International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2395 2020 2020 Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Pakistan;Department of Mathematics, Thal university Bhakkar, Punjab, Pakistan Muhammad Kamran Department of Mathematics, Thal university Bhakkar, Punjab, Pakistan. Nadeem Salamat Department of Mathematics, Thal university Bhakkar, Punjab, Pakistan. Shahzaib Ashraf Faculty of Engineering, Future University in Egypt Ahmed M. Hassan Department of Computer Science, College of Computer, Qassim University, Buraydah 51452, Saudi Arabia; Data Engineering and Semantics Research Unit, Faculty of Sciences of Sfax, University of Sfax, Sfax, Tunisia. Walid Karamti Neutrosophic sets can be used to model uncertain data in real-world applications. To increase the use of complex neutrosophic sets, the space of quaternion numbers is investigated in this work. Analysts in complex contexts can benefit from the knowledge and direction that quaternion neutrosophic sets can offer by modeling complicated systems and capturing the interactions between various factors. Division algebras are used in some applications, such as particular formulations of class field theory, but they are generally far less important than quaternion numbers. Three-dimensional information with imaginary membership, imaginary indeterminacy, and imaginary non-membership functions is represented using quaternion neutrosophic sets. Intriguing quaternion numbers give us useful results when we analyze complicated data. Some basic characteristics of the derived concepts are examined. Novel quaternion-based operations and the analysis of order relations and logic operations are also explored based on neutrosophic set theory. For modeling uncertainty in quaternion-based systems, quaternion neutrosophic sets are helpful. Other fuzzy sets are unable to adequately capture the sophisticated fuzzy information that they can represent, such as uncertainty in both size and direction. The capacity to define fuzzy distance and similarity metrics is one of its intriguing qualities. We also present two quaternion distance measures and evaluate their properties. We use quaternion representations and measurements in a neutrosophic framework for decision-making models, and the results are excellent. Additionally, it shows readers how to construct the connections between traits and alternatives that are used in decision-making issues. An example is provided at the end to help illustrate the suggested strategy and provide additional context. Finally, we employ a different distance metric that is illustrated in the reliability section to validate the developed methodologies. It is possible to address the findings of studies on the application of quaternion neutrosophic sets for addressing various types of uncertainty in optimization problems related to the design and management of complex systems. 2024 2024 244 262 10.54216/IJNS.230220 https://www.americaspg.com/articleinfo/21/show/2395