Technological advancements have facilitated the growth of interconnected devices across various applications, which, in turn, impact the overall quality of experience. Latency-sensitive applications, in particular, require services to be delivered within stringent deadlines. Selecting the optimal server in multi-core edge computing environments, while adhering to these deadline constraints, remains a challenging issue. Traditional server selection approaches typically rely on proximity, where servers located near users are prioritized. However, these methods become inefficient when a server, although close to many users, becomes overloaded, resulting in its frequent selection over other, less burdened servers. To address this inefficiency, a fuzzy logic-based framework is proposed for server selection, aimed at offloading tasks to the most suitable servers while considering factors such as deadlines, server core capacity, and transmission delay. The proposed approach is evaluated under realistic conditions, emphasizing deadlines for task offloading. Through comprehensive simulations, the fuzzy server selection algorithm demonstrates its superiority over traditional schemes, significantly enhancing the quality of service.