Using fuzzy numbers in knapsack problems

Using fuzzy numbers in knapsack problems

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Article ID: iaor20021988
Country: Netherlands
Volume: 135
Issue: 1
Start Page Number: 158
End Page Number: 176
Publication Date: Nov 2001
Journal: European Journal of Operational Research
Authors: ,
Keywords: fuzzy sets
Abstract:

This paper investigates knapsack problems in which all of the weight coefficients are fuzzy numbers. This work is based on the assumption that each weight coefficient is imprecise due to the use of decimal truncation or rough estimation of the coefficient by the decision-maker. To deal with this kind of imprecise data, fuzzy sets provide a powerful tool to model and solve this problem. Our work intends to extend the original knapsack problem into a more generalized problem that would be useful in practical situations. As a result, our study shows that the fuzzy knapsack problem is an extension of the crisp knapsack problem, and that the crisp knapsack problem is a special case of the fuzzy knapsack problem.

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