A Primal-Dual Algorithm for Solving Multiobjective Linear Optimization Problems with Fuzzy Variables

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GHAZNAVI M.; Azodi A.; GHORANI M.

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Journal: Journal of Operational Research in its Applications Year:2020 | Volume:17 | Issue:3 (66) Page(s): 1-22

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Title

A Primal-Dual Algorithm for Solving Multiobjective Linear Optimization Problems with Fuzzy Variables

Author(s)

GHAZNAVI M. | Azodi A. | GHORANI M. | Issue Writer Certificate

Keywords

Fuzzy Multiobjective Linear ProgrammingQ1

Primal-Dual SimplexQ1

Fuzzy RankingQ2

Fuzzy Pareto Optimal SolutionQ1

Abstract

The fuzzy Primal-Dual Simplex method is a new and efficient method for solving linear programming problems with fuzzy variables. This algorithm is based on duality results and, similar to the dual simplex method, begins with dual feasibility and proceeds to primal feasibility. An important difference between the dual simplex method and the primal-dual method is that in the primal-dual algorithm, it is not required that the dual feasible solution to be basic. In this paper, we develop the Primal-Dual Simplex method for solving Fuzzy Multiobjective Linear Programming problems. To this end, we utilize the fuzzy weighted sum scalarization method to present a fuzzy single objective optimization problem related to the Fuzzy Multiobjective Linear Programming problem. Then, by partitioning the weights of the weighted sum problem, we generalize the single objective primal-dual algorithm to fuzzy multiobjective problems. By using the presented algorithm, we can find a set of Fuzzy Pareto Optimal Solutions. Presenting a set of Fuzzy Pareto Optimal Solutions to the decision maker, enables him\her to select the best solution based on his\her preferences. Finally, we apply the proposed algorithm for solving a three-objective optimization problem with fuzzy variables and compare the results with some existing methods.

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APA: Copy

GHAZNAVI, M., Azodi, A., & GHORANI, M.. (2020). A Primal-Dual Algorithm for Solving Multiobjective Linear Optimization Problems with Fuzzy Variables. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), 17(3 (66) ), 1-22. SID. https://sid.ir/paper/406968/en

Vancouver: Copy

GHAZNAVI M., Azodi A., GHORANI M.. A Primal-Dual Algorithm for Solving Multiobjective Linear Optimization Problems with Fuzzy Variables. JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS)[Internet]. 2020;17(3 (66) ):1-22. Available from: https://sid.ir/paper/406968/en

IEEE: Copy

M. GHAZNAVI, A. Azodi, and M. GHORANI, “A Primal-Dual Algorithm for Solving Multiobjective Linear Optimization Problems with Fuzzy Variables,” JOURNAL OF OPERATIONAL RESEARCH AND ITS APPLICATIONS (JOURNAL OF APPLIED MATHEMATICS), vol. 17, no. 3 (66) , pp. 1–22, 2020, [Online]. Available: https://sid.ir/paper/406968/en

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