Volume 25 , Issue 1 , PP: 130-136, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
Raed Hatamleh 1 , Ayman Hazaymeh 2
Doi: https://doi.org/10.54216/IJNS.250111
In this paper, we present the topological space of intervals based neutrosophic real numbers , where we clarify how neutrosophic real intervals can be expressed according to the neutrosophic partial order relation, and we use these intervals to build a topological space. On the other hand, we use a similar argument to build a topological space over the intervals of refined neutrosophic numbers, with many illustrated and related examples on open and closed sets.
neutrosophic number , topological space , open set , closed set , neutrosophic interval.
[1] Kandasamy, W. V., & Smarandache, F. (2006). Some neutrosophic algebraic structures and neutrosophic N-algebraic structures. Infinite Study.
[2] Abobala, M. (2021).On refined neutrosophic matrices and their application in refined neutrosophic algebraic equations. Journal of Mathematics,2021(1),5531093.
[3] Olgun, N., Hatip, A., Bal, M., and Abobala, M. (2021). 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.
[4] Hatamleh, R., Zolotarev, V. A.( 2015).On Model Representations of Non-Selfadjoint Operators with Infinitely Dimensional Imaginary Component. Journal of Mathematical Physics, Analysis, Geometry,11(2), 174–186. https://doi.org/10.15407/mag11.02.174
[5] Abobala, M., Bal, M., & Hatip, A. (2021). A review on recent advantages in algebraic theory of neutrosophic matrices. International Journal of Neutrosophic Science, 68-86.
[6] Abobala, M., Ziena, B. M., Doewes, R., & Hussein, Z. (2022). The Representation of Refined Neutrosophic Matrices by Refined Neutrosophic Linear Functions. Int. J. Neutrosophic Sci, 19, 342-349.
[7] T.Qawasmeh, A. Qazza, R. Hatamleh, M.W. Alomari, R. Saadeh. (2023). Further accurate numerical radius inequalities. Axiom-MDPI, 12 (8), 801.
[8] Ahmad, K. D., Thjeel, N. N., Zahra, M. A., & Jaleel, R. A. (2022). On the Classification of n-Refined Neutrosophic Rings and Its Applications in Matrix Computing Algorithms and Linear Systems. International Journal Of Neutrosophic Science, 18(4).
[9] T.Qawasmeh,R.Hatamleh.(2023).A new contraction based on H-simulation functions in the frame of extended b-metric spaces and application.International Journal of Electrical and Computer Engineering, 13 (4),4212-4221.
[10] Zeina, M. B., & Abobala, M. (2023). A novel approach of neutrosophic continuous probability distributions using AH-isometry with applications in medicine. In Cognitive Intelligence with Neutrosophic Statistics in Bioinformatics (pp. 267-286). Academic Press.
[11] Hatamleh, R., Zolotarev, V. A.(2006).Triangular Models of Commutative Systems of Linear Operators Close to Unitary Operators.Ukrainian Mathematical Journal,68(5),791–811. https://doi.org/10.1007/s11253-016-1258-6.
[12] M. Abobala and A. Hatip.(2021).An Algebraic Approach to Neutrosophic Euclidean Geometry. Neutrosophic Sets and Systems, vol. 43, pp. 114-123.
[13] Ayman Hazaymeh, Rania Saadeh, Raed Hatamleh, Mohammad W Alomari, Ahmad Qazza,(2023). A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates,”Axioms-MDPI, ,12(9),803.
[14] Agboola, A.A.A.( 2015). On Refined Neutrosophic Algebraic Structures”, Neutrosophic Sets and Systems,Vol.10, pp. 99-101.
[15] Heilat, A. S., Zureigat, H., Hatamleh, R., Batiha, B.(2021 ).New Spline Method for Solving Linear Two-Point Boundar Value Problems. European Journal of Pure and Applied Mathematics, 14(4), 1283–1294.
[16] I. M. Hanafy, A. A. Salama and K.M. Mahfouz. (2013). Neutrosophic crisp events and its probability. International Journal of Mathematics and Computer Applications Research, 3 (1),171-178.
[17] Kim, J., Lee, J. G., & Hur, K. (2021). Intuitionistic neutrosophic crisp sets and their application to topology. Infinite Study.
[18] A. M. AL-Odhari. , (2015). On infra topological space International Journal of Mathematical Archive,6(11), 179-184.
[19] Al-Husban, A. (2021). Multi-fuzzy hypergroups. Italian Journal of Pure and Applied Mathematics, 46, 382-390.
[20] Sankari, H., and Abobala, M.( 2020). Neutrosophic Linear Diophantine Equations With two Variables. Neutrosophic Sets and Systems, Vol. 38, pp. 22-30.
[21] Abobala, M., & Allouf, A. (2023). On A Novel Security Scheme for The Encryption and Decryption of 2×2 Fuzzy Matrices with Rational Entries Based on The Algebra of Neutrosophic Integers and El-Gamal Crypto-System. Neutrosophic Sets and Systems, 54, 19-32.
[22] Al-Husban, A., Al-Qadri, M. O., Saadeh, R., Qazza, A., & Almomani, H. H. (2022). Multi-fuzzy rings. WSEAS Trans. Math, 21, 701-706.
[23] Hasan Sankari, Mohammad Abobala. (2023). On a Generalization of RSA Crypto-system By Using 2-Cyclic Refined Integers. Journal of Cybersecurity and Information Management, 12 (1), 67-73 (Doi: https://doi.org/10.54216/JCIM.120106).
[24] Al-Husban, A., & Salleh, A. R. (2015).Complex fuzzy ring. In 2015 International Conference on Research and Education in Mathematics (ICREM7) (pp. 241-245). IEEE
[25] Ayman Hazaymeh, Ahmad Qazza, Raed Hatamleh, Mohammad W Alomari, Rania Saadeh . (2023). On Further Refinements of Numerical Radius Inequalities. Axiom-MDPI,12(9),807.
[26] Merkepci, M., & Abobala, M. (2023). Security Model for Encrypting Uncertain Rational Data Units Based on Refined Neutrosophic Integers Fusion and El Gamal Algorithm. Infinite Study.
[27] Al-Husban, A., Amourah, A., & Jaber, J. J. (2020). Bipolar complex fuzzy sets and their properties. Italian Journal of Pure and Applied Mathematics, 43, 754-761
[28] AL-Nafee, A. B., Al-Hamido, R. K., & Smarandache, F. (2019). Separation axioms in neutrosophic crisp topological spaces. Infinite Study.
[29] . Riad K. Al-Hamido. (2018). Neutrosophic crisp bi-topological spaces, Neutrosophic Sets and Systems 21, 66-73.
[30] Hazaymeh Ayman.(2023).Time Effective Fuzzy Soft Set and Its Some Applications with and Without a Neutrosophic. International", Journal of Neutrosophic Science 23(.2), 129-29.