In this paper, a new fuzzy multi-attribute decision making framework for group decision making is proposed. The proposed framework combines both the concept of fuzzy outranking and fuzzy attributes to provide a more flexible way of comparing the alternatives. It consists of three steps. In the first step, the preferences of the decision makers are gathered and then aggregated. In the second step, the attributes are normalized by considering the threshold and the target values of each attribute. At the last step, the results of the previous steps are used as input to a fuzzy multi-attribute decision making approach in order to rank and/or select alternatives. A fuzzy logic based computation is applied in each step for the imprecise or ambiguous data.