An interactive algorithm for large scale multiple objective programming problems with fuzzy parameters through TOPSIS approach

Abstract

In this paper, we extend TOPSIS (Technique for Order Preference by Similarity Ideal Solution) for solving Large Scale Multiple Objective Programming problems involving fuzzy parameters. These fuzzy parameters are characterized as fuzzy numbers. For such problems, the α-Pareto optimality is introduced by extending the ordinary Pareto optimality on the basis of the α-Level sets of fuzzy numbers. An interactive fuzzy decision making algorithm for generating α-Pareto optimal solution through TOPSIS approach is provided, where a decision maker (DM) is asked to specify the degree α and the relative importance of objectives. Finally, a numerical example is given to clarify the main results developed in the paper.

Solving Large-scale Three-level Linear Fractional Programming Problem with Rough Coefficient in Objective Function

“…The three level large scale linear programming problem is solved by adopting the leader-follower Stackelberg strategy combine with Dantzig and Wolf decomposition method [7,8,9].…”

A Decomposition Algorithm for Solving a Three Level Large Scale linear Programming Problem

“…The three level large scale linear programming problem is solved by adopting the leader-follower Stakelberg strategy combine with Dantzig and Wolf decomposition method ( [3,7,9]). One first gets the optimal solution that is acceptable to FLDM using the decomposition method to break the large scale problem into n-sub problems that can be solved directly.…”

“…Osman et al [12] presented a method for solving a special class of large scale fuzzy multi-objective integer problems depending on the decomposition algorithm. Furthermore Abo-Sinna and Abou-Elenin extended TOPSIS for solving large scale multiple objective programming involving fuzzy parameters [3]. These fuzzy parameters are characterized as fuzzy numbers, the α-Pareto optimality is introduced by extending the ordinary Pareto optimality on the basis of the α-level sets of fuzzy numbers.…”

“…El-Sawy et al [9] introduced an algorithm for decomposing the parametric space in large scale linear vector optimization problems under fuzzy environment. Recently, notable studies have been done in the area of multi-level and multi-objective large scale programming problems ( [3,4,6,12]). Benzi et al [6] developed and compared multi-level algorithms for solving large scale bound constrained nonlinear problems via interior point methods.…”

“…In large scale programming which closely describes and represents the real world decision situations, various factors of the real system should be reflected in the description of the objective function and constraints. Naturally these objective function and constraints involve many parameters and the experts may assign them different values ( [1,2,3,4]). After the publication of the Dantzig and Wolfe decomposition method [7], there have been numerous subsequent works on large scale linear and nonlinear programming problems with block angular structure ( [1,6,12]).…”