Developing Two Efficient Models for Fuzzy Multi-Choice Knapsack Problem

Multi-choice knapsack problem is a branch of regular knapsack problem where the objects are classified in different classes and each class has one and only one representative in final solution. Although it is assumed that each object belongs to just one class, sometimes this assumption is not valid in real problems. In this case an object may belong to the several classes. In fuzzy multi-choice knapsack problem (FMCKP), fuzzy sets are applied to show that each object is a member of each class with a membership grade. In this paper we proposed two new models for fuzzy multi-choice knapsack problem. These models have a fuzzy constraint and so we applied the fuzzy linear programming (FLP) approach to solve them. Typical examples show the capability and efficiency of the proposed models.