References

[1] Smarandache, F., " A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set,

Neutrosophic Probability", American Research Press. Rehoboth, 2003.

[2] Alhamido, R., and Gharibah, T., "Neutrosophic Crisp Tri-Topological Spaces", Journal of New Theory, Vol.

23 , pp.13-21. 2018.

[3] Edalatpanah. S.A., "Systems of Neutrosophic Linear Equations", Neutrosophic Sets and Systems, Vol. 33,

pp. 92-104. 2020.

[4] Agboola, A.A.A., "On Refined Neutrosophic Algebraic Structures," Neutrosophic Sets and Systems,Vol.10,

pp. 99-101. 2015.

[5] Olgun, N., Hatip, A., Bal, M., and Abobala, M., " A Novel Approach To Necessary and Sufficient

Conditions For The Diagonalization of Refined Neutrosophic Matrices", International Journal of Neutrosophic

Science, Vol. 16, pp. 72-79, 2021.

[6] Abobala, M, "n-Cyclic Refined Neutrosophic Algebraic Systems Of Sub-Indeterminacies, An Application

To Rings and Modules", International Journal of Neutrosophic Science, Vol. 12, pp. 81-95 . 2020.

[7] Smarandache, F., "Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Sets", Inter. J. Pure Appl.

Math., pp. 287-297. 2005.

[8] M. Ali, F. Smarandache, M. Shabir and L. Vladareanu., "Generalization of Neutrosophic Rings and

Neutrosophic Fields", Neutrosophic Sets and Systems, vol. 5, pp. 9-14, 2014.

[9] Anuradha V. S., "Neutrosophic Fuzzy Hierarchical Clustering for Dengue Analysis in Sri Lanka",

Neutrosophic Sets and Systems, vol. 31, pp. 179-199. 2020.

[10] Olgun, N., and Hatip, A., "The Effect Of The Neutrosophic Logic On The Decision Making, in Quadruple

Neutrosophic Theory And Applications", Belgium, EU, Pons Editions Brussels,pp. 238-253. 2020.

[11] Abobala, M., Bal, M., and Hatip, A.," A Review On Recent Advantages In Algebraic Theory Of

Neutrosophic Matrices", International Journal of Neutrosophic Science, Vol. 17, 2021.

[12] Turksen, I., "Interval valued fuzzy sets based on normal forms", Fuzzy Sets and Systems, 20, pp.191-210,

1986. 1986.

[13] Smarandache, F., " n-Valued Refined Neutrosophic Logic and Its Applications in Physics", Progress in

Physics, 143-146, Vol. 4, 2013.

[14] Abobala, M., Bal, M., Aswad, M., "A Short Note On Some Novel Applications of Semi Module

Homomorphisms", International journal of neutrosophic science, 2022.

[15] Hatip, A., and Olgun, N., "On Refined Neutrosophic R-Module", International Journal of Neutrosophic

Science, Vol. 7, pp.87-96. 2020.

[16] Bal, M., and Abobala, M., "On The Representation Of Winning Strategies Of Finite Games By Groups and

Neutrosophic Groups", Journal Of Neutrosophic and Fuzzy Systems, 2022.

[17] Smarandache F., and Abobala, M., "n-Refined Neutrosophic Vector Spaces", International Journal of

Neutrosophic Science, Vol. 7, pp. 47-54. 2020.

[18] Sankari, H., and Abobala, M., "Solving Three Conjectures About Neutrosophic Quadruple Vector Spaces",

Neutrosophic Sets and Systems, Vol. 38, pp. 70-77. 2020.

[19] Adeleke, E.O., Agboola, A.A.A., and Smarandache, F., "Refined Neutrosophic Rings II", International

Journal of Neutrosophic Science, Vol. 2(2), pp. 89-94. 2020.

[20] Abobala, M., On Refined Neutrosophic Matrices and Their Applications In Refined Neutrosophic Algebraic

Equations, Journal Of Mathematics, Hindawi, 2021

[21] Abobala, M., A Study of Maximal and Minimal Ideals of n-Refined Neutrosophic Rings, Journal of Fuzzy

Extension and Applications, Vol. 2, pp. 16-22, 2021.

[22] Abobala, M., " Semi Homomorphisms and Algebraic Relations Between Strong Refined Neutrosophic

Modules and Strong Neutrosophic Modules", Neutrosophic Sets and Systems, Vol. 39, 2021.

[23] Abobala, M., "On Some Neutrosophic Algebraic Equations", Journal of New Theory, Vol. 33, 2020.

[24] Abobala, M., On The Representation of Neutrosophic Matrices by Neutrosophic Linear Transformations,

Journal of Mathematics, Hindawi, 2021.

[25] Abobala, M., "On Some Algebraic Properties of n-Refined Neutrosophic Elements and n-Refined

Neutrosophic Linear Equations", Mathematical Problems in Engineering, Hindawi, 2021

[26] Kandasamy V, Smarandache F., and Kandasamy I., Special Fuzzy Matrices for Social Scientists . Printed in

the United States of America,2007, book, 99 pages.

[27] Khaled, H., and Younus, A., and Mohammad, A., " The Rectangle Neutrosophic Fuzzy Matrices", Faculty

of Education Journal Vol. 15, 2019. (Arabic version).

[28] Abobala, M., Partial Foundation of Neutrosophic Number Theory, Neutrosophic Sets and Systems, Vol. 39 ,

2021.

[29] F. Smarandache, Neutrosophic Theory and Applications, Le Quy Don Technical University, Faculty of

Information technology, Hanoi, Vietnam, 17th May 2016.

[30] Sankari, H, and Abobala, M., " On A New Criterion For The Solvability of non Simple Finite Groups and

m-Abelian Solvability, Journal of Mathematics, Hindawi, 2021.

[31] Giorgio, N, Mehmood, A., and Broumi, S.," Single Valued neutrosophic Filter", International Journal of

Neutrosophic Science, Vol. 6, 2020.

[32] Abobala, M., "A Study Of Nil Ideals and Kothe's Conjecture In Neutrosophic Rings", International Journal

of Mathematics and Mathematical Sciences, hindawi, 2021

[33] Abobala, M., Hatip, A., Olgun, N., Broumi, S., Salama, A,A., and Khaled, E, H., The algebraic creativity In

The Neutrosophic Square Matrices, Neutrosophic Sets and Systems, Vol. 40, pp. 1-11, 2021.

[34]Alhamido, K., R., "A New Approach of neutrosophic Topological Spaces", International Journal of

neutrosophic Science, Vol.7, 2020.

[35] Abobala, M., "Neutrosophic Real Inner Product Spaces", Neutrosophic Sets and Systems, Vol. 43, 2021.

[36] Abobala, M., "On Some Special Elements In Neutrosophic Rings and Refined Neutrosophic Rings", Journal

of New Theory, vol. 33, 2020.

[37] Abobala, M., and Hatip, A., "An Algebraic Approach To Neutrosophic Euclidean Geometry", Neutrosophic

Sets and Systems, Vol. 43, 2021.

[38] Sundar, J., Vadivel, A., " New operators Using Neutrosophic Open Sets", Journal Of Neutrosophic and

Fuzzy Systems, 2022.

[39] Sankari, H, and Abobala, M, " A Contribution to m-Power Closed Groups", UMM-Alqura University

Journal for Applied Sciences, KSA, 2020.

[40] Abobala, M., "On The Characterization of Maximal and Minimal Ideals In Several Neutrosophic Rings",

Neutrosophic Sets and Systems, Vol. 45, 2021.

[41] Chellamani, P., and Ajay, D., "Pythagorean neutrosophic Fuzzy Graphs", International Journal of

Neutrosophic Science, Vol. 11, 2021.

[42] Prem Kumar Singh, Fourth dimension data representation and its analysis using Turiyam Context, Journal

of Computer and Communications, 2021, Vol. 9, no. 6, pp. 222-

229,DOI: 10.4236/jcc.2021.96014, https://www.scirp.org/journal/paperinformation.aspx?paperid=110694

[43] Prem Kumar Singh, NeutroAlgebra and NeutroGeometry for Dealing Heteroclinic Patterns. In: Theory and

Applications of NeutroAlgebras as Generalizations of Classical Algebras, IGI Global Publishers, April 2022,

Chapter 6, DOI: 10.4018/978-1-6684-3495-6, ISBN13: 9781668434956

[44] Prem Kumar Singh, Three-way n-valued neutrosophic concept lattice at different granulation, International

Journal of Machine Learning and Cybernetics, Springer, November 2018, Vol 9, Issue 11, pp. 1839-1855.

[45] Abobala, M., Hatip, A., Bal,M.," A Study Of Some Neutrosophic Clean Rings", International journal of

neutrosophic science, 2022.

[46] Prem Kumar Singh, AntiGeometry and NeutroGeometry Characterization of Non-Euclidean Data Sets,

Journal of Neutrosophic and Fuzzy Systems, Nov 2021, Volume 1, Issue 1, pp. 24-33, ISSN:

, DOI: https://doi.org/10.54216/JNFS.0101012 [76] Singh, P,K., " Anti-geometry and NeutroGeometry

Characterization of Non-Euclidean Data", Journal of Neutrosophic and Fuzzy Systems, vol. 1, 2022

[47] Singh, P,K., " Data With Turiyam Set for Fourth Dimension Quantum Information Processing", Journal of

Neutrosophic and Fuzzy Systems, vol.1, 2022.

[48] Singh, P, K., Ahmad, K., Bal, M., Aswad, M.," On The Symbolic Turiyam Rings", Journal of Neutrosophic

and Fuzzy Systems, 2022.

[49] Ibrahim, M., and Abobala, M., "An Introduction To Refined Neutrosophic Number Theory", Neutrosophic

Sets and Systems, Vol. 45, 2021.

[50] Abobala, M., " n-Refined Neutrosophic Groups I", International Journal of Neutrosophic Science, Vol. 0,

pp. 27-34. 2020.

[51] Abobala, M., "Classical Homomorphisms Between n-refined Neutrosophic Rings", International Journal of

Neutrosophic Science", Vol. 7, pp. 74-78. 2020.

[52] Abobala, M., On Some Special Substructures of Neutrosophic Rings and Their Properties, International

Journal of Neutrosophic Science", Vol. 4 , pp. 72-81, 2020.

[53] Sankari, H., and Abobala, M.," AH-Homomorphisms In neutrosophic Rings and Refined Neutrosophic

Rings", Neutrosophic Sets and Systems, Vol. 38, pp. 101-112, 2020.

[54] Hatip, A., Alhamido, R., and Abobala, M., "A Contribution to Neutrosophic Groups", International Journal

of Neutrosophic Science", Vol. 0, pp. 67-76 . 2019.

[55] Hatip, A., and Abobala, M., "AH-Substructures In Strong Refined Neutrosophic Modules", International

Journal of Neutrosophic Science, Vol. 9, pp. 110-116 . 2020.

[56] Aswad, M., " A Study Of neutrosophic Differential Equation By using A Neutrosophic Thick Function",

neutrosophic knowledge, Vol. 1, 2020.

[57] Aswad, M., " A Study of The Integration Of Neutrosophic Thick Function", International journal of

neutrosophic Science, 2020.

[58] Aswad, F, M., " A Study of Neutrosophic Complex Number and Applications", Neutrosophic Knowledge,

Vol. 1, 2020.