Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution

Hamiden Abd El- Wahed; Faisal; Ashraf; Zahari; Heba Ghareb; Abdalwali

doi:https://doi.org/10.54216/IJNS.230120

Full Length Article

Volume 23 • Issue 1 • PP: 287-298 • 2024

Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution

Hamiden Abd El- Wahed Khalifa ^1*

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,

Faisal Al-Sharqi ²

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,

Ashraf Al-Quran ³

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,

Zahari Rodzi ⁴

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,

Heba Ghareb Goma ⁵

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,

Abdalwali Lutfi

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¹Department of Mathematics, College of Science and Arts, Qassim University, Al- Badaya 51951, Saudi Arabia; Department of Operations and Management Research, Faculty of Graduate Studies for St

²Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq

³Preparatory Year Deanship, King Faisal University, Hofuf, Al-Ahsa, 31982, Saudi Arabia

⁴College of Computing, Informatics and Mathematics, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia

⁵Department of Mathematics and Statistics, Institute for Management Information Systems, Suiz, Egypt

⁶Department of Accounting, College of Business, King Faisal University, Al-Ahsa 31982, Saudi Arabia; MEU Research Unit, Middle East University, Amman, Jordan; Applied Science Research Center,

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.230120

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Received: May 27, 2023 Revised: August 11, 2023 Accepted: November 26, 2023

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Abstract

In this paper, a bi-level chance constrained programming problem is considered when the coefficients of the objective function is presented as neutrosophic numbers and the right- hand side of the constraints is normal variables and the constraints have a joint probability distribution. While the probability problem and applying the score and accurate functions the problem is converted into an equivalent deterministic non- linear programming problem, a fuzzy programming approach is applied by defining membership function. A linear membership function is used for obtaining optimal compromise solution. A numerical example is given to illustrate the proposed methodology.

Keywords

Optimization neutrosophic set single valued neutrosophic numbers Chance- constrained programming Bi- level linear programming Decision Making Normal distribution Joint constraints Incomplete Gamma function &nbsp Membership function Fuzzy programming approach Optimal compromise solution

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Khalifa, Hamiden Abd El- Wahed, Al-Sharqi, Faisal, Al-Quran, Ashraf, Rodzi, Zahari, Goma, Heba Ghareb, Lutfi, Abdalwali. "Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution." International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 1, 2024, pp. 287-298. DOI: https://doi.org/10.54216/IJNS.230120

Khalifa, H., Al-Sharqi, F., Al-Quran, A., Rodzi, Z., Goma, H., Lutfi, A. (2024). Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution. International Journal of Neutrosophic Science, Volume 23(Issue 1), 287-298. DOI: https://doi.org/10.54216/IJNS.230120

Khalifa, Hamiden Abd El- Wahed, Al-Sharqi, Faisal, Al-Quran, Ashraf, Rodzi, Zahari, Goma, Heba Ghareb, Lutfi, Abdalwali. "Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution." International Journal of Neutrosophic Science Volume 23, no. Issue 1 (2024): 287-298. DOI: https://doi.org/10.54216/IJNS.230120

Khalifa, H., Al-Sharqi, F., Al-Quran, A., Rodzi, Z., Goma, H., Lutfi, A. (2024) 'Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution', International Journal of Neutrosophic Science, Volume 23(Issue 1), pp. 287-298. DOI: https://doi.org/10.54216/IJNS.230120

Khalifa H, Al-Sharqi F, Al-Quran A, Rodzi Z, Goma H, Lutfi A. Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution. International Journal of Neutrosophic Science. 2024;Volume 23(Issue 1):287-298. DOI: https://doi.org/10.54216/IJNS.230120

H. Khalifa, F. Al-Sharqi, A. Al-Quran, Z. Rodzi, H. Goma, A. Lutfi, "Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution," International Journal of Neutrosophic Science, vol. Volume 23, no. Issue 1, pp. 287-298, 2024. DOI: https://doi.org/10.54216/IJNS.230120

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