International Journal of Neutrosophic Science

This work is dedicated to give the reader a wide review for recent advantages in the algebraic study of neutrosophic matrices, refined neutrosophic matrices, and n-refined neutrosophic matrices.

Neutrosophic topological groups are neutrosophic groups in an algebraic sense together with neutrosophic continuous group operations. In this article, we have presented neutrosophic bi-topological groups with illustrative examples. We have also defined eight new models of neutrosophic bi-topological groups. Neutrosophic bi-topological group that depends on two neutrosophic topologies group is more general than the neutrosophic topological group. Finally, Some basic properties of neutrosophic bi-topological groups were studied.

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.

This paper introduced the concept of neutrosophic multi topological space. The definitions of the interior, closure, exterior, and boundary of neutrosophic multiset is defined and also, its propositions will be studied with examples. 

Jurisprudential decisions always reflect confidence in the law. The more wrong a judge's decision is, the greater the reaction will be. This is something we all know. But today, the reactions to the decisions of the judges are increasing in a negative way. Because, making so many conscientious decisions or transferring cases to higher courts have widely increased. This means that people's objections to the decisions increase. To avoid such problems in judges' decisions, an algorithm is introduced in this article. The mentioned algorithm shows every decision given by judges as generalized set-valued neutrosophic quadruples and calculates its similarity to the ideal decision by Hamming similarity measure on generalized set-valued neutrosophic quadruples. The algorithm is introduced in such a way that it decides whether the decision to be made in each case is similar to the decision made by the judge or not. This allows us to see how correct the judges’ decisions are. The closer the algorithm result is to 1, the more accurate the decision. You can judge decisions according to this accuracy value and it is aimed to reduce the problems such as objections to the decisions.