FGP approach based on stanojevic’s normalization technique for multi-level multi-objective linear fractional programming problem with fuzzy parameters

Abstract

This paper aims to present a Fuzzy Goal Programming (FGP) method taking the help of Taylor series approximation and normalization technique due to Stanojevic to solve multi-level multi-objective linear fractional programming problem with fuzzy parameters (MLMOLFPP-FP). Firstly, a crisp model of the problem is developed using level sets followed by the construction of membership functions which are non-linear in nature. These are then linearized using first order Taylor series approximation and normalization technique [1]. The normalization technique ensures that the obtained linear membership functions have their range within the permissible limit of [0, 1]. The compromise solution for each level is calculated through FGP method. Each level decision maker imposes some preference bounds on the decision variable associated with him/her to avoid decision deadlock. Finally, the original MLMOLFPP-FP is reduced into a linear programming problem (LPP) through FGP technique where the highest degree of the membership goals is attained by minimizing the negative deviational variables. Euclidean distance function helps us to select the best FGP model from the two FGP models described to solve the MLMOLFPP-FP.