In this paper, we consider the fuzzy open shop scheduling problem with parallel machines in each working stage where processing times are vague and are represented by fuzzy numbers. An open shop scheduling problem with parallel machines in each working stage under this condition is close to the real production scheduling conditions. A mixed-integer fuzzy programming (MIFP) model is presented to formulate this problem with the objective of minimizing makespan. To solve small-sized instances, an interactive fuzzy satisfying solution procedure is applied. Since this problem is known as a class of NP-hard, a novel discrete electromagnetism-like (DEM) is proposed to solve medium to large size examples. The DEM algorithm employs a completely difference approach. It makes use the crossover operators to calculate force and move particle is used. We employ Taguchi method to evaluate the effects of different operators and parameters on the performance of DEM algorithm. Finally to assess the performance of the algorithm, the results are compared with an existing EM algorithm from the literature and benchmark problems. The result exhibited the ability of the proposed DEM algorithm to converge to the efficient solutions.