aspg-21-2829-1791468592 20261008140952 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2024 24 3 M. Palanikumar Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu 602105, India T. T. Raman Department of Mathematics, St. Joseph’s Institute of Technology, OMR, Chennai-600119, India A. Swaminathan Department of Mathematics, Agni College of Technology, Thalambur, Chennai-600130, India. Aiyared Iampan Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. The purpose of this article is to present a novel approach to the (δ,ε) interval-valued neutrosophic set (IVNS). This is an extension of the IVNS. As a result of this article, we will discuss the concept of (δ,ε) interval valued neutrosophic weighted averaging (IVNWA), (δ,ε) interval-valued neutrosophic weighted geometric (IVNWG), (δ,ε) generalized interval-valued neutrosophic weighted averaging (GIVNWA) and (δ,ε) generalized interval-valued neutrosophic weighted geometric (GIVNWG). Additionally, the (δ,ε) IVNS approach is characterized by idempotency, boundedness, commutativity and monotonicity. 2024 220 232 2829 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.240319 https://www.americaspg.com/journal/21/article/2829 https://www.americaspg.com/storage/11716570335.pdf