Two-machines scheduling problem with fuzzy allowable time constraint

We have already introduced many fuzzy concepts to scheduling problem and discussed so called fuzzy scheduling problems. In this paper, we introduce fuzzy allowable time concept newly to two identical machine problems, which is a fuzzy version of Garey and Johnson. That is, there are two identical machines and fuzzy ready times and deadlines are associated with each job, i.e., membership functions representing a satisfaction degree of start times and completion times are considered for each job and the minimal one of these is to be maximized. Further, among jobs, there exists a fuzzy precedence relation, which is a fuzzy relation with membership function representing satisfaction degree of precedence order of each job pair, and again the minimal one of these is to be maximized. The aim is to maximize both minimal degrees at a time if possible, but usually there exists no schedule maximizing both of them, and so we seek nondominated schedules.