Semiconductor manufacturing is a complicated flexible job-shop scheduling problem (FJSP) of combinatorial complexity. Because of the adoption of advanced process control and advanced equipment control, the processing time in advanced wafer fabs become uncertain. Existing approaches considering constant processing time may not be appropriate to address the present problem in a real setting. In practice, processing times can be represented as intervals with the most probable completion time somewhere near the middle of the interval. A fuzzy number that is a generalized interval can represent this processing time interval exactly and naturally. This paper developed a hybrid approach integrating a particle swarm optimization algorithm with a Cauchy distribution and genetic operators (HPSO+GA) for solving an FJSP by finding a job sequence that minimizes the makespan with uncertain processing time. In particular, the proposed hybridized HPSO+GA approach employs PSO for creating operation sequences and assigning the time and resources for each operation, and then uses genetic operators to update the particles for improving the solution. To estimate the validity of the proposed approaches, experiments were conducted to compare the proposed approach with conventional approaches. The results show the practical viability of this approach. This paper concludes with discussions of contributions and recommends directions for future research.