A Method for Solving Fuzzy Multi-Dimensional 0-1 Knapsack Problems

Abstract

This article is intended to present a 0-1 knapsack problem with multiple constraints under fuzzy environment, which all coefficients in the problem are represented as fuzzy numbers. We propose an approximate algorithm for solving the problem without transforming it into a crisp problem, keeping coefficients as fuzzy numbers in the process of the calculation. In the interpretation of the constraints, the degree satisfying the inequality relation between fuzzy numbers is defined on the basis of the agreement index. This degree is related to the areas of the membership functions of the fuzzy numbers in both sides of the constraint, so it takes into account the shapes of fuzzy numbers. The proposed algorithm is compared with the algorithm based on possibility theory, and the properties and differences of the solutions are shown.