Assignment Problem (A.P.) originates from the classical problems where the objective is tofind the optimum assignment of a number of jobs (tasks) to an equal number of machines (or workers)at a minimum cost or minimum time. The multi-objective assignment problem refers to a special class ofvector minimum linear programming problems. In this paper, we use a special type of linear and nonlinearmembership functions to solve the multi-objective assignment problem. It gives an optimalcompromise solution. The result obtained by using a linear membership function has been comparedwith the solution obtained by using non-linear membership functions. Numerical example has beenprovided to illustrate the solution procedure.