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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 23 , Issue 1 , PP: 287-298, 2024 | Cite this article as | XML | Html | PDF | Full Length Article

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 * , Faisal Al-Sharqi 2 , Ashraf Al-Quran 3 , Zahari Rodzi 4 , Heba Ghareb Goma 5 , Abdalwali Lutfi 6

  • 1 Department 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 Statistical Research, Cairo University, Giza 12613, Egypt - (Ha.Ahmed@qu.edu.sa)
  • 2 Department of Mathematics, Faculty of Education for Pure Sciences, University Of Anbar, Ramadi, Anbar, Iraq - (faisal.ghazi@uoanbar.edu.iq)
  • 3 Preparatory Year Deanship, King Faisal University, Hofuf, Al-Ahsa, 31982, Saudi Arabia - (aalquran@kfu.edu.sa)
  • 4 College of Computing, Informatics and Mathematics, UiTM Cawangan Negeri Sembilan, Kampus Seremban, 73000 Negeri Sembilan, Malaysia - (zahari@uitm.edu.my)
  • 5 Department of Mathematics and Statistics, Institute for Management Information Systems, Suiz, Egypt - (dr.heba@suezmis.edu.eg)
  • 6 Department 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, Applied Science Private University, Amman 11931, Jordan - (aalkhassawneh@kfu.edu.sa)

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

    Received: May 27, 2023 Revised: August 11, 2023 Accepted: November 26, 2023
    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 ,   , Membership function , Fuzzy programming approach , Optimal compromise solution

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    Cite This Article As :
    Abd, Hamiden. , Al-Sharqi, Faisal. , Al-Quran, Ashraf. , Rodzi, Zahari. , Ghareb, Heba. , 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. , no. , 2024, pp. 287-298. DOI: https://doi.org/10.54216/IJNS.230120
    Abd, H. Al-Sharqi, F. Al-Quran, A. Rodzi, Z. Ghareb, 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, (), 287-298. DOI: https://doi.org/10.54216/IJNS.230120
    Abd, Hamiden. Al-Sharqi, Faisal. Al-Quran, Ashraf. Rodzi, Zahari. Ghareb, Heba. 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 , no. (2024): 287-298. DOI: https://doi.org/10.54216/IJNS.230120
    Abd, H. , Al-Sharqi, F. , Al-Quran, A. , Rodzi, Z. , Ghareb, 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 , () , 287-298 . DOI: https://doi.org/10.54216/IJNS.230120
    Abd H. , Al-Sharqi F. , Al-Quran A. , Rodzi Z. , Ghareb 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. (): 287-298. DOI: https://doi.org/10.54216/IJNS.230120
    Abd, H. Al-Sharqi, F. Al-Quran, A. Rodzi, Z. Ghareb, 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, vol. , no. , pp. 287-298, 2024. DOI: https://doi.org/10.54216/IJNS.230120

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