Neutrosophic Topology Research Articles

ON A WEAK FORM OF SEMI-OPEN FUNCTION BY NEUTROSOPHICATION

In this study, a new perspective in neutrosophic topology is brought to some open set definitions in general topology and previously interpreted in different ways in some other non-standard topological spaces. Then, some types of functions and continuity are introduced using these new open sets. In addition to these, the relations between the types of open sets, which we have brought different perspectives, with the continuity and function types that we reinterpreted in neutrosophic topology, are examined and these relations are clarified by giving examples and counterexamples.

THE NEUTROSOPHIZE OF NEW CONTINUITY SPECIES

In this study, after giving the necessary definitions in the preliminaries and explaining the process that make this study necessary is explained in the introduction, in the third section, some types of open set that were previously defined in general topology and various non-standard topological spaces are presented and the relationships between them are explained with the help of a diagram. Then, the concept of neutrosophic af-open set is defined and its relations with other open set types are examined and their properties are investigated in neutrosophic topology. In the following sections, the concept of af-open set is generalized and different types of continuities are introduced using these new concepts of open set, and the connections between them are illustrated with examples and diagrams.

On Q^*-closed Sets in Fuzzy Neutrosophic Τopology: Principles, Proofs, and Examples

This paper aims to present a new concept of sets known as fuzzy neutrosophic Q^*-closed sets in fuzzy neutrosophic topology. In this study, we explore and investigate more novel properties of these classes by some new definitions, theorems, and propositions. Therefore, a group of examples is presented and discussed to clarify the relationships between the new study of Q^*-closed sets with other sets.

Neutrosophic Generalized Topological Space

In classical topology, the generalized topological space develops the topological space and supra topological space. In this work, we define and study neutrosophic generalized topological space which is more generalization than the neutrosophic supra topological space, this space may be opening a new horizon and new direction in neutrosophic topology. Also, we study new “neutrosophic open (closed) sets” in this new space such as “neutrosophic generalized open (closed) sets”, “neutrosophic generalized semi open (closed) sets”, “neutrosophic generalized pre open (closed) sets”, “neutrosophic generalized a-open (closed) sets”, and we obtain its basic Properties and study the relations between them. Finally, we introduced “the associated interior and closure operators” in neutrosophic generalized topological space.

Ideals and Filters on Neutrosophic Topologies Generated by Neutrosophic Relations

Recently, Milles and Hammami presented and studied the concept of a neutrosophic topology generated by a neutrosophic relation. As a continuation in the same direction, this paper studies the concepts of neutrosophic ideals and neutrosophic filters on that topology. More precisely, we offer the lattice structure of neutrosophic open sets of a neutrosophic topology generated via a neutrosophic relation and examine its different characteristics. Furthermore, we enlarge to this lattice structure the notions of ideals (respectively, filters) and characterize them with regard to the lattice operations. We end this work by studying the prime neutrosophic ideal and prime neutrosophic filter as interesting types of neutrosophic ideals and neutrosophic filters.

An Introduction to Single-Valued Neutrosophic Primal Theory

This article explores the interconnections among the single-valued neutrosophic grill, single-valued neutrosophic primal and their stratification, uncovering their fundamental characteristics and correlated findings. By introducing the notion of a single-valued neutrosophic primal, a broader framework including the fuzzy primal and intuitionistic fuzzy primal is established. Additionally, the concept of a single-valued neutrosophic open local function for a single-valued neutrosophic topological space is presented. We introduce an operator based on a single-valued neutrosophic primal, illustrating that the single-valued neutrosophic primal topology is finer than the single-valued neutrosophic topology. Lastly, the concept of single-valued neutrosophic open compatibility between the single-valued neutrosophic primal and single-valued neutrosophic topologies is introduced, along with the establishment of several equivalent conditions related to this notion.

Some Properties of α^g-Closed Sets in Fuzzy Neutrosophic Topology

The present paper offers a new notion of sets known as fuzzy neutrosophic ^g-closed sets in fuzzy neutrosophic topology. It is an extended form of work conducted by Fatimah et.al. [1-3]. It investigates several properties of fuzzy neutrisophic ^ g- closed sets and explores a number of examples as to shed the light on the new characteristics of ^g-closed sets as well as some associated relations between them with other sets.

Betam-Closed Sets in Fuzzy Neutrosophic Topological Spaces

The current work offers a new concept of sets and called uzzy eutrosophic m-closed sets in fuzzy neutrosophic topology. In fact, the research is an extended form of a research conducted by F. M. Mohammed et.al. [1-7]. It explores a number of noteworthy examples to shed the light on the new characteristics and attributes of these recently formed conceptions, as well as some associated interactions between them.

Foundation of Revolutionary Topologies: An Overview, Examples, Trend Analysis, Research Issues, Challenges, and Future Directions


 We now found nine new topologies, such as: NonStandard Topology, Largest Extended NonStandard Real Topology, Neutrosophic Triplet Weak/Strong Topologies, Neutrosophic Extended Triplet Weak/Strong Topologies, Neutrosophic Duplet Topology, Neutrosophic Extended Duplet Topology, Neutrosophic MultiSet Topology, and recall and improve the seven previously founded topologies in the years (2019-2023), namely: NonStandard Neutrosophic Topology, NeutroTopology, AntiTopology, Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, SuperHyperTopology, and Neutrosophic SuperHyperTopology. They are called avantgarde topologies because of their innovative forms.

New Types of Topologies and Neutrosophic Topologies

In this paper, we recall the six new types of topologies that we introduced in the last years (2019-2022), such as: Refined Neutrosophic Topology, Refined Neutrosophic Crisp Topology, NeutroTopology, AntiTopology, SuperHyperTopology, and Neutrosophic SuperHyperTopology.

An Introduction to M-Open Sets in Fuzzy Neutrosophic Topological Spaces

A new classes of sets called fuzzy neutrosophic M-open sets and fuzzy neutrosophic M-Closed sets in fuzzy neutrosophic topology are introduced some characterizations of these notions have been presented. After given the fundamental definitions of the new notions, we studided some theorems, propositions and some necessary relations with examples related to these notions had been discussed.

Fermatean Neutrosophic Topological Spaces and an Application of Neutrosophic Kano Method

The main objective of this paper is to redefine the concept of Fermatean neutrosophic sets as well as to introduce topological structure on Fermatean neutrosophic sets. The idea of Fermatean neutrosophic sets is the hybrid model of Fermatean fuzzy sets and neutrosophic sets to utilize key features of these structures. Topological data analysis for indeterminate and uncertain information is a rapidly developing field. Motivated by this recent trend, the idea of Fermatean neutrosophic topology is proposed, which is an extension of neutrosophic topology and Fermatean fuzzy topology. Some fundamental properties of Fermatean neutrosophic topology are explored and related results are investigated. Certain properties provided in the classical topological space that may not be valid in this space is one of the factors that makes the study important. Moreover, an application is made for the problem of seeking reasonable solutions to customer expectations by using the neutrosophic Kano method, which is an interesting illustration of neutrosophic decision making.

Neutrosophic Beta Omega Closed Sets in Neutrosophic Topological Spaces

We introduce and examine several applications of neutrosophic beta omega closed sets namely , , , , in this study. We also introduce the concept of neutrosophic betaomega continuous mapping in neutrosophic topology. Furthermore, we study the relation between the neutrosophic betaomega continuous mapping with the already existing neutrosophic continuous mapping. In addition, we discuss the properties of neutrosophic betaomega continuous mapping.

Topology on Rough Pentapartitioned Neutrosophic Set

The main focus of this article is to introduce the notion of rough pentapartitioned neutrosophic set and rough pentapartitioned neutrosophic topology by using rough pentapartitioned neutrosophic lower approximation, rough pentapartitioned neutrosophic upper approximation, and rough pentapartitioned neutrosophic boundary region. Then, we provide some basic properties, namely operations on rough pentapartitioned neutrosophic set and rough pentapartitioned neutrosophic topology. By defining rough pentapartitioned neutrosophic set and topology, we formulate some results in the form of theorems, propositions, etc. Further, we give some examples to justify the definitions introduced in this article.

Pythagorean m-polar Fuzzy Neutrosophic Topology with Applications

Pythagorean m-polar Fuzzy Neutrosophic Topology with Applications

A Creative Approach on Bipolar Neutrosophic Nano Topology

In this article, Bipolar neutrosophic nano topology is introduced and some of its properties are studied. We found that, it is difficult to find a nano topology for every bipolar neutrosophic set. So we introduced a bipolar neutrosophic nano topology, which is a generalization of bipolar neutrosophic nano topology and its fundamental features are investigated with appropriate examples. This approach is used for real life multi criteria decision making situations. The practical problems may be solved by finding CORE values through the criterion reduction.One can apply the basis of the bipolar neutrosophic nano topology as the key factors of a particular decision making problem using topological reduction of attributes in complete or incomplete information system.

Generalized of A-Closed Set and Ƈ- Closed Set in Fuzzy Neutrosophic Topological Spaces

In this research paper, a new two classes of sets called fuzzy neutrosophic generalized A-closed sets and fuzzy neutrosophic generalized Ƈ-Closed sets in fuzzy neutrosophic topology are introduced and some of their properties have been investigated. We give some theorems, propositions and some necessary examples related to presented definitions. Then, we discuss the relations among the new defined sets.

A New Single-Valued Neutrosophic Rough Sets and Related Topology

(Fuzzy) rough sets are closely related to (fuzzy) topologies. Neutrosophic rough sets and neutrosophic topologies are extensions of (fuzzy) rough sets and (fuzzy) topologies, respectively. In this paper, a new type of neutrosophic rough sets is presented, and the basic properties and the relationships to neutrosophic topology are discussed. The main results include the following: (1) For a single-valued neutrosophic approximation space U , R , a pair of approximation operators called the upper and lower ordinary single-valued neutrosophic approximation operators are defined and their properties are discussed. Then the further properties of the proposed approximation operators corresponding to reflexive (transitive) single-valued neutrosophic approximation space are explored. (2) It is verified that the single-valued neutrosophic approximation spaces and the ordinary single-valued neutrosophic topological spaces can be interrelated to each other through our defined lower approximation operator. Particularly, there is a one-to-one correspondence between reflexive, transitive single-valued neutrosophic approximation spaces and quasidiscrete ordinary single-valued neutrosophic topological spaces.

Neutrosophic Soft Filter Structures Concerning Soft Points

In this paper, the concept of neutrosophic soft filter (NSF) and its basic properties are introduced. Later, we set up a neutrosophic soft topology with the help of an NSF. We also give the notions of the greatest lower bound and the least upper bound of the family of neutrosophic soft filters (NSFs), NSF subbase, NSF base and explore some basic properties of them.

Introduction to Neutrosophic Soft Bitopological Spaces

In this study, the concept of neutrosophic soft bitopological space is defined and it is one of the few studies that have dealt with this concept. In addition, pairwise neutrosophic soft open (closed) set on neutrosophic soft bitopological spaces are studied. Supra neutrosophic soft topology is defined by pairwise neutrosophic soft open sets. Important theorems related to the subject supported with many examples for a better understanding of the subject are given.