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In this study, as a generalized form of multiple valued neutrosophic numbers and neutrosophic quadruple numbers, multiple generalized set-valued neutrosophic quadruple numbers and sets are defined and their basic properties are given. Thus, a new structure is obtained in which multi-valued neutrosophic sets and neutrosophic quadruple sets are used together. Also, optimistic union, pessimistic union, average union, pessimistic intersection, optimistic intersection, average intersection operators are defined for multiple generalized set-valued neutrosophic quadruples. Thus, multiple generalized set-valued neutrosophic quadruple sets were made usable in decision-making applications. Researchers can obtain more objective results in decision making applications by using these operators. [ABSTRACT FROM AUTHOR]

In this study, some constructions related to interval generalized set-valued neutrosophic quintuple sets and score and certainty functions are given. Moreover, optimistic union, pessimistic union, mean union, optimistic intersection, pessimistic intersection and mean intersection operators are defined for interval generalized set-valued neutrosophic quintuple set. Thus, interval generalized set-valued neutrosophic quintuple set are effectively used in decision making applications. An example application was realised using these operators and functions. With this application, the use of operators and functions in decision making methods was demonstrated. In addition, it was concluded that similar or different results can be obtained by using different operators. In addition, the importance of choosing the appropriate operator for the problem in decision making applications was mentioned for the decision making process. Researchers can obtain more objective results in decision making processes by using the operators and functions in this study. [ABSTRACT FROM AUTHOR]

In this paper; new properties for neutrosophic triplet groups are introduced. A notion of neutrosophic triplet metric space is given and properties of neutrosophic triplet metric spaces are studied. Neutrosophic triplet vector space and neutrosophic triplet normed space are also studied and some of their properties are given. Furthermore, we also show that these neutrosophic triplet notionsare different from the classical notions.

In this article, we define firstly generalized Euclid distance measure and generalized Euclid similarity measure based on generalized set valued neutrosophic quadruple numbers. Also, we show that generalized Euclid distance measure and generalized Euclid similarity measure satisfy the distance measure conditions and similarity measure conditions, respectively. Furthermore, we define a score function for generalized Euclid similarity measure. In addition, we generalize an algorithm, for single valued neutrosophic set, based on generalized Euclid similarity measure and generalized set valued neutrosophic quadruple numbers. Also, we give a multi criteria decision making applications for this generalized algorithm. This application based on patients, diseases, drugs and this application is different from previous applications because of generalized Euclid similarity measure and generalized set valued neutrosophic quadruple numbers. Furthermore, this application has different result according to some previous similarity measure. Thus, this application can used for covid-19 treatment due to structure of generalized Euclid similarity measure and generalized set valued neutrosophic quadruple numbers [ABSTRACT FROM AUTHOR]

Neutrosophic triplet theory has an important place in neutrosophic theory. Since the neutrosophic triplet set (Nts), which have the feature of having multiple unit elements, have different units than the classical unit, they have more features than the classical set. Also, Banach spaces are complete normed vector space defined by real and complex numbers that are studied historically in functional analysis. Thus, normed space and Banach space have an important place in functional analysis. In this article, neutrosophic triplet m - Banach spaces (NtmBs) are firstly obtained. Then, some definitions and examples are given for NtmBs. Based on these definitions, new theorems are given and proved. In addition, it is shown that NtmBs is different from neutrosophic triplet Banach space (NtBs). Furthermore, it is shown that relationship between NtmBs and NtBs. So, we added a new structure to functional analysis and neutrosophic triplet theory. [ABSTRACT FROM AUTHOR]

In this article, neutrosophic triplet partial bipolar metric spaces are obtained. Then some definitions and examples are given for neutrosophic triplet partial bipolar metric space. Based on these definitions, new theorems are given and proved. In addition, neutrosophic triplet partial bipolar metric spaces have been shown to be different from classical partial metric space, neutrosophic triplet partial metric space and neutrosophic triplet metric space. Thus, we add a new structure in neutrosophic triplet theory. [ABSTRACT FROM AUTHOR]

In this chapter, neutrosophic triplet partial g - metric spaces are obtained. Then, some definitions and examples are given for neutrosophic triplet partial g - metric space. Based on these definitions, new theorems are given and proved. In addition, it is shown that neutrosophic triplet partial g - metric spaces are different from the classical g - metric spaces, neutrosophic triplet metric spaces. Thus, we add a new structure in neutrosophic triplet theory. Also, thanks to neutrosophic triplet partial g - metric space, researchers can obtain new fixed point theorems for neutrosophic triplet theory. [ABSTRACT FROM AUTHOR]

Smarandache introduced neutrosophic quadruple sets and neutrosophic quadruple numbers [45] in 2015. These sets and numbers are real or complex number valued. In this study, we firstly introduce set valued neutrosophic quadruple sets and numbers. We give some known and special operations for set valued neutrosophic quadruple numbers. Furthermore, Smarandache and Ali obtained neutrosophic triplet groups [30] in 2016. In this study, we firstly give neutrosophic triplet groups based on set valued neutrosophic quadruple number thanks to operations for set valued neutrosophic quadruple numbers. In this way, we define new structures using the together set valued neutrosophic quadruple number and neutrosophic triplet group. Thus, we obtain new results for set valued neutrosophic quadruple numbers and neutrosophic triplet groups based on set valued neutrosophic quadruple number. [ABSTRACT FROM AUTHOR]

In this article, a notion of neutrosophic triplet (NT) normed ring space is given and properties of NT normed ring spaces are studied. We demonstrate that NT normed ring is different from the classical one. Also, we show that a neutrosophic triplet normed ring can be a neutrosophic triplet norm when certain conditions are met. [ABSTRACT FROM AUTHOR]

In this paper, we propose some transformations based on the centroid points between single valued neutrosophic numbers. We introduce these transformations according to truth, indeterminacy and falsity value of single valued neutrosophic numbers. We propose a new similarity measure based on falsity value between single valued neutrosophic sets. Then we prove some properties on new similarity measure based on falsity value between falsity value between single valued neutrosophic sets. Furthermore, we propose similarity measure based on falsity value between single valued neutrosophic sets based on the centroid points of transformed single valued neutrosophic numbers. We also apply the proposed similarity measure between single valued neutrosophic sets to deal with pattern recognition problems. [ABSTRACT FROM AUTHOR]