In decision making problems that contain multiple and conflicting objectives, it is not an easy and straightforward task to determine the most preferred solution of a decision maker. In this study, an interactive method is proposed to converge to the most preferred solution of the decision maker. The proposed method elicits preference information from the decision maker in consecutive iterations and reduces the solution space accordingly. The decision maker evaluates a limited number of solutions in each iteration and makes decisions that impose low cognitive burden. These decisions are modeled by a weighted Lα function, a preference function that is flexible and compatible with behavior of real decision makers. To enhance the efficiency of the proposed method, the solutions presented for evaluation in each iteration are determined with the help of a filtering approach. Data from annual university rankings of Times Higher Education is used to assess the performance of the proposed method. Experiments are carried out with three different university sets evaluated with respect to five criteria. The results show that the proposed method successfully converges to the most preferred solution.