aspg-21-2103-1791472104 20261008150824 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 22 2 Abuobida M. A. Alfahal Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Mohammad Abobala Tishreen University, Department Of Mathematics, Latakia, Syria Yaser Ahmad Alhasan Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Raja Abdullah Abdulfatah Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia In this paper, we find necessary and sufficient conditions for a weak fuzzy complex integer triple (X,Y, Z) style='mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif; mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'>X,Y,Z to be a pythagoras triple, and for an anti-weak fuzzy complex integer triple style='mso-bidi-font-size:10.0pt;font-family:"Cambria Math",serif; mso-ascii-font-family:"Cambria Math";mso-hansi-font-family:"Cambria Math"; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; font-style:italic;mso-bidi-font-style:normal'> style='mso-bidi-font-style:normal'> font-family:"Cambria Math",serif;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi'>X,Y,Z 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 08 14 2103 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.220201 https://www.americaspg.com/journal/21/article/2103 https://www.americaspg.com/storage/71749422170.pdf