aspg-21-913-1791475285 20261008160125 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2021 17 1 Necmiye Merve Sahin Faculty of Law, Hasan Kalyoncu University, Gaziantep 27410, Turkey Merve Sena Uz Department of Mathematics, Gaziantep University, Gaziantep27310-Turkey In this article, an algorithm has been introduced that enables judges to see the decisions that should be made in a way that is closest to the conscience and the law, without transferring the cases to the higher authorities, without anyone objecting to their decisions. This algorithm has been introduced depending on the generalized set-valued neutrosophic quadruple numbers and the Euclidean similarity measure in sets, what the decision is made by considering all the situations, regardless of which case the defendants come before the judge, how similar these decisions are to the legal decisions that should be made. In this way, we can easily see the decisions given to the accused in all kinds of cases, and we can arrange the decisions according to the similarity value. The closer the similarity value is to 1, the more correct the judge's decision from a legal point of view. 2021 41 60 913 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.170103 https://www.americaspg.com/journal/21/article/913 https://www.americaspg.com/storage/4658.pdf