In this paper a TOPSIS method based on the theory of intuitionistic fuzzy set (IFS) is proposed which will suitably deal with vagueness and hesitancy. A fuzzy TOPSIS decision making model using entropy weight for dealing with multiple criteria decision making (MCDM)problems under intuitionistic fuzzy environment is proposed and also weight determining methods based on Regular Increasing Monotone (RIM) method and Gaussian methodare utilised. A numerical illustration is given for the application of the proposed model.