توسعه مسيله كوله پشتي چندانتخابي 1-0 با استفاده از مجموعه هاي فازي

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 be respected in real problems. In this case an object may be belongs to the several classes. We have used the fuzzy sets concept to show that each object may be a member of each class with a membership grade. We called it a fuzzy multi-choice knapsack problem (FMCKP). We consider two objectives for the problem: The first one is to maximize the profit of selected combination and the second one is to minimize the total differences of the deviation of ideal relation for each class. Developing such a hi-objective model, we applied the fuzzy linear programming (FLP) approach to solve it. Experiments on a lot of typical examples show the capability and efficiency of the proposed model.