This study investigated an approach for incorporating statistics with fuzzy sets in the flow-shop sequencing problem. This work is based on the assumption that the precise value for the processing time of each job is unknown, but that some sample data are available. A combination of statistics and fuzzy sets provides a powerful tool for modeling and solving this problem. Our work intends to extend the crisp flow-shop sequencing problem into a generalized fuzzy model that would be useful in practical situations. In this study, we constructed a fuzzy flow-shop sequencing model based on statistical data, which uses level (1-α,1-β) interval-valued fuzzy numbers to represent the unknown job processing time. Our study shows that this fuzzy flow-shop model is an extension of the crisp flow-shop problem and the results obtained from the fuzzy flow-shop model provides the same job sequence as that of the crisp problem.
