aspg-21-2465-1791475487 20261008160447 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 23 3 Hamiden Abd El- Wahed Khalifa 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 Resea Ashraf Al-Quran Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa, Saudi Arabia Faisal Al-Sharqi University Headquarter, Department of Scholarships and Cultural Relations, University of Anbar, Ramadi; College of Pharmacy, National University of Science and Technology, Dhi Qar, Iraq Binyamin Yusoff Special Interest Group on Modelling and Data Analytics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Malaysia Khadiga W. Nahar Tajer Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass 51452, Saudi Arabia Abeer T. Faisal University Headquarter, Department of Scholarships and Cultural Relations, University of Anbar, Ramadi Ali M. Alorsan Bany Awad Deanship of Development and Quality Assurance, King Faisal University, Al-Ahsa 31982, Saudi Arabia 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. 2024 87 96 2465 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.230308 https://www.americaspg.com/journal/21/article/2465 https://www.americaspg.com/storage/71706726074.pdf