Increased competition and the globalization of markets have made the purchasing function an increasingly vital activity in supply chain management. The most crucial decision in purchasing is the selection of appropriate suppliers which reduce purchasing costs, decrease production lead time, increase customer satisfaction and strengthen corporate competitiveness. This decision is complicated when buyers face multiple suppliers, multiple conflicting criteria and imprecise parameters. In this study a multiple sourcing supplier selection problem is considered as a multiple objective linear programming problem with fuzzy demand level and/or fuzzy aspiration levels of objectives. Three objective functions are minimizing the total monetary costs, maximizing the total quality and maximizing the service level of purchased items respectively. In order to solve the problem, a novel interactive solution procedure which integrates three well-known fuzzy mathematical models is presented. The proposed approach handles three different scenarios related with mainly the sources of fuzziness and can be efficiently used to obtain non-dominated solutions. Interactivity gives the Decision Maker opportunity to incorporate his/her preferences during the iterations of the optimization process. A numerical example is given to illustrate how the approach is utilized.