This paper deals with the fuzzy hybrid flow shop (FHFS) scheduling inspired by a real apparel process. A parallel greedy (PG) algorithm is proposed to solve the FHFS problems with setup time (ST) and lot size (LS). The fuzzy model is used to define the uncertain setup and processing time and due dates. The setup and processing times are defined by a triangular fuzzy number. Also, the fuzzy due date (FDD) is denoted by a doublet. The tardiness, the tardy jobs, the setup and idle time, and the total flow time are minimized by the proposed PG algorithm. The effectiveness of the proposed PG algorithm is demonstrated by comparing it with the genetic algorithm in the literature. A real-world application in an apparel process is done. According to the results, the proposed PG algorithm is an efficient heuristic method for FHFS scheduling problems with ST and LS in real-world applications.