International Journal of Engineering and Technical Research (IJETR) ISSN: 2321-0869 (O) 2454-4698 (P), Volume-3, Issue-10, October 2015 152 www.erpublication.org Abstract— In this paper, we extend TOPSIS (Technique for Order Preference by Similarity Ideal Solution) for solving Large Scale Two-level Linear Multiple Objective Programming problems with fuzzy parameters in the right-hand side of the independent constraints (FLS-TL-LMOP). In order to obtain a compromise ( satisfactory) solution to the above problems using the TOPSIS approach, a modified formulas for the distance function from the positive ideal solution (PIS ) and the distance function from the negative ideal solution (NIS) are proposed and modeled to include all the objective functions of both the first and the second levels. An interactive decision making algorithm for generating a compromise ( satisfactory) solution through TOPSIS approach is provided where the first level decision maker (FLDM) is asked to specify the membership function for each fuzzy parameter , the maximum negative and positive tolerance values, the power p of the distance functions, the degree α and the relative importance of the objectives. Finally, a numerical example is given to clarify the main results developed in the paper. Index Terms— Interactive decision making, multiple objective programming problems, two-level programming, TOPSIS, block angular structure, large scal programming, fuzzy programming, fuzzy parameters. I. INTRODUCTION The decentralized planning has been recognized as an important decision-making problem. It seeks to find a simultaneous compromise among the various objective functions of the different divisions. Twoi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and that is of the follower at the second level. The decision-maker at each level attempts to optimize his individual objective, which usually depends in part on the variables controlled by the decision-maker at the other levels and their final decisions are executed sequentially where the upper-level decision-maker makes his decision firstly, [4, 5, 25]. Abo–Sinna, M. A. and Abou-El-Enien, T. H. M. [1], introduce an algorithm for solving large scale multiple objective decision making (LSMODM) problems by use of TOPSIS.Abo–Sinna, M. A. and Abou-El-Enien, T. H. M. [2], extend TOPSIS for solving interactive large scale multiple Objective programming problems involving fuzzy parameters. An interactive fuzzy decision making algorithm * Tarek. H. M. Abou-El-Enien , Department of Operations Research & Decision Support, Faculty of Computers & Information, Cairo University, 5 Dr. Ahmed Zoweil St. - Orman -Postal Code 12613 - Giza – Egypt. ** Mahmoud A. Abo-Sinna, Department of Mathematical Science, Faculty of Science, Princess Nora Bint Abdul Rahman university,Riyadh, Saudi Arabia. for generating α-Pareto optimal solution through TOPSIS approach is provided where the decision maker (DM) is asked to specify the degree α and the relative importance of objectives. Abou-El-Enien, T. H. M. [6], focus on the solution of a Large Scale Integer Linear Vector Optimization Problems with chance constraints (CHLSILVOP) using TOPSIS approach, where such problems has block angular structure of the constraints. He introduced an algorithm based on TOPSIS approach to solve CHLSILVOP with constraints of block angular structure. Abou-El-Enien, T. H. M. [8] ,extend TOPSIS method for solving Linear Fractional Vector Optimization problems (LFVOP) of a special type, An interactive decision making algorithm for generating a compromise solution through TOPSIS approach is provided where the decision maker (DM) is asked to specify the degree α and the relative importance of the objectives. Finally, a numerical example is given to clarify the main results developed in the paper. Baky, I. A. and Abo-Sinna, M. A. [12] proposed a TOPSIS algorithm for bi-level multiple objective decision making problems. Abo–Sinna, M. A. and Abou-El-Enien, T. H. M. [3] , extend TOPSIS method for solving Large Scale Bi-level Linear Vector Optimization Problems (LS-BL-LVOP). They further extended the concept of TOPSIS for LS-BL-LVOP. Abou-El-Enien, T. H. M. [9], extended TOPSIS for solving a special type of Two-Level Integer Linear Multiple Objectives Decision Making (ST-TL-IL MODM) Problems with block angular structure. In order to obtain a compromise ( satisfactory) integer solution to the ST-TL-ILMODM problems with block angular structure using the proposed TOPSIS approach, a modified formulas for the distance function from the positive ideal solution (PIS ) and the distance function from the negative ideal solution (NIS) are proposed and modeled to include all the objective functions of the two levels. In every level, as the measure of “Closeness” dp-metric is used, a k-dimensional objective space is reduced to two –dimensional objective space by a first-order compromise procedure. Abou-El-Enien, T. H. M. [10], extended TOPSIS method for solving Two-Level Large Scale Linear Multiobjective Optimization Problems with Stochastic Parameters in the right hand side of the constraints (TL-LSLMOP-SP) rhs of block angular structure. In order to obtain a compromise ( satisfactory) solution to the (TL-LSLMOP-SP) rhs of block angular structure using the proposed TOPSIS method, a modified formulas for the distance function from the positive ideal solution (PIS ) and the distance function from the negative ideal solution (NIS) are proposed and modeled to include all the objective functions of the two levels. Abou-El-Enien, T. H. M. [7] , presents many algorithms for solving different kinds of Large Scale Linear Interactive TOPSIS Algorithm for Fuzzy Large Scale Two-Level Linear Multiple Objective Programming Problems Tarek H. M. Abou-El-Enien, Mahmoud A. Abo-Sinna