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Constructing a fuzzy flow-shop sequencing model based on statistical data. (English) Zbl 1006.68018
Summary: 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 ($1-\alpha$, $1-\beta$) 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.
##### MSC:
 68M20 Performance evaluation of computer systems; queueing; scheduling
##### Keywords:
fuzzy sets; flow-shop sequencing