Volume 11, Issue 2 (9-2025)
mmr 2025, 11(2): 16-38 |
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pourofoghi F. Solving linear fractional programming problem in uncertainty environment with grey parameters. mmr 2025; 11 (2) :16-38
URL: http://mmr.khu.ac.ir/article-1-3427-en.html
URL: http://mmr.khu.ac.ir/article-1-3427-en.html
Department of Mathematics, Payame Noor University, Tehran, Iran , f_pourofoghi@pnu.ac.ir
Abstract: (35 Views)
| The fractional programming problem is an important nonlinear programming tool used in various fields such as resource allocation, transportation, production planning, etc. Due to the uncertainty in real-world problems, it is very difficult to determine the definite coefficients for the mathematical model of the problems. Therefore, the coefficients of the mathematical model of the problems are considered as uncertain. One of the approaches to dealing with uncertainty, in addition to probability, stochastic, fuzzy theory, is the theory of grey systems. In this paper, a linear fractional programming problem with grey coefficients in the objective function is considered. To solve these problems, the grey parameter whitening method is often used, which causes the solution obtained in this method not to reflect the uncertainty of the grey parameters in the optimal solution. To solve this problem, in this paper, an algorithm is presented, based on which, according to the type of objective function of the grey linear fractional programming problem, it is converted into two grey linear programming subproblems, and then the solution of the grey linear fractional programming problem is determined by solving those two subproblems. By implementing the proposed method, the solution of the grey linear fractional programming problem is determined as interval grey numbers, and as a result, the uncertainty in the objective function is reflected in the final result. Finally, to demonstrate the effectiveness of the proposed method, an example has been solved with the proposed method. To demonstrate the effectiveness of the proposed method, the solution obtained from the proposed method was evaluated with the solutions obtained from other methods, for example, the two grey number ranking methods of Hu and Wang and the center and grey degree. It was shown that the solution obtained from the proposed method is better than other solution methods. |
Type of Study: S |
Subject:
Mat
Received: 2024/10/26 | Revised: 2025/11/8 | Accepted: 2025/07/30 | Published: 2025/09/6 | ePublished: 2025/09/6
Received: 2024/10/26 | Revised: 2025/11/8 | Accepted: 2025/07/30 | Published: 2025/09/6 | ePublished: 2025/09/6
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