Due to the complicated data dependencies between the tasks in a workflow application and the heterogeneous resources in edge-cloud environments, it is difficult to select an optimal tasks-servers solution for scheduling workflow applications in the complex environments. Current research on workflow applications scheduling is mainly concentrated on certain conditions, ignoring the fact that the scheduling environments usually fluctuate. In this article, we deal with reducing the execution cost of multiple workflow applications within the corresponding deadline constraints and improving the network robustness in fuzzy edge-cloud environments. Triangular Fuzzy Numbers (TFNs) are employed to describe the computing capacity of servers and the bandwidth between them in uncertain environments. Specially, a novel Scheduling Strategy based on Particle Swarm Optimization algorithm employing the Quadratic Penalty Function (SSPSO_QPF) is proposed for scheduling multiple workflow applications. Compared with other classic scheduling strategies, simulation results demonstrate that the proposed strategy can generate feasible scheduling schemes even with the strict deadline constraints, and significantly reduce the fuzzy execution cost of multiple workflow applications.