We use a novel interactive possibility linear programming (PLP) approach to solve a flow shop scheduling problem with imprecise processing times and due dates of jobs. The proposed approach uses a strategy of minimizing the most possible value of the imprecise total cost, maximizing the possibility of obtaining lower total cost, and minimizing the risk of obtaining higher total cost simultaneously. The proposed model minimizes the weighted mean completion time. For the first time in a fuzzy flow shop scheduling problem, the proposed PLP approach considers the overall degree of decision maker (DM) satisfaction. A number of instances are generated at random and the proposed model is then solved by the Lingo software package and the results are reported. Scheduling is assigning a finite number of resources to a number of jobs over time, usually with a decision that optimizes one or more objectives. In most manufacturing systems, to complete a job, a set of processes are needed to be performed serially. Emergence of advanced manufacturing systems such as computer aided design/computer aided manufacturing (CAD/CAM), flexible manufacturing system (FMS), and computer integrated manufacturing (CIM) have increased the importance of flow shop scheduling [1]. A flow shop scheduling problem addresses determination of sequencing N jobs needed to be processed on M machines to optimize the performance measures such as makespan, tardiness, work in process, number of tardy jobs, idle time, etc. In flow shop scheduling, the processing routes are the same for all the jobs [1]. In the permutation flow-shop, passing is not allowed. Thus, the sequencing of different jobs that visit a set of machines is in the same order. In the general flow shop, passing is permitted. Therefore, the job sequence on each machine may be different [2]. Flow shop scheduling problems are popular in the area of scheduling and there have been numerous investigations of these problems [3]. However, in real-world scheduling problems, these parameters are often encountered with uncertainties. Accordingly, scheduling problems have been mainly branched into two categories: Deterministic scheduling and uncertain (stochastic, fuzzy, etc.) scheduling [4].