Fuzzy programming approach to solve multi objective linear fractional program with homogeneous constraints

In this paper we propose a fuzzy programming methodology for multi objective linear fractional program (MOLFP) when some of its constraints are homogeneous. The proposed methodology works for the minimization of the perpendicular distances between the parallel hyper planes at the optimum points of the objective functions and a compromise optimal solution is obtained as a result of minimization of supremum perpendicular distance. We also prove that the development of transformation matrix T which converts the given problem into another problem with fewer constraints, hold in MOLFP problem with proposed methodology. A pseudo code computer program is constructed for the development of transformation matrix. A comparative analysis of with and without using transformation matrix in the proposed methodology is performed on a numerical example.