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Journal articles on the topic 'Neutrosophic vector spaces'

Author: Grafiati

Published: 2 June 2025

Last updated: 31 July 2025

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1

Kungumaraj, E., E. Lathanayagam, Utpal Saikia, et al. "Neutrosophic Topological Vector Spaces and its Properties." International Journal of Neutrosophic Science 23, no. 2 (2024): 63–76. http://dx.doi.org/10.54216/ijns.230206.

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The algebraic structures Group, Ring, Field and Vector spaces are important innovations in Mathematics. Most of the theoretical concepts of Mathematics are based on the theorems related to these algebraic structures. Initially many mathematicians developed theorems related to all these algebraic structures. In 20th century most of the researchers introduced the theorems on the algebraic structures with Fuzzy and Intuitionistic fuzzy sets. Recently in 21st century the researchers concentrated on Neutrosophic sets and introduced the algebraic structures like Neutrosophic Group, Neutrosophic Ring

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2

Khan, Vakeel A., Ayhan Esi, Mobeen Ahmad, and Mohammad Daud Khan. "Continuous and bounded linear operators in neutrosophic normed spaces." Journal of Intelligent & Fuzzy Systems 40, no. 6 (2021): 11063–70. http://dx.doi.org/10.3233/jifs-202189.

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In this article, we show that the addition and scalar multiplication in neutrosophic normed spaces are continuous. The neutrosophic boundedness and continuity of linear operators between neutrosophic normed spaces are examined. Moreover, we analyzed that the set of all neutrosophic continuous linear operators and the set of all neutrosophic bounded linear operators from neutrosophic normed spaces into another are vector spaces.

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3

W.B., Vasantha Kandasamy, Ilanthenral Kandasamy, and Florentin Smarandache. "Neutrosophic Quadruple Vector Spaces and Their Properties." Mathematics 7, no. 8 (2019): 758. http://dx.doi.org/10.3390/math7080758.

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In this paper authors for the first time introduce the concept of Neutrosophic Quadruple (NQ) vector spaces and Neutrosophic Quadruple linear algebras and study their properties. Most of the properties of vector spaces are true in case of Neutrosophic Quadruple vector spaces. Two vital observations are, all quadruple vector spaces are of dimension four, be it defined over the field of reals R or the field of complex numbers C or the finite field of characteristic p, Z p ; p a prime. Secondly all of them are distinct and none of them satisfy the classical property of finite dimensional vector s

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4

Malath., F. Aswad. "n-Cyclic Refined Neutrosophic Vector Spaces and Matrices." Neutrosophic Knowledge 3, no. 2 (2021): 6–13. https://doi.org/10.5281/zenodo.5507528.

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This paper is dedicated to study for the first time the concept of n-cyclic refined neutrosophic vector space as a direct application of n-cyclic refined neutrosophic sets. Also, It presents some elementary properties of these spaces such as homomorphisms and subspaces. On the other hand, this work defines n-cyclic refined neutrosophic real matrices, and illustrates some examples to clarify these structures.

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5

J., J., J. Aldring, S. John Borg, and D. Ajay. "Extended Refined Neutrosophic Vector Spaces, Subspaces and their Application." International Journal of Neutrosophic Science 26, no. 1 (2025): 40–54. https://doi.org/10.54216/ijns.260104.

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The objective of this paper is to present a perspective of Refined Neutrosophic Vector Space (r-NVS), Sub spaces and some basic operations on Refined Neutrosophic Sets such as Algebraic sum and Algebraic product. Further some basic propositions, lemma and examples are presented. Finally an application on Refined Neutrosophic Vector Space is presented in the field of e-Commerce buyer oriented product (Smart Phones) ranking to illustrate the advantage of representing r-NVS.

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6

Celik, Mehmet, and Necati Olgun. "On The Classification of Neutrosophic Complex Inner Product Spaces." Galoitica: Journal of Mathematical Structures and Applications 2, no. 1 (2022): 29–32. http://dx.doi.org/10.54216/gjmsa.020104.

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The objective of this paper is to study the neutrosophic complex inner product spaces over neutrosophic complex field C(I). Also, it determines the necessary and sufficient condition of a neutrosophic complex vector space to be a complex inner product space by using semi module isomorphisms.

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7

Al-Basri, Fatma, and Asawer Khdeidan. "Convergence of Filters on Bornological Vector Spaces and Neutrosophic Filters." International Journal of Neutrosophic Science 24, no. 4 (2024): 126–32. http://dx.doi.org/10.54216/ijns.240409.

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In this research, we construct new type of convergence of bornological vector spaces called convergence of filters through using conception bounded sets. As well, we have considered several characteristics of these concepts like Fréchet filter associated with sequence, filter that has a unique limit and ultra-filter which is very useful in the study of neutrosophic topological spaces and neutrosophic filters.

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8

Salman, Nabil Khuder, Bolívar Villalta Jadan, and Marcos Lalama Flores. "On n-Refined Neutrosophic Vector Spaces For Some Special Values 3≤ n ≤6." International Journal of Neutrosophic Science 23, no. 2 (2024): 08–15. http://dx.doi.org/10.54216/ijns.230201.

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This work is dedicated to study some different types of n-refined neutrosophic vector spaces for different values of n between 3 and 6. Where we present some related algebraic concepts such as 3-refined neutrosophic homomorphism, 4-refined neutrosophic homomorphism, 5-refined neutrosophic homomorphism, and 6-refined neutrosophic homomorphism. Also, we provide some theorems to clarify the algebraic behaviour of 3-refined, 4-refined, 5-refined, and 6-refined neutrosophic subspaces.

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9

Abobala, Mohammad. "On the Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations." Journal of Mathematics 2021 (February 24, 2021): 1–5. http://dx.doi.org/10.1155/2021/5591576.

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The objective of this paper is to study the representation of neutrosophic matrices defined over a neutrosophic field by neutrosophic linear transformations between neutrosophic vector spaces, where it proves that every neutrosophic matrix can be represented uniquely by a neutrosophic linear transformation. Also, this work proves that every neutrosophic linear transformation must be an AH-linear transformation; i.e., it can be represented by classical linear transformations.

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10

Şahin, Mehmet, and Abdullah Kargın. "Neutrosophic triplet normed space." Open Physics 15, no. 1 (2017): 697–704. http://dx.doi.org/10.1515/phys-2017-0082.

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AbstractIn 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.

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11

Taffach, Nader Mahmoud. "An Introduction to Symbolic 2-Plithogenic Vector Spaces Generated from The Fusion of Symbolic Plithogenic Sets and Vector Spaces." Neutrosophic Sets and Systems 54 (April 11, 2023): 45–57. https://doi.org/10.5281/zenodo.7817603.

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The fusion of symbolic plithogenic sets with algebraic structures generates novel algebraic neutrosophic structures that generalize the classical known structures. The objective of this paper is to define the concept of symbolic 2-plithogenic vector space over a symbolic 2-plitogenic field. Concepts such as AH-subspace and AH-linear transformation will be presented and discussed in terms of theorems.

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12

Alaa, Alaa, and Mohammed A. Hilal. "Some results on approximation in neutrosophic normed space." International Journal of Neutrosophic Science 24, no. 4 (2024): 389–96. http://dx.doi.org/10.54216/ijns.240429.

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Neutrosophic normed linear spaces are the main significant notion in the study of classical functional analysis under a neutrosophic environment to handle indeterminate and inconsistent information. Where the neutrosophic norm function assigns to each vector in the linear space a neutrosophic number, which is a number with a truth, indeterminacy, and falsity component. The main aim of this work is to study and discuss the important properties of proximinality of specific sets and new results for a large class in neutrosophic normed space. Moreover, we show some results closely related proximai

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13

Ahmed, Ahmed, and Necati Olgun. "On the Concepts of Two- Fold Fuzzy Vector Spaces and Algebraic Modules." Journal of Neutrosophic and Fuzzy Systems 7, no. 2 (2023): 46–52. http://dx.doi.org/10.54216/jnfs.070205.

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The concept of two-fold algebras is generated by merging some special sets such as fuzzy sets, neutrosophic sets or plithogenic sets with various algebraic structures. The main objective of this research paper is to provide a strict mathematical definition and a general study of two-fold fuzzy vector spaces defined over the real numbers and also two-fold fuzzy vector spaces defined over the complex numbers, as well as two-fold fuzzy algebraic modules defined over commutative rings with unity. The elementary properties and algebraic operations of those structures will be explained through many

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14

Alfahal, Abuobida M. A., Yaser A. Alhasan, Raja A. Abdulfatah, and Rozina Ali. "On the Split-Complex Neutrosophic Numbers and Their Algebraic Properties." International Journal of Neutrosophic Science 20, no. 3 (2023): 25–32. http://dx.doi.org/10.54216/ijns.200303.

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The objective of this paper is to define for the first time the concept of split-complex numbers as a new generalization of classical split-complex numbers by using neutrosophic numbers. Also, we study the elementary properties of this new numerical class such as equations, conjugates, and vector spaces formed by it. On the other hand, some special AH-subspaces will be presented and handled with many corresponding examples.

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15

Alsadig, Alsadig. "Trademark Empowerment using Optimal Neutrosophic Topological Vector Space for Maximizing Customer Attraction." International Journal of Neutrosophic Science 24, no. 3 (2024): 138–50. http://dx.doi.org/10.54216/ijns.240312.

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Neutrosophic set is introduced as a generalization of intuitionistic fuzzy set, where any elements x ∈ X we have membership (T), non-membership (F), and indeterminacy (I)degrees. Neurosophic vague topological spaces are presented in various notations like neurosophic vague compactness and continuity. Trademarks are the essential components of intellectual property that allow owner to earn profit based on their name. In this industry, retailers typically use feedback channels like customer care service, website review complaints and suggestions boxes to gain user reviews on service satisfaction

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16

M.A., Ibrahim, Agboola A.A.A., Badmus B.S., and Akinleye S.A. "On Refined Neutrosophic Vector Spaces II." August 19, 2020. https://doi.org/10.5281/zenodo.3991492.

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The concept of refined neutrosophic vector spaces was introduced by Ibrahim et al. in [20] and the present paper is the continuation of the work. In the present paper, further studies on neutrosophic vector spaces are presented. Specifically, linear dependence, independence, bases and dimensions of refined neutrosophic vector spaces are studied with several results and examples presented. Also,refined neutrosophic homomorphisms of refined neutrosophic vector spaces are studied and existence of linear maps between weak refined neutrosophic vector spaces and weak neutrosophic vector spaces are e

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17

Agboola, A. A. A., and S. A. Akinleye. "Neutrosophic Vector Spaces." Neutrosophic Sets and Systems 4, 2014 (May 5, 2014). https://doi.org/10.5281/zenodo.571579.

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The objective of this paper is to study neutrosophic vector spaces. Some basic definitions and properties of the classical vector spaces are generalized. It is shown that every neutrosophic vector space over a neutrosophic field (resp. a field) is a vector space. Also, it is shown that an element of a neutrosophic vector space over a neutrosophic field can be infinitely expressed as a linear combination of some elements of the neutrosophic vector space. Neutrosophic quotient spaces and neutrosophic vector space homomorphism are also studied.

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Agboola, A.A.A., and S.A. Akinleye. "Neutrosophic Vector Spaces." July 1, 2015. https://doi.org/10.5281/zenodo.22603.

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The objective of this paper is to study neutrosophic vector spaces. Some basic definitions and properties of the classical vector spaces are generalized. It is shown that every neutrosophic vector space over a neutrosophic field (resp. a field) is a vector space. Also, it is shown that an element of a neutrosophic vector space over a neutrosophic field can be infinitely expressed as a linear combination of some elements of the neutrosophic vector space. Neutrosophic quotient spaces and neutrosophic vector space homomorphism are also studied.

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19

admin, admin, A. A. A. Agboola, B. S. Badmus, and S. A. Akinleye. "On Refined Neutrosophic Vector Spaces II." International Journal of Neutrosophic Science, 2020, 22–36. http://dx.doi.org/10.54216/ijns.090102.

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The concept of refined neutrosophic vector spaces was introduced by Ibrahim et al. in [20] and the present paper is the continuation of the work. In the present paper, further studies on neutrosophic vector spaces are presented. Specifically, linear dependence, independence, bases and dimensions of refined neutrosophic vector spaces are studied with several results and examples presented. Also, refined neutrosophic homomorphisms of refined neutrosophic vector spaces are studied and existence of linear maps between weak refined Neutrosophic vector spaces and weak neutrosophic vector spaces are

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20

Ibrahim, M. A., A. A. A. Agboola, B. S. Badmus, and S. A. Akinleye. "On Refined Neutrosophic Vector Spaces I." International Journal of Neutrosophic Science, 2020, 97–109. http://dx.doi.org/10.54216/ijns.070202.

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The objective of this paper is to present the concept of a refined neutrosophic vector space. Weak(strong) refined neutrosophic vector spaces and subspaces, and, strong refined neutrosophic quotient vector spaces are studied. Several interesting results and examples are presented. It is shown that every weak (strong) refined neutrosophic vector space is a vector space and it is equally shown that every strong refined neutrosophic vector space is a weak refined neutrosophic vector space.

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21

M.A., Ibrahim, Agboola A.A.A., Badmus B.S., and Akinleye S.A. "On Refined Neutrosophic Vector Spaces I." August 19, 2020. https://doi.org/10.5281/zenodo.3991409.

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The objective of this paper is to present the concept of a refined neutrosophic vector space. Weak(strong) refined neutrosophic vector spaces and subspaces, and, strong refined neutrosophic quotient vector spaces are studied. Several interesting results and examples are presented. It is shown that every weak (strong) refined neutrosophic vector space is a vector space and it is equally shown that every strong refined neutrosophic vector space is a weak refined neutrosophic vector space. 

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22

Smarandache, Florentin, and Mohammad Abobala. "n-Refined Neutrosophic Vector Spaces." International Journal of Neutrosophic Science, 2020, 47–54. http://dx.doi.org/10.54216/ijns.070104.

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This paper introduces the concept of n-refined neutrosophic vector spaces as a generalization of neutrosophic vector spaces, and it studies elementary properties of them. Also, this work discusses some corresponding concepts such as weak/strong n-refined neutrosophic vector spaces, and n-refined neutrosophic homomorphisms.

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23

Mohammad, Abobala. "Neutrosophic Real Inner Product Spaces." June 8, 2021. https://doi.org/10.5281/zenodo.4914853.

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The objective of this work is to define for the first time the concept of inner product in a neutrosophic vector space V(I) and a refined neutrosophic vector space V(𝐼1 ,𝐼2 ) . Also, this paper introduces many interesting properties of neutrosophic real inner products and establishes the theoretical foundations of neutrosophic functional analysis such as neutrosophic normed spaces, refined neutrosophic normed spaces, neutrosophic real inner product spaces, refined neutrosophic inner product spaces, orthogonal basis, neutrosophic and refined neutrosophic Cauchy- Schwartz inequality.

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24

A., Elrawy. "The neutrosophic vector spaces- another approach." October 2, 2022. https://doi.org/10.5281/zenodo.7135358.

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In this paper, we introduce and define a new version of a neutrosophic vector space. Indeed, this approach is a generalization of the notion of fuzzy vector space. Also, we study the neutrosophic subspace and linear independence. Furthermore, this study builds the basis and dimension of a neutrosophic vector space. Finally, we investigate the properties of the introduced notations. 

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A.A.A., Agboola, and Akinleye S.A. "Neutrosophic Hypervector Spaces." September 5, 2010. https://doi.org/10.5281/zenodo.22999.

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26

Alaswad, Malath F. "A Review On Some Neutrosophic Algebraic Linear Structures." International Journal of Neutrosophic Science, 2021. http://dx.doi.org/10.54216/ijns.140204.

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This paper is dedicated to reviewing some of the basic concepts in neutrosophic linear algebra and its generalizations, especially neutrosophic vector spaces, refined neutrosophic, and n-refined neutrosophic vector spaces. Also, this work gives the interested reader a strong background in the study of neutrosophic matrix theory and n-refined neutrosophic matrix theory. We study elementary properties of these concepts such as Kernel, AH-Quotient, and dimension.

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27

Mohammad, Abobala. "AH-Subspaces in Neutrosophic Vector Spaces." August 18, 2020. https://doi.org/10.5281/zenodo.3989654.

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In this paper, we introduce the concept of AH-subspace of a neutrosophic vector space and AHS-linear transformations. We study elementary properties of these concepts such as Kernel, AH-Quotient, and dimension. 

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28

Hasan, Sankari, and Abobala Mohammad. "Solving Three Conjectures about Neutrosophic Quadruple Vector Spaces." December 1, 2020. https://doi.org/10.5281/zenodo.4300602.

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aim of this paper is to answer Smarandache conjectures about neutrosophic quadruple vector spaces. This paper depends on the concept of weak n-refined neutrosophic vector space to prove that an NQ vector space V defined over the field F

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29

Abobala, Mohammad. "AH-Subspaces in Neutrosophic Vector Spaces." International Journal of Neutrosophic Science, 2020, 80–86. http://dx.doi.org/10.54216/ijns.060204.

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In this paper, we introduce the concept of AH-subspace of a neutrosophic vector space and AHS-linear transformations. We study elementary properties of these concepts such as Kernel, AH-Quotient, and dimension.

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30

Mohammad, Abobala. "A Study of AH-Substructures in n-Refined Neutrosophic Vector Spaces." August 19, 2020. https://doi.org/10.5281/zenodo.3991478.

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The aim of this paper is to define and study for the first time AH-substructures in n-refined neutrosophic vector spaces such as weak/strong AH-subspaces, and weak/strong AH-linear transformations between two n-refined neutrosophic vector spaces. Also, this paper introduces some elementary properties of these concepts. 

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admin, admin. "A Study of AH-Substructures in n-Refined Neutrosophic Vector Spaces." International Journal of Neutrosophic Science, 2020, 74–85. http://dx.doi.org/10.54216/ijns.090202.

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The aim of this paper is to define and study for the first time AH-substructures in n-refined neutrosophic vector spaces such as weak/strong AH-subspaces, and weak/strong AH-linear transformations between two n-refined neutrosophic vector spaces. Also, this paper introduces some elementary properties of these concepts.

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Abdullah, Kargın, Dayan Azize, Yıldız İsmet, and Kılıç Adil. "Neutrosophic Triplet m – Banach Spaces." December 1, 2020. https://doi.org/10.5281/zenodo.4300539.

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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 definiti

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33

Mehmet, Şahin, and Kargın Abdullah. "Neutrosophic triplet normed space." August 27, 2017. https://doi.org/10.5281/zenodo.1413241.

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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.

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34

Merkepci, Hamiyet, and Katy D. Ahmad. "On The 3-Refined Neutrosophic Analytical Structures and Number Theoretical Concepts." 54 (April 10, 2023): 1–18. https://doi.org/10.5281/zenodo.7814475.

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The main goal of this paper is to study several structures generated by using 3-refined neutrosophic numbers, where we find the mathematical formulas of 3-refined neutrosophic real functions. Also, the inner products over 3-refined neutrosophic vector spaces and orthogonal properties. In addition, we present the foundations of 3-refined neutrosophic number theory, especially division, congruencies, and some related equations.

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35

Bal, Mikail, Prem Kumar Singh, and Katy D. Ahmad. "A Short Introduction To The Symbolic Turiyam Vector Spaces and Complex Numbers." Journal of Neutrosophic and Fuzzy Systems, 2022, 76–87. http://dx.doi.org/10.54216/jnfs.020107.

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This paper is dedicated to define for the first time the concept of Symbolic Turiyam vector space as a generalization of the corresponding neutrosophic one by using the algebra of symbolic Turiyam set. Also, we illustrate many examples to show and clarify the validity of this work.

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Vasantha, Kandasamy, Kandasamy Ilanthenral, and Smarandache Florentin. "Neutrosophic Quadruple Algebraic Codes over Z2 and their properties." May 3, 2020. https://doi.org/10.5281/zenodo.3782891.

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In this paper we for the rst time develop, dene and describe a new class of algebraic codes using Neutrosophic Quadruples which uses the notion of known value, and three unknown triplets (T; I; F) where T is the truth value, I is the indeterminate and F is the false value. Using this Neutrosophic Quadruples several researchers have built groups, NQ-semigroups, NQ-vector spaces and NQ linear algebras. However, so far NQ algebraic codes have not been developed or dened. These NQ-codes have some peculiar properties like the number of message symbols are always xed as 4-tuples, that is why we call

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P, Jayaraman. "Cyclic normal fuzzy neutrosopic soft G-modular structures acting on a group." May 20, 2019. https://doi.org/10.5281/zenodo.3050515.

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In this paper, we explain classical concept of the fuzzy soft sets to express the idea of cyclic normal fuzzy neutrosopic soft G-modular structures acting on a group. Neutrosopic soft set theory is studied as an eective parametric tool to discuss with uncertainities. We also investigate the relationship between cyclic fuzzy neutrosopic soft G-modules and classical modules. We study their concerned properties in terms of soft set operations, soft image, soft pre-image, soft anti image, -inclusion of neutrosopic fuzzy soft sets and linear combinations of the vector spaces. Furthermore we show ap

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38

Surapati, Pramanik, and Mondal Kalyan. "COTANGENT SIMILARITY MEASURE OF ROUGH NEUTROSOPHIC SETS AND ITS APPLICATION TO MEDICAL DIAGNOSIS." April 14, 2015. https://doi.org/10.5281/zenodo.23142.

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Similarity measure plays an important role in medical diagnosis. In this paper, a new rough cotangent similarity measure between two rough neutrosophic sets is proposed. The notion of rough neutrosophic set is used as vector representations in 3D-vector space. The rating of all elements in rough neutrosophic set is expressed with the upper and lower approximation operator and the pair of neutrosophic sets which are characterized by truth-membership degree, indeterminacy-membership degree, and falsitymembership degree. A numerical example of the medical diagnosis is provided to show the ef

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M.A., Ibrahim, and Agboola A.A.A. "NeutroVectorSpaces I." October 4, 2020. https://doi.org/10.5281/zenodo.4065462.

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  Recently, the concept of NeutroAlgebraic and AntiAlgebraic Structures were introduced and analyzed by Florentin Smarandache. His new approach to the study of Neutrosophic Structures presents a more robust tool needed for managing uncertainty, incompleteness, indeterminate and imprecise information. In this paper, we introduce for the first time the concept of NeutroVectorSpaces. Specifically, we study a particular class of the NeutroVectorSpaces called of type 4 <em>S </em>and their elementarily properties are presented. It is shown that the NeutroVectorSpaces of type 4 <em>S </em>may c

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