Multi-level Multi-objective Linear plus Linear Fractional Programming Problem Based on FGP Approach

In the paper, multilevel multi-objective linear plus linear fractional programming problem is presented. The objective functions of level decision makers are characterized by linear plus linear fractional form of decision variables. Linear system constraints are considered. Each level decision maker possesses more than one objective functions. Membership function for each objective function is constructed by taking individual best solution of each objective function as aspiration level. The nonlinear membership functions are transformed into linear membership functions by using first order Taylor’s series. Three FGP models are developed to solve the converted multi-objective multilevel problems with linear constraints. Euclidean distance function is used to select the best compromise solution. A numerical example is solved to illustrate the proposed approach.