<p>In addressing the challenges of solving real-life transportation problems, we frequently encounter uncertainties and hesitation stemming from some uncontrollable circumstances. To cope with such challenges, various mathematical tools have been introduced by researchers. In this paper, we introduce a new ranking approach for triangular and trapezoidal intuitionistic fuzzy sets. This approach is based on the concept of degrees of membership and non-membership of intuitionistic fuzzy sets. We also include some numerical examples to demonstrate the effectiveness of our proposed ordering approach. Furthermore, we discuss on finding optimal solution of intuitionistic fuzzy transportation problems. To perform this, we have utilized this ordering approach to develop methods for finding initial basic feasible solutions and optimal solutions to transportation problems. Also, the method is elaborated by some adopted case studies which are followed by graphical representation and discussion of the observations. At length, we perform statistical tests and analyze the results to discuss the importance of our proposed approach.</p>