International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2829 2020 2020 Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu 602105, India admin admin Department of Mathematics, St. Joseph’s Institute of Technology, OMR, Chennai-600119, India T. T. Raman Department of Mathematics, Agni College of Technology, Thalambur, Chennai-600130, India. A. Swaminathan Department of Mathematics, School of Science, University of Phayao, Mae Ka, Mueang, Phayao 56000, Thailand. Aiyared Iampan 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 2024 220 232 10.54216/IJNS.240319 https://www.americaspg.com/articleinfo/21/show/2829