Fuzzy approach with linear and some non-linear membership functions for solving multi-objective assignment problems

Assignment Problem (A.P.) originates from the classical problems where the objective is to find 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 of vector minimum linear programming problems. In this paper, we use a special type of linear and non- linear membership functions to solve the multi-objective assignment problem. It gives an optimal compromise solution. The result obtained by using a linear membership function has been compared with the solution obtained by using non-linear membership functions. Numerical example has been provided to illustrate the solution procedure. Keywords - Assignment Problem, Multi-criteria decision making, Linear membership function, Non-linear membership function