International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2458 2020 2020 Department of Mathematics, Saveetha School of Engineering, Saveetha University, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India M. Palanikumar Department of Mathematics, Bharath Institute of Higher Education and Research, Tamil Nadu, Chennai-600073, India K. Arulmozhi Department of Mathematics, Al-Ameen Engineering College, Erode. K. Sundareswari 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. Aiyared Iampan 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 2024 18 28 10.54216/IJNS.230302 https://www.americaspg.com/articleinfo/21/show/2458