aspg-21-3891-1791475925 20261008161205 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2025 26 4 Ali Ibrahim Mansour Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq Amal A. Ibrahim Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq Auday Hekmat Mahmood Department of Mathematics, College of Education, Mustansiriyah University, Baghdad, Iraq Let style='mso-bidi-font-style:normal'> 107%;font-family:"Cambria Math",serif;mso-fareast-font-family:"Times New Roman"; mso-fareast-theme-font:minor-fareast;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-ansi-language:EN-US;mso-fareast-language: EN-US;mso-bidi-language:AR-SA'> M be the direct product of an associative ring style='mso-bidi-font-style:normal'> 107%;font-family:"Cambria Math",serif;mso-fareast-font-family:Calibri; mso-fareast-theme-font:minor-latin;mso-bidi-font-family:"Times New Roman"; mso-bidi-theme-font:major-bidi;mso-ansi-language:EN-US;mso-fareast-language: EN-US;mso-bidi-language:AR-SA'> "Cambria Math",serif;mso-fareast-font-family:Calibri;mso-fareast-theme-font: minor-latin;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'> m:val="script"/>Ɽ . In the work the concepts of Endo Bi-Antiderivation, Jordan Endo Bi-Antiderivation and Quasi Endo Bi-Antiderivation on a ring normal'> mso-fareast-font-family:"Times New Roman";mso-fareast-theme-font:minor-fareast; mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font:major-bidi; mso-ansi-language:EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA'> m:val="script"/>M are introduced, furthermore the relations between these bi-additive mappings are given. As essential point, we searched for appropriate conditions that make equivalence between Jordan Endo Bi-Antiderivation and Quasi Endo Bi-Antiderivation. Also, we prove the same results for the generalized case of neutrosophic rings. 2025 21 27 3891 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.260403 https://www.americaspg.com/journal/21/article/3891 https://www.americaspg.com/storage/61749743827.pdf