Preference ratio-based maximum operator approximation and its application in fuzzy flow shop scheduling

Maximum operator distorts the shape(s) of Triangular Fuzzy Numbers (TFNs) and Trapezoidal Fuzzy Numbers (TrFNs) in many problems such as Flow shop scheduling, job-shop scheduling and project scheduling. In this paper, we introduce an appropriate approximation for the maximum operator, in which the weak-dominance fuzzy numbers are ranked based on the concept of preference ratio. Since in most practical cases the due dates and the processing time of scheduling are not deterministic, we consider the scheduling problems with fuzzy processing time. Finally we develop a novel fuzzy CDS algorithm in fuzzy flow shop scheduling by applying the preference ratio concept through an example.