International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2103 2020 2020 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Abuobida M. A. Alfahal Tishreen University, Department Of Mathematics, Latakia, Syria Mohammad Abobala Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Yaser Ahmad Alhasan Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Raja Abdullah Abdulfatah In this paper, we find necessary and sufficient conditions for a weak fuzzy complex integer triple (X,Y, Z) to be a pythagoras triple, and for an anti-weak fuzzy complex integer triple   to be a Pythagoras triple  (X,Y, Z), where we prove that the non-linear Fermat's Diophantine equation  has three different types of solutions according to the value of . All types will be solved and discussed in terms of theorems and examples that explains how the algorithms work 2023 2023 08 14 10.54216/IJNS.220201 https://www.americaspg.com/articleinfo/21/show/2103