In sequencing situations, it may affect parameters used to determine an optimal order in the queue, and consequently the decision of whether (or not) to rearrange the queue by sharing the realized cost savings. In this paper, we extend one machine sequencing situations and their related cooperative games under fuzzy uncertainty. Here, the agents costs per unit of time and processing time in the system are fuzzy intervals. In the sequel, we define sequencing fuzzy interval games and show that these games are convex. Further, fuzzy equal gain splitting rule is given. Finally, a numerical example is illustrated priority based scheduling algorithm.