aspg-21-2631-1791475990 20261008161310 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 1 Tuqa A. H. Al-Tamimi Department of Mathematics, College of Education for Pure Science, University of Babylon, Hillah, Iraq Luay A. A. Al-Swidi Department of Mathematics, College of Education for Pure Science, University of Babylon, Hillah, Iraq Ali H. M. Al-Obaidi Department of Mathematics, College of Education for Pure Science, University of Babylon, Hillah, Iraq Fuzzy sets and their various generalizations, especially neutrosophic and multineutrosophic sets, have had an essential imprint in other scientific, engineering, and applied fields. This came from the characteristics of membership functions that determine the extent to which members belong to their sets, which is an important criterion. Hence, the idea of building the optimal membership function for fuzzy set using the arithmetic mean, we called this set by partner sets of a neutrosophic set of style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-bidi-font-family:"Times New Roman";mso-bidi-theme-font: major-bidi'>n -type. 2024 08 13 2631 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240101 https://www.americaspg.com/journal/21/article/2631 https://www.americaspg.com/storage/21712004487.pdf