International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2465 2020 2020 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 Abd El- Wahed Khalifa Basic Sciences Department, Preparatory Year Deanship, King Faisal University, Al-Ahsa, Saudi Arabia Ashraf Al Al-Quran 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 Al Al-Sharqi Special Interest Group on Modelling and Data Analytics, Faculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Malaysia Binyamin .. Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass 51452, Saudi Arabia Khadiga W. Nahar Tajer University Headquarter, Department of Scholarships and Cultural Relations, University of Anbar, Ramadi Abeer T. Faisal Deanship of Development and Quality Assurance, King Faisal University, Al-Ahsa 31982, Saudi Arabia Ali M. Alorsan Bany Awad 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 2024 87 96 10.54216/IJNS.230308 https://www.americaspg.com/articleinfo/21/show/2465