In order to ensure sustainable activities, companies independent upon working with defrent supplier's .In the manufacturing industries, raw material and assembly parts main comprise as much as 70 percent of production cost. For that, a purchasing department can play a vital role in reducing costs, and a purchasing manager's skill in performing his/her responsibility of choosing proper suppliers can greatly contribute to achieving that goal. This article focuses on the above-mentioned subject due to the importance of supplier choice for companies. Since the first times in history when the need for choosing proper suppliers was felt, many different methods and strategies have been utilized for such a task. Because of nature of that challenge, decision makers are faced with more than one criteria and high number of such criteria makes the challenge even more complex for them. Multi-criteria decision making has frequently been one of the approaches used by decision makers in the evaluation and selection of suppliers. In the research of this thesis a model of fuzzy multi-criteria and non-additive fuzzy integral has been presented for the supplier selection. The advantage of this model is that with the aid of Fuzzy Analytic Network Process the effects of the criteria on each other can be analyzed and with the fuzzy measure and fuzzy integral methods these interdependent relation between effects can be eliminated.