Neutrosophic Crisp Research Articles

Stable Neutrosophic Crisp Topological Space

The significance and influence of neutrosophic crisp set theory in numerous scientific domains, particularly topology, led us to construct a new definition of topology based on neutrosophic crisp sets, allowing us to regulate its key mathematical ideas. Therefore, we constructed this definition and dubbed it stable neutrosophic crisp topology, where we went over the key idea which is the interior with the vital features.

Necessary and Sufficient Conditions for a Stability of the Concepts of Stable Interior and Stable Exterior via Neutrosophic Crisp Sets

The general direction for generating any stable neutrosophic crisp topology is through base or the stable neutrosophic crisp interior concept, which is closed in the finite intersection process and not closed in the union process, likewise the stable neutrosophic crisp exterior is closed in the finite union process but not closed in finite intersection. Our research deals with finding necessary and sufficient condition for the finite union and finite intersection to be closed respectively using the concept of confused crisp sets.

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.

On the topological category of neutrosophic crisp sets

In this work, we explicitly characterize local separation axioms as well as generic separation axioms in the topological category of neutrosophic crisp sets, and examine their mutual relationship. Moreover, we characterize several distinct notions of closedness, compactness and connectedness in NCSet, and study their relationship with each other.

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.

Neutrosophic Crisp Generalized αg-Continuous Functions

This paper provided new concepts of neutrosophic crisp continuous functions named neutrosophic crisp αg-continuous, neutrosophic crisp gα-continuous, neutrosophic crisp gαg-continuous, neutrosophic crisp gαg*-continuous and neutrosophic crisp gαg(**)-continuous functions and their relations.

New Operators Using Neutrosophic Crisp Open Set

In this paper, we introduce new sets in neutrosophic crisp topology called neutrosophic crisp frontier, neutrosophic crisp border and neutrosophic crisp exterior with the help of neutrosophic crisp open sets in neutrosophic crisp topological space. Also, we discuss the basic and important properties of them and the relations between them. Finally, many examples are presented.

Neutrosophic Crisp Generalized sg-Closed Sets and their Continuity

In this paper, we delivered pioneering notions of closed sets in the neutrosophic crisp sense. In other words, we discussed -closed sets, -closed sets, and -closed sets in neutrosophic crisp topological space. Moreover, the subsequent innovative ideas are established, for instance, -closure and -interior in neutrosophic crisp topological space, and obtaining numerous of their highlights. Besides, we submitted different kinds of neutrosophic crisp continuous functions and their associations.

Emerging Trends in Social Networking Systems and Generation Gap with Neutrosophic Crisp Soft Mapping

This paper aims to introduce the novel concept of neutrosophic crisp soft set (NCSS), including various types of neutrosophic crisp soft sets (NCSSs) and their fundamental operations. We define NCS-mapping and its inverse NCS-mapping between two NCS-classes. We develop a robust mathematical modeling with the help of NCS-mapping to analyze the emerging trends in social networking systems (SNSs) for our various generations. We investigate the advantages, disadvantages, and natural aspects of SNSs for five generations. With the changing of the generations, it is analyzed that emerging trends and the benefits of SNSs are increasing day by day. The suggested modeling with NCS-mapping is applicable in solving various decision-making problems.

Nnc δ-OPEN SETS

A new strong forms of sets called N -neutrosophic crisp δ-open sets and N -neutrosophic crisp δ-closed sets in N -neutrosophic crisp topological space are introduced in this article. Also, discuss their properties and examples are related to N -neutrosophic crisp δ open sets along with their near sets in N -neutrosophic crisp topological spaces.

On Some New Concepts of Weakly Neutrosophic Crisp Separation Axioms

On Some New Concepts of Weakly Neutrosophic Crisp Separation Axioms

On New Types of Weakly Neutrosophic Crisp Closed Functions

On New Types of Weakly Neutrosophic Crisp Closed Functions

On new concepts of neutrosophic crisp open sets

Our work announces novel concepts called neutrosophic crisp i-open sets, neutrosophic crisp inter-open sets and neutrosophic crisp ii-open sets by generalizing neutrosophic crisp open set in neutrosophic crisp topological space. Numerous properties and characterizations of these concepts are studied, and the relationships of these concepts with various other concepts of neutrosophic crisp open sets are illustrated.

Neutrosophic Crisp minimal Structure

In this paper, the neutrosophic crisp minimal structure which is a more general structure than the neutrosophic minimal structure is built on neutrosophic crisp sets. The necessary arguments which are neutrosophic minimal crisp open set, neutrosophic minimal crisp closed set, neutrosophic crisp minimal closure, and neutrosophic crisp minimal interior are defined and their basic properties are presented. Also, the neutrosophic crisp minimal structure subspace of neutrosophic crisp minimal structure is defined and studied some of its properties. Finally, many examples are presented.

On Neutrosophic Crisp Generalized Alpha Generalized Closed Sets

This study reveals new concepts of neutrosophic crisp closed sets named neutrosophic crisp g-closed sets, neutrosophic crisp αg-closed sets, neutrosophic crisp gα-closed sets, and neutrosophic crisp gαg-closed sets. Furthermore, their ultimate features in neutrosophic crisp topological spaces are examined. Moreover, the consequent new concepts are introduced, such as neutrosophic crisp gαg-closure and neutrosophic crisp gαg-interior and finding some of their characteristics.

On Binary Neutrosophic Crisp Points And Binary Neutrosophic Neighborhoods

As a generalization of crisp topology, neutrosophic crisp topology was introduced. As a progression, binary neutrosophic crisp sets were introduced in this article and their properties were also studied. With the idea that neutrosophic crisp points forms the basis for the neutrosophic neighborhood structures, new points namely binary neutrosophic crisp points were introduced in this article. Owing to the new points, binary neutrosophic neighborhood structure in the new space named as binary neutrosophic crisp topological space is framed. Eventually properties of binary neutrosophic crisp neighborhoods were discussed.

On New Types of Weakly Neutrosophic Crisp Open Mappings

This work employs the conceptions of neutrosophic crisp a-open and semi-a-open sets to distinguish some novel forms of weakly neutrosophic crisp open mappings; for instance, neutrosophic crisp a-open mappings, neutrosophic crisp a*-open mappings, neutrosophic crisp a**-open mappings, neutrosophic crisp semi-a-open mappings, neutrosophic crisp semi-a*-open mappings, and neutrosophic crisp semi-a**-open mappings. Moreover, the close connections between these forms of weakly neutrosophic crisp open mappings and the viewpoints of neutrosophic crisp open mappings are explained. Additionally, various theorems and related features and notes are submitted.

On Neutrosophic Crisp Sets and Neutrosophic Crisp Mathematical Morphology

In this paper, we analyze the basic algebraic operations of neutrosophic crisp sets andtheir properties, show that some operations of neutrosophic crisp sets with type 2 and type 3 arenot closed by counter examples, and give some new operations. Then, discuss some morphologicaloperators in neutrosophic crisp mathematical morphology, and study the application to edgeextraction of color images, and give some Python programs and related experimental results.

Separation Axioms in Nnc Topological Spaces via Nnc e-open Sets

The main idea of this research is to define a new neutrosophic crisp points in neutrosophic crisp topological space namely (NncPN ), the concept of Nnc limit point was defined using (NncPN ), with some of its properties, the separation axioms (Nnceτi -space (i = 0,1, 2) were constructed in neutrosophic crisp topological space using (NncPN ) and examine the relationship between them in details.

N-Valued Refined Neutrosophic Crisp Sets

The main purpose of this manuscript is to expand the notion of neutrosophic crisp set (NCS) by presenting the notion of n-valued refined neutrosophic crisp set with some illustration examples. We also establish some of its set-theoretical operations.