regions of China, local governments in the global crisp coalition can achieve their emission reduction targets with the lowest aggregated cost. However, Hebei fails to satisfy its individual rationality if there is no cost sharing. Therefore, the Hukuhara–Shapley value is used to allocate the aggregated cost among these regions so that the grand coalition is stable. However, the Beijing–Tianjin–Hebei regions cannot achieve their emission reduction targets in the global fuzzy coalition without government subsidies.