In this paper, we propose an exponential-related function (ER) and develop an intuitionistic fuzzy TOPSIS model based on the function (IF-TOPSISEF) to solve multi-attribute decision making (MADM) problems in which the performance ratings are expressed in intuitionistic fuzzy sets (IFSs). The main advantage of this new approach is that the exponential-related function is able to represent the aggregated effect of the positive and negative evaluations in the performance ratings of alternatives based on the intuitionistic fuzzy set (IFS) data. It also serves as a mean for the computations of the separation measures of each alternative from the intuitionistic fuzzy positive and negative ideal solutions to determine the relative closeness coefficients. To demonstrate the effectiveness of the proposed method, the proposed IF-TOPSISEF is applied for the evaluation of the concept designs of a part in an HDD machine (The drill pipe slider), and for some hypothetical examples.