Generalized Hamming Similarity Measure Based on Neutrosophic Quadruple Numbers and Its Applications to Law Sciences

Abstract

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.

Keywords

• neutrosophic quadruple sets
• generalized set valued neutrosophic quadruple sets and numbers
• hamming similarity measure
• decision-making applications
• law applications