Using fuzzy numbers in knapsack problems |
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| Institution: | 1. Department of Physics, Institute of Science, Banaras Hindu University, Varanasi 221005, India;2. Institute of Radio Physics and Electronics, University of Calcutta, Kolkata 700009, India;3. S. K. Mitra Centre for Research in Space Environment, Institute of Radio Physics and Electronics, University of Calcutta, Kolkata 700009, India |
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| 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 coefficients 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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