International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2913 2020 2020 Department of Mathematics, Little Flower College-680103, Guruvayoor, India M. M. Department of Mathematics and Physics, College of Engineering, Australian University, West Mishref, Safat 13015, Kuwait. Sadeq Damrah Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa, 13133, Jordan Ibraheem Abu Falahah Department of Mathematics, Faculty of Science and Technology, Irbid National University, P.O. Box: 2600 Irbid, Jordan Abdallah Al Al-Husban Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai, Tamil Nadu 602105, India M. Palanikumar We introduce the new type neutrosophic interval-valued set (NIVS) problems relevant to multiple attribute decision making (MADM). Pythagorean interval-valued fuzzy set (PIVFS) and neutrosophic set (NS) can be extended into new type neutrosophic interval-valued set. We discusses new type neutrosophic interval-valued weighted averaging (new type NIVWA), new type neutrosophic interval-valued weighted geometric (new type NIVWG), generalized new type neutrosophic interval-valued weighted averaging (new type GNIVWA) and generalized new type neutrosophic interval-valued weighted geometric (new type GNIVWG). A number of algebraic properties of new type NIVSs have been established such as associativity, distributivity and idempotency. Using expert judgments and criteria, we will be able to decide which options are the most appropriate. Several of the proposed and current models are also compared in order to demonstrate the reliability and usefulness of the models under study. Additionally, the findings of the study are fascinating and intriguing.   2024 2024 335 351 10.54216/IJNS.240424 https://www.americaspg.com/articleinfo/21/show/2913