In this paper, we consider two flow-shop machines which process jobs in batches in the presence of fuzzy due-dates and fuzzy machines capacity. After jobs in a batch are processed on the first machine, they are moved together to the second machine with negligible transportation time. The due-data of each job is flexible i.e. a fuzzy requirement with membership function, describing non-decreasing satisfaction degree about setting due-date of each job. The capacity on the second machine is also assumed to be flexible i.e. a membership function describing non-decreasing satisfaction degree on machine capacity, is introduced. Under these settings, we find an optimal batch sequence and batch contents maximizing both the satisfaction degrees. But usually we cannot optimize two objectives at a time. So we seek non-dominated schedule after defining dominance between schedules. The algorithms are based on linear programming formulations of the corresponding problems.