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An Approach to Solve Fuzzy Knapsack Problem in Investment and Business Model
Abstract
In this chapter, the author studies the knapsack problem with fuzzy weights for single and bi-objective function. The knapsack problem has been widely used in the investment and business model. In real-world decision-making situations, the existence of fuzziness of the weights and the profit is a common requirement. To overcome this difficulty, these weights and profit can be considered as a triangular fuzzy number. Thus, a fuzzy knapsack problem is introduced. The author introduces the possibility index which gives the possibility of choosing the items with fuzzy weights for knapsack with crisp capacity. The possibility index gives an idea to choose the solution according to the decision maker's choice. The dynamic programming approach using multi-stage decision making has been given for the different type of decision makers to find the solution. An investment problem in an imprecise environment has been defined as a fuzzy knapsack problem and the solution procedure is given to demonstrate the methodology.
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