The ranking approach is one of the most used techniques in solving the fuzzy optimization problems. This article defines a novel ranking function to compare the trapezoidal fuzzy numbers (TrFNs).The fuzzy linear programming problem (FLPP) and fuzzy data envelopment analysis (FDEA) models are converted into its corresponding crisp LP problem and crisp DEA models. The ranking function associated with the risk factors that represent the decision maker's attitude towards taking the risk. The crisp LP problem solves with the different risk factors to obtain the optimum solution, and the crisp DEA model solves with the different risk factors to get the comparative efficiency scores of the DMUs. The DMUs are ranked and classified into efficient and inefficient groups according to the efficiency score obtained in crisp DEA model. Two different numerical examples are given to establish the existence and usability of the suggested methodologies for FLPP and FDEA models.