The fuzzy assignment method works for any problems in which one to one matching is called for in the light of the given payoffs where the total payoff is sought to minimized or maximized. Throughout this paper, solving technique absolutely think about as an assignment problem with the assistance of trapezoidal membership functions and its arithmetic operations. Solving procedure has been applied from the approach of fuzzy Hungarian method using Robust Ranking technique. The fuzzified version of the problem has been mentioned with the assistance of a numerical example associated it's proving that the Robust ranking methodology offers an efficient tool for handling the assignment problem. Finally the optimum solution with in the kind of fuzzy numbers and verified its solution with in the nature of fuzzy membership functions. © 2014 IEEE.