Fuzzy approach to multilevel knapsack problems

This study proposes a fuzzy approach for solving the multiobjective and multilevel knapsack problems (KPs). The problem was first formulated as a multilevel programming problem with multiple decision makers (DMs). Then the degree of satisfaction of each DM was established and represented by their individual membership functions. The recursive formulation of dynamic programming was used to solve the decisions of the interrelated stages. The overall satisfaction of the decision was obtained through this stage-wise operation on the hierarchical structure. Capacity allocation was developed and a step-by-step solution procedure was illustrated. A detailed comparison between multiobjective and multilevel KPs was also carried out. Finally, the possible use of turnpike theorem in KPs was scrutinized in the fuzzy domain.