In this work, we introduce the idea of generalized interval-valued Neutrosophic sets. After providing the fundamental definitions of operations related to these sets, we establish several key properties and explore the relationships between generalized interval-valued Neutrosophic sets and other related concepts. Finally, we extend the notion of generalized Neutrosophic topological spaces to incorporate generalized interval-valued Neutrosophic topological spaces. We define the concept of generalized interval-valued Neutrosophic g-continuous function between two generalized interval-valued Neutrosophic topological spaces. Lastly, an application has been shown in decision making problem.

In this paper, the notion of generalized Neutrosophic soft open set (GNSOS) in Neutrosophic soft open set (GNSOS) in Neutrosophic soft topological structures relative to Neutrosophic soft points is introduced. The concept of generalized Neutrosophic soft separation axioms in Neutrosophic soft topological spaces with respect to

Several attempts have been made to deal with uncertain input and output data in Data Envelopment Analysis (DEA). However, due to the limitation of these methods, they cannot be applied for solving DEA with indeterminacy, impreciseness, vagueness, inconsistent and incompleteness information. So this paper for the first time, deals with the Neutrosophic Data Envelopment Analysis and present a new model to solve it.

In this paper the meanings of Neutrosophic special $n$-dominating set,  Neutrosophic special $n$-domination number, inverse Neutrosophic special domination set (number) and  inverse Neutrosophic special $n$-domination number are introduced and some of related results are investigated. Finally, an application of inverse Neutrosophic special dominating set in decision making under ashy clauses between certainty and uncertainty is provided. In fact, we present a decision-making problem in real-world applied example which discusses the factors influencing a companys efficiency. The presented model is, in fact, a factor-based model wherein the impact score of each factor is divided into two types of direct and indirect influences.

The notion of a Neutrosophic quadruple BCI-commutative ideal in a neutro-sophic quadruple BCI-algebra is introduced, and several properties are investigated. Rela-tions between a Neutrosophic quadruple ideal and a Neutrosophic quadruple BCI-commutative ideal are discussed, and conditions for the Neutrosophic quadruple ideal to be a Neutrosophic quadruple BCI-commutative ideal are given. Conditions for the Neutrosophic quadruple set to be a Neutrosophic quadruple BCI-commutative ideal are provided, and the extension property of a Neutrosophic quadruple BCI-commutative ideal is considered.

In this paper, the notions of single-valued intuitionistic Neutrosophic sets and single-valued intuitionistic Neutrosophic graphs are introduced. Also, the concepts of degree and total degree of a node in single-valued intuitionistic Neutrosophic graphs are presented. Then the concepts of irregular single-valued intuitionistic Neutrosophic graphs, highly irregular Neutrosophic intuitionistic single-valued intuitionistic Neutrosophic graphs and neighborly irregular single-valued intuitionistic Neutrosophic graphs are expressed.

The objective of this study is to incorporate topological space into the realm of n-Cylindrical Fuzzy Neutrosophic Sets (n-CyFNS), which are the most novel type of fuzzy Neutrosophic sets. In this paper, we introduce n-Cylindrical Fuzzy Neutrosophic Topological Spaces (n-CyFNTS), n-Cylindrical Fuzzy Neutrosophic (n-CyFN) open sets, and n-CyFN closed sets. We also defined the n-CyFN base, n-CyFN subbase, and some related theorems here.

In this paper we recall our concepts of nth-Power Set of a Set, SuperHyperOperation, SuperHyperAxiom, SuperHyperAlgebra, and their corresponding Neutrosophic SuperHyperOperation, Neutrosophic SuperHyper-Axiom and Neutrosophic SuperHyperAlgebra. In general, in any field of knowledge, one actually encounters SuperHyperStructures (or more accurately (m, n)-SuperHyperStructures).

This article explains a particular category of Neutrosophic subsets of G-submodules, specifically r-Neutrosophic subsets, where r ∈ [0, 1]. The algebra of r-Neutrosophic subsets of G-submodules is dis-cussed, along with some fundamental characteristics of their sum. Definitions and theorems related to this concept are provided to clarify the properties of an arbitrary non-empty family of r-Neutrosophic subsets of G-submodules.

This article explains a particular category of Neutrosophic subsets of G-submodules, specifically r-Neutrosophic subsets, where r ∈ [0, 1]. The algebra of r-Neutrosophic subsets of G-submodules is dis-cussed, along with some fundamental characteristics of their sum. Definitions and theorems related to this concept are provided to clarify the properties of an arbitrary non-empty family of r-Neutrosophic subsets of G-submodules.