TOPSIS Based Algorithm for Solving Multi - objective 2 Multi - level Programming Problem with Fuzzy 3 Parameters 4

The paper proposes TOPSIS method for solving multi-objective multi-level programming 13 problem (MO-MLPP) with fuzzy parameters via fuzzy goal programming (FGP). At first, λ cut 14 method is used to transform the fuzzily described MO-MLPP into deterministic MO-MLPP. Then, 15 for specific λ , we construct the membership functions of distance functions from positive ideal 16 solution (PIS) and negative ideal solution (NIS) of all level decision makers (DMs). Thereafter, FGP 17 based multi-objective decision model is established for each level DM for obtaining individual 18 optimal solution. A possible relaxation on decisions for all DMs is taken into account for 19 satisfactory solution. Subsequently, two FGP models are developed and compromise optimal 20 solutions are found by minimizing the sum of negative deviational variables. To recognize the 21 better compromise optimal solution, the concept of distance functions is utilized. Finally, a novel 22 algorithm for MO-MLPP involving fuzzy parameters is provided and an illustrative example is 23 solved to verify the proposed procedure. 24