This paper investigates multiconstraint 0-1 knapsack problems (MCKP) in which all of the weight coefficients are fuzzy numbers. This study is based on the assumption that each weight coefficient is imprecise due to the use of decimal truncation or rough estimation of the coefficients by the decision-maker. To deal with this kind of imprecise data, we use fuzzy sets as a tool to model and solve the problem. Our work intends to extend the MCKP into a more generalized imprecise problem that would be useful in practical situations. As a result, we propose a generalized fuzzy MCKP model, and then extend it to another fuzzy multi-objective programming model. These models are much easier for the decision-maker to specify a range value than to give an exact value for each object weight.