Wireless mesh network (WMN) with wireless backhaul technology provides last-mile Internet connectivity to the end-users. In multi-radio multi-channel WMN (MRMC-WMN), routers provide multiple concurrent transmissions among end-users. The existence of interference among concurrent transmissions severely degrades the network performance. A well-organized channel assignment (CA) scheme significantly alleviates the interference effect. But in trying to minimize interference, the CA scheme may affect the network connectivity. So, the CA scheme has to consider both these two conflicting issues. In this paper, as part of the initial configuration of WMNs, we propose a game theory-based load-unaware CA scheme to minimize the co-channel interference and to maximize the network connectivity. To adapt to the varying network traffic, we propose a dynamic channel assignment scheme. This scheme measures the traffic-load condition of the working channels of each node. Whenever a node finds an overloaded channel, it initiates a channel switch. Channel switching based on the fixed threshold may result in a channel over/underutilization. For optimal channel utilization, we propose a fuzzy logic-based approach to compute the channel switch threshold. The contending nodes and their densities and loads dominantly affect the network capacity and hence the performance. In the context of network capacity enhancement, we have addressed these factors and focused on increasing the network capacity. The simulation results indicate that our proposed load-unaware and load-aware CA schemes outperform the other related load-unaware and load-aware CA approaches.