1
Department of Mathematics, College of Science and Arts, Al- Badaya 51951, Qassim University, Saudi Arabia; Department of Operations Research, Faculty of Graduate Studies for Statistical Research, Cairo University, Giza 12613, Egypt
(hamiden@cu.edu.eg)
2
Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa, Saudi Arabia
(aalquran@kfu.edu.sa)
3
University Headquarter, Department of Scholarships and Cultural Relations, University of Anbar, Ramadi; College of Pharmacy, National University of Science and Technology, Dhi Qar, Iraq
(faisal.ghazi@uoanbar.edu.iq)
4
Special Interest Group on Modelling and Data Analytics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Malaysia
(binyamin@umt.edu.my)
5
Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass 51452, Saudi Arabia
(khadiganahar@gmail.com)
6
University Headquarter, Department of Scholarships and Cultural Relations, University of Anbar, Ramadi
(abeert2017@uoanbar.edu.iq)
7
Deanship of Development and Quality Assurance, King Faisal University, Al-Ahsa 31982, Saudi Arabia
(abanyawad@kfu.edu.sa)
Abstract :
This article considers a bi-level linear programming with single valued trapezoidal fuzzy neutrosophic cost coefficient matrix and Pythagorean fuzzy parameters in the set of constraints both in the right and left sides. Based on the score functions of the neutrosophic numbers and Pythagorean fuzzy numbers, the model is changed to the corresponding crisp bi-level linear programming (BLP) problem. This problem is designated as a Pythagorean fuzzy bi-level linear programming (PFBLP) problem under neutrosophic environment. Kuhn-Tucker's conditions for optimality are necessary and sufficient for the existence of the optimal solution to a BLP problem. Using the suggested methodology, the problem is formulated as a single-objective non-linear programming problem with several variables and constraints. Two typical numerical examples are examined to illustrate the proposed approach.
Keywords :
Optimization; Optimization problems; Bi-level programming; Pythagorean fuzzy number; Neutrosophic set; Single valued neutrosophic numbers; Treapezoidal neutrosophic numbers; Kuhn-Tucker's optimality conditions; Decision Making; GAMS computer package.
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| Style | # |
|---|---|
| MLA | Hamiden Abd El- Wahed Khalifa, Ashraf Al-Quran, Faisal Al-Sharqi, Binyamin Yusoff , Khadiga W. Nahar Tajer, Abeer T. Faisal, Ali M. Alorsan Bany Awad. "Utilization of neutrosophic Kuhn-Tucker’s optimality conditions for Solving Pythagorean fuzzy Two-Level Linear Programming Problems." International Journal of Neutrosophic Science, Vol. 23, No. 3, 2024 ,PP. 87-96 (Doi : https://doi.org/10.54216/IJNS.230308) |
| APA | Hamiden Abd El- Wahed Khalifa, Ashraf Al-Quran, Faisal Al-Sharqi, Binyamin Yusoff , Khadiga W. Nahar Tajer, Abeer T. Faisal, Ali M. Alorsan Bany Awad. (2024). Utilization of neutrosophic Kuhn-Tucker’s optimality conditions for Solving Pythagorean fuzzy Two-Level Linear Programming Problems. Journal of International Journal of Neutrosophic Science, 23 ( 3 ), 87-96 (Doi : https://doi.org/10.54216/IJNS.230308) |
| Chicago | Hamiden Abd El- Wahed Khalifa, Ashraf Al-Quran, Faisal Al-Sharqi, Binyamin Yusoff , Khadiga W. Nahar Tajer, Abeer T. Faisal, Ali M. Alorsan Bany Awad. "Utilization of neutrosophic Kuhn-Tucker’s optimality conditions for Solving Pythagorean fuzzy Two-Level Linear Programming Problems." Journal of International Journal of Neutrosophic Science, 23 no. 3 (2024): 87-96 (Doi : https://doi.org/10.54216/IJNS.230308) |
| Harvard | Hamiden Abd El- Wahed Khalifa, Ashraf Al-Quran, Faisal Al-Sharqi, Binyamin Yusoff , Khadiga W. Nahar Tajer, Abeer T. Faisal, Ali M. Alorsan Bany Awad. (2024). Utilization of neutrosophic Kuhn-Tucker’s optimality conditions for Solving Pythagorean fuzzy Two-Level Linear Programming Problems. Journal of International Journal of Neutrosophic Science, 23 ( 3 ), 87-96 (Doi : https://doi.org/10.54216/IJNS.230308) |
| Vancouver | Hamiden Abd El- Wahed Khalifa, Ashraf Al-Quran, Faisal Al-Sharqi, Binyamin Yusoff , Khadiga W. Nahar Tajer, Abeer T. Faisal, Ali M. Alorsan Bany Awad. Utilization of neutrosophic Kuhn-Tucker’s optimality conditions for Solving Pythagorean fuzzy Two-Level Linear Programming Problems. Journal of International Journal of Neutrosophic Science, (2024); 23 ( 3 ): 87-96 (Doi : https://doi.org/10.54216/IJNS.230308) |
| IEEE | Hamiden Abd El- Wahed Khalifa, Ashraf Al-Quran, Faisal Al-Sharqi, Binyamin Yusoff, Khadiga W. Nahar Tajer, Abeer T. Faisal, Ali M. Alorsan Bany Awad, Utilization of neutrosophic Kuhn-Tucker’s optimality conditions for Solving Pythagorean fuzzy Two-Level Linear Programming Problems, Journal of International Journal of Neutrosophic Science, Vol. 23 , No. 3 , (2024) : 87-96 (Doi : https://doi.org/10.54216/IJNS.230308) |