International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1374 2020 2020 Department of Mathematics, Saveetha School of Engineering, Saveetha University, Saveetha Institute of Medical and Technical Sciences, Chennai-602105, India M. Palanikumar Laboratory of Information Processing, Faculty of Science Ben MSik, University of Hassan II, Casablanca, Morocco Said Broumi We discuss innovative square root Diophantine neutrosophic normal interval-valued set (SRDioNSNIVS)- based approaches to multiple attribute decision-making (MADM) problems. Square root neutrosophic sets, interval-valued Diophantine neutrosophic sets and neutrosophic normal interval-valued (NSNIV) sets are both extensions of square root Diophantine neutrosophic sets. In this section, we will look over several aggregating operations and how those interpretations have evolved over time. The article is focused on a novel idea known as square root NSNIV weighted averaging (SRDioNSNIVWA), square root NSNIV weighted geometric (SRDioNSNIVWG), generalized square root NSNIV weighted averaging (GSRDioNSNIVWA), and generalized square root NSNIV weighted geometric (GSRDioNSNIVWG). In order to solve MADM problems, we also begin an algorithm based on the aforementioned operators. The use of the euclidean and hamming distances is described, and examples from real-world situations are given. The main characteristics of these sets under various algebraic operations will be discussed in this communication. They are more practical and straightforward, and the ideal choice may be determined quickly. As a result, the defined models are more accurate and closely tied to Φ. In order to show the reliability and usefulness of the models under examination, we also compare a few of the proposed and current models. The study’s results are also fascinating and intriguing. 2022 2022 63 84 10.54216/IJNS.190307 https://www.americaspg.com/articleinfo/21/show/1374