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In this paper, we develop a new method of decision-making algorithm with Hausdorff distance and Hausdorff similarity measures based on generalized set-valued neutrosophic quadruple numbers. To establish the algorithm, we define Hausdorff distance measure and Hausdorff similarity measure on generalized setvalued neutrosophic quadruple. Next, we give a new method of decision-making application for impact of online learning on the learner. Also, we obtain different result from some previous applications (based on neutrosophic sets) for decision making algorithm. Thanks to our decision-making algorithm and similarity measure, researchers can obtain new applications for other decision making problems.

Neutrosophic quadruple numbers are the newest field studied in neutrosophy. Neutrosophic quadruple numbers, using the certain extent known data of an object or an idea, help us uncover their known part and moreover they allow us to evaluate the unknown part by the trueness, indeterminacy and falsity values. In this study, we generalized Hamming similarity measures for the generalized set-valued neutrosophic quadruple sets and numbers. We showed that generalized Hamming measure satisfies the similarity measure condition. Also, we generalized an algorithm for the generalized set-valued neutrosophic quadruple sets and numbers, we gave a multi-criteria decision making application for using the this generalized algorithm. In this application, we examined which of the laws established in different situations were more efficient. Furthermore, we obtained different result compared to previous algorithm and previous similarity measure based on singlevalued neutrosophic numbers. Therefore, we have shown that generalized set-valued neutrosophic quadruplet sets and numbers, a new field of neutrosophic theory, are more useful for decision-making problems in law science and more precise results are obtained. The application in this study can be developed and used in decision-making applications for law science and other sciences. © 2021. All Rights Reserved.

Topology is a branch of mathematic that deals with the specific definitions given for spatial structure concepts, com-pares different definitions and explores the connections between the structures described on the sets. Also, neutrosophic triplet metric and neutrosophic triplet topology are a new concept in neutrosophy and they are completely different from classical structures. In this paper, we firstly study neutrosophic triplet metric topology. Furthermore, we give some new definitions and properties for neutrosophic triplet metric space, neutrosophic triplet topology and neutrosophic triplet metric topology. Thus, we obtain neutrosophic triplet metric topology using the neutrosophic triplet metric and neutrosophic triplet topology. Also, we show relationship between neutrosophic triplet metric space and neutrosophic triplet topology.