Neutrosophic Metric Spaces


Book Description

In present paper, the definition of new metric space with neutrosophic numbers is given. Several topological and structural properties have been investigated. The analogues of Baire Category Theorem and Uniform Convergence Theorem are given for Neutrosophic metric spaces.




Neutrosophic Fixed Point Theorems and Cone Metric Spaces


Book Description

The intention of this paper is to give the general de nition of cone metric space in the context of the neutrosophic theory. In this relation, we obtain some fundamental results concerting xed points for weakly compatible mapping.




FIXED POINT THEOREMS IN NEUTROSOPHIC METRIC SPACES


Book Description

In this paper, we introduce the neutrosophic cantractive and neutrosophic mapping. We establish some results on fixed points of a neutrosophic mapping.




Toplogical and Geometric KM-Single Valued Neutrosophic Metric Spaces


Book Description

This paper introduces the novel concept of KM-single valued neutrosophic metric spaces as an especial generalization of KM-fuzzy metric spaces, investigates several topological and structural properties and presents some of its applications. This study also considers the metric spaces and constructs KM-single valued neutrosophic spaces with respect to any given triangular norms and triangular conorms.




Neutrosophic Triplet Partial v-Generalized Metric Space


Book Description

In this chapter, study the notion of neutrosophic triplet partial v-generalized metric space. Then, we give some definitions and examples for neutrosophic triplet partial v-generalized metric space and obtain some properties and prove these properties. Furthermore, we show that neutrosophic triplet partial v-generalized metric space is different from neutrosophic triplet v-generalized metric space and neutrosophic triplet partial metric space.




Neutrosophic Algebraic Structures and Their Applications


Book Description

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more.




Clustering Neutrosophic Data Sets and Neutrosophic Valued Metric Spaces


Book Description

In this paper, we define the neutrosophic valued (and generalized or G) metric spaces for the first time. Besides, we newly determine a mathematical model for clustering the neutrosophic big data sets using G-metric. Furthermore, relative weighted neutrosophic-valued distance and weighted cohesion measure, is defined for neutrosophic big data set. We offer a very practical method for data analysis of neutrosophic big data although neutrosophic data type (neutrosophic big data) are in massive and detailed form when compared with other data types.




Fixed Point Results for Contraction Theorems in Neutrosophic Metric Spaces


Book Description

In this article, we present fixed and common fixed point results for Banach and Edelstein contraction theorems in neutrosophic metric spaces. Then some properties and examples are given for neutrosophic metric spaces. Thus, we added a new path in neutrosophic theory to obtain fixed point results. We investigate and prove some contraction theorems that are extended to neutrosophic metric space with the assistance of Grabiec.




Neutrosophic Sets and Systems, Vol. 36, 2020


Book Description

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Some articles in this issue: n-Refined Neutrosophic Modules, A Neutrosophic Approach to Digital Images, A Novel Method for Neutrosophic Assignment Problem by using Interval-Valued Trapezoidal Neutrosophic Number.




Neutrosophic Sets and Systems, vol. 50/2022


Book Description

“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation and with their spectrum of neutralities in between them (i.e. notions or ideas supporting neither nor ). The and ideas together are referred to as . Neutrosophy is a generalization of Hegel's dialectics (the last one is based on and only). According to this theory every idea tends to be neutralized and balanced by and ideas - as a state of equilibrium. In a classical way , , are disjoint two by two. But, since in many cases the borders between notions are vague, imprecise, Sorites, it is possible that , , (and of course) have common parts two by two, or even all three of them as well. Neutrosophic Set and Neutrosophic Logic are generalizations of the fuzzy set and respectively fuzzy logic (especially of intuitionistic fuzzy set and respectively intuitionistic fuzzy logic).