aspg-21-2458-1791475402 20261008160322 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 23 3 M. Palanikumar Department of Mathematics, Saveetha School of Engineering, Saveetha University, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India K. Arulmozhi Department of Mathematics, Bharath Institute of Higher Education and Research, Tamil Nadu, Chennai-600073, India K. Sundareswari Department of Mathematics, Al-Ameen Engineering College, Erode. Aiyared Iampan Fuzzy Algebras and Decision-Making Problems Research Unit, School of Science, University of Phayao, 19 Moo 2, Tambon Mae Ka, Amphur Mueang, Phayao 56000, Thailand. We introduce the concept of new type of Diophantine neutrosophic set. A Diophatine neutrosophic set is the new type of a neutrosophic set and Diophatine fuzzy set (DioFS). We discuss Diophantine neutrosophic weighted averaging (DioNWA), Diophantine neutrosophic weighted geometric (DioNWG), generalized Diophantine neutrosophic weighted averaging(GDioNWA), generalized Diophantine neutrosophic weighted geometric (GDioNWG). In this article, we define the Euclidean distance (ED), Hamming distance (HD) and operator laws. By analyzing new type of Diophantine neutrosophic set through algebraic operations, we discuss its properties. 2024 18 28 2458 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.230302 https://www.americaspg.com/journal/21/article/2458 https://www.americaspg.com/storage/51706628633.pdf