The rapid development of the air transportation industry has increased air traffic, posing challenges to the task of airport gate assignment (AGA) for flights. Most past studies have solved the AGA problem (AGAP) using deterministic models, which are incapable of dealing with uncertainty and dynamic conditions at airports. Thus, this research employs fuzzy theory and proposes a triangular membership function to handle flight uncertainty in the AGAP. In addition, an improved metaheuristic, termed the improved Shuffled Frog-Leaping Algorithm (ISFLA), is proposed to circumvent the computationally intractable problems commonly faced by exact approaches when handling large instances. In this research, the AGAP is first formulated as a stochastic Mixed-Integer Linear Programming (MILP) model, with stochastic flight lateness and earliness considered. The objective of this model is to minimize the total cost, which consists of three sub-costs: passenger walking distances, non-preferred gate (NPG) assignments for planes, and fuzzy idle times of gates. These three sub-costs correspond to the major concerns of passengers, airlines, and airports, respectively. The cooperation between the ISFLA and the triangular membership function demonstrates their capability to effectively handle big AGAP instances. Furthermore, the experimental results show that the ISFLA outperforms the standard SFLA, Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Firefly Algorithm (FA).