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In decision making problems there may be cases in which decision makers do not have an in-depth knowledge of the problem to be solved. In such cases, more and more research has been conducted within a fuzzy or intuitionistic fuzzy framework. In this paper, we investigate the group decision making problems in which all the evaluation information provided by the decision makers is characterized by intuitionistic fuzzy decision matrices where each of the elements is expressed as intuitionistic fuzzy numbers (IFNs), and both weights of attributes and decision makers weights are incompletely known, which may be constructed by IFNs. By employing a projection model, fractional programming models are developed to determine the closeness interval values of alternatives. The interval values are subsequently used to aggregate into an overall interval value for each alternative, and the likelihood is applied to ranking and selection of alternatives. Feasibility and effectiveness of the developed models are illustrated with an example of investment decision problem.