Abstract
The 0-1 knapsack problem with imprecise profits and imprecise weights of items is considered. The imprecise parameters are modeled as fuzzy intervals. A method of choosing a solution under the uncertainty is proposed and two methods for solving the constructed models are provided.
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Dubois D., Prade H. (1998). Possibility theory: an approach to computerized processing of uncertainty. New York: Plenum Press
Garey M.R., Johnson D.S. (1979). Computers and intractability: A guide to theory of NP-completeness. San Francisco, CA: Freeman
Herrera F., Verdegay J.L. (1996). Fuzzy boolean programming problems with fuzzy costs: A general study. Fuzzy Sets and Systems 81: 57–76
Inuiguchi M., Ramik J. (2000). Possibillistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection. Fuzzy Sets and Systems 111: 3–28
Kuchta D. (2002). A generalisation of an algorithm solving the fuzzy multiple choice knapsack problem. Fuzzy Sets and Systems 127(2): 131–140
Lin F.T., Yao J.S. (2001). Using fuzzy numbers in knapsack problems. European Journal of Operational Research 135: 158–176
Martello S., Toth P. (1990). Knapsack problems: Algorithms and computer implementations. Chichester, New York: Wiley
Martello S., Pisinger D., Toth P. (2000). New trends in exact algorithms for the 0-1 knapsack problem. European Journal of Operational Research 123: 325–332
Okada S., Gen M. (1994). Fuzzy multiple choice knapsack problem. Fuzzy Sets and Systems 67: 71–80
Zadeh L. (1978). Fuzzy sets as a basis for a theory of possibility. Fuzy Sets and Systems 1: 3–28
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Kasperski, A., Kulej, M. The 0-1 knapsack problem with fuzzy data. Fuzzy Optim Decis Making 6, 163–172 (2007). https://doi.org/10.1007/s10700-007-9000-3
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DOI: https://doi.org/10.1007/s10700-007-9000-3