W- Hausdorff Separation Axiom in Second Order Interval Valued Fuzzy Topological Spaces

Bhavani Gokila; Vijayalakshmi V.

doi:https://doi.org/10.54216/IJNS.260315

Full Length Article

Volume 26 • Issue 3 • PP: 221-228 • 2025

W- Hausdorff Separation Axiom in Second Order Interval Valued Fuzzy Topological Spaces

Bhavani Gokila D. ^1*

mail

,

Vijayalakshmi V. M. ²

mail

¹Research Scholar, Department of Mathematics, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, India

²Assistant Professor, Department of Science and Humanities, School of Engineering, Avinashilingam Institute for Home Science and Higher Education for Women, India

* Corresponding Author.

DOI https://doi.org/10.54216/IJNS.260315

format_quote Cite this article

Received: January 14, 2025 Revised: February 10, 2025 Accepted: March 06, 2025

View PDF open_in_new

Abstract

We studied and introduced a concept SIVFT then present the concept of SIVF subspace and SIVF product topology in SIVF topological spaces. W-Hausdorff Separation Axiom in SIVF topological spaces and its basics are studied.

Keywords

IVF set (IVFs) IVF topology (IVFT) Second order fuzzy set (SFs) Second order fuzzy topology (SFT) Second order IVF set (SIVFs) Second order IVF topology (SIVFT) SIVF subspace SIVFW-Hausdorff space

References

[1] M. Ali, A. Kilicman, and A.Z. Khameneh, "Separation Axioms of Interval Valued Fuzzy Soft Topology Via Quasi-Neighbourhood Structure," MDPI, vol. 8, no. 178, pp. 1-17, 2020.

[2] K.K. Azad, "Fuzzy Hausdorff Spaces and Fuzzy Perfect Mappings," Journal of Mathematical Analysis and Applications, vol. 82, pp. 297-305, 1981.

[3] D. Bhavani Gokila and V.M. Vijayalakshmi, "Interval valued Fuzzy W-Hausdorff Spaces," Advances and Applications in Mathematical Sciences, vol. 21, no. 2, pp. 793-804, 2021.

[4] H. Bustince, "Indicator of Inclusion Grade for Interval Valued Fuzzy Sets: Application to Approximate Reasoning Based on Interval Valued Fuzzy Sets," International Journal of Approximate Reasoning, vol. 23, no. 3, pp. 137-209, 2000.

[5] C.L. Chang, "Fuzzy Topological Spaces," Journal of Mathematical Analysis and Applications, vol. 24, pp. 182-190, 1968.

[6] P. Das, "Fuzzy Topology on Fuzzy Sets, Product Fuzzy Topology and Fuzzy Topological Groups," Fuzzy Sets and Systems, vol. 100, pp. 367-372, 1998.

[7] D. Dubois and H. Prade, "Interval Valued Fuzzy Sets, Possibility Theory and Imprecise Probability," Proc. of International Conference in Fuzzy Logic and Technology, pp. 8-10, 2005.

[8] S. Ganguly and S. Saha, "On Separation Axioms and Separations of Connected Sets in Fuzzy Topological Spaces," Bulletin of the Calcutta Mathematical Society, vol. 79, pp. 215-225, 1987.

[9] T.E. Gantner, R.C. Steinlage, and R.H. Warren, "Compactness in Fuzzy Topological Spaces," Journal of Mathematical Analysis and Applications, vol. 62, pp. 547-562, 1978.

[10] M.H. Ghanim, E.E. Kerre, and A.S. Mashhour, "Separation Axioms, Subspaces and Sums in Fuzzy Topology," Journal of Mathematical Analysis and Applications, vol. 102, pp. 189-202, 1984.

[11] Y.B. Jun, C.S. Kim, and K.O. Yang, "Cubic Sets," Annals of Fuzzy Mathematics and Informatics, vol. 4, no. 1, pp. 83-98, 2012.

[12] A. Kalaichelvi, "A Study of Second Order Fuzzy Structures," Ph.D. Thesis, Avinashilingam Institute for Home Science and Higher Education for Women, Coimbatore, Tamil Nadu, India, 2000.

[13] A. Kandil, O. Tantawy, M. Yakout, and S. Saleh, "Separation Axioms in Interval Valued Fuzzy Topological Spaces," Applied Mathematics and Information Sciences, vol. 5, no. 2, pp. 1-19, 2011.

[14] A.K. Katsaras, "Ordered Fuzzy Topological Spaces," Journal of Mathematical Analysis and Applications, vol. 84, pp. 44-58, 1981.

[15] H.U. Khan, A. Khan, and N.H. Sarmin, "Cartesian Product of Interval Valued Fuzzy Ideals in Ordered Semi Group," Journal of Prime Research in Mathematics, vol. 12, pp. 120-129, 2016.

[16] Q. Liang and J.M. Mendel, "Interval Type-2 Fuzzy Logic Systems: Theory and Design," IEEE Transactions on Fuzzy Systems, vol. 8, no. 5, pp. 535-550, 2000.

[17] R. Lowen, "Fuzzy Topological Spaces and Fuzzy Compactness," Journal of Mathematical Analysis and Applications, vol. 56, pp. 621-633, 1976.

[18] G. Meng, "The Basic Theories of Interval Valued Fuzzy Sets," Mathematica Applicate, vol. 6, no. 2, pp. 212-217, 1993.

[19] S.S. Miah and M.R. Amin, "Mappings in Fuzzy Hausdorff Spaces in Quasi-Coincidence Sense," Journal of Bangladesh Academy of Sciences, vol. 41, no. 1, pp. 47-56, 2017.

[20] T.K. Mondal and S.K. Samanta, "Topology of Interval Valued Fuzzy Sets," Indian Journal of Pure and Applied Mathematics, vol. 30, pp. 23-38, 1999.

[21] P.V. Ramakrishnan and L.G. Nayagam, "Hausdorff Interval Valued Fuzzy Filters," Journal of Korean Mathematical Society, vol. 39, no. 1, pp. 137-148, 2002.

[22] S.E. Rodabaugh, "The Hausdorff Separation Axiom for Fuzzy Topological Spaces," Topology and its Applications, vol. 11, pp. 319-334, 1980.

[23] K.EI. Saady and M.Y. Bakeir, "Separation Axioms in Fuzzy Topological Ordered Spaces," Fuzzy Sets and Systems, vol. 98, pp. 211-215, 1998.

[24] S. Saleh, "On Category of Interval Valued Fuzzy Topological Spaces," Annals of Fuzzy Mathematics and Informatics, vol. 4, no. 2, pp. 385-392, 2012.

[25] R. Srivastava, S.N. Lal, and A.K. Srivastava, "Fuzzy Hausdorff Topological Spaces," Journal of Mathematical Analysis and Applications, vol. 81, pp. 497-506, 1981.

[26] S. Vijayabalaji, "Cartesian Product and Homomorphism of Interval Valued Fuzzy Linear Space," International Journal of Open Problems in Computational Mathematics, vol. 5, no. 4, pp. 93-103, 2012.

[27] R.H. Warren, "Neighborhoods, Bases and Continuity in Fuzzy Topological Spaces," Rocky Mountain Journal of Mathematics, vol. 8, no. 3, pp. 459-470, 1978.

[28] P. Wuyts and R. Lowen, "On Separation Axioms in Fuzzy Topological Spaces: Fuzzy Neighbourhood Spaces and Fuzzy Uniform Spaces," Journal of Mathematical Analysis and Applications, vol. 93, pp. 27-47, 1983.

[29] L.A. Zadeh, "Fuzzy Sets," Information and Control, vol. 8, no. 3, pp. 338-353, 1965.

[30] L.A. Zadeh, "The Concept of a Linguistic Variable and its Application to Approximate Reasoning – I," Information Sciences, vol. 8, pp. 199-249, 1975.

[31] A. Zeb, S. Abdullah, M. Khan, and Majid, "Cubic Topology," International Journal of Computer Science and Information Security, vol. 14, no. 8, pp. 659-669, 2016.

Cite This Article

Choose your preferred format

format_quote

D., Bhavani Gokila, M., Vijayalakshmi V.. "W- Hausdorff Separation Axiom in Second Order Interval Valued Fuzzy Topological Spaces." International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 3, 2025, pp. 221-228. DOI: https://doi.org/10.54216/IJNS.260315

D., B., M., V. (2025). W- Hausdorff Separation Axiom in Second Order Interval Valued Fuzzy Topological Spaces. International Journal of Neutrosophic Science, Volume 26(Issue 3), 221-228. DOI: https://doi.org/10.54216/IJNS.260315

D., Bhavani Gokila, M., Vijayalakshmi V.. "W- Hausdorff Separation Axiom in Second Order Interval Valued Fuzzy Topological Spaces." International Journal of Neutrosophic Science Volume 26, no. Issue 3 (2025): 221-228. DOI: https://doi.org/10.54216/IJNS.260315

D., B., M., V. (2025) 'W- Hausdorff Separation Axiom in Second Order Interval Valued Fuzzy Topological Spaces', International Journal of Neutrosophic Science, Volume 26(Issue 3), pp. 221-228. DOI: https://doi.org/10.54216/IJNS.260315

D. B, M. V. W- Hausdorff Separation Axiom in Second Order Interval Valued Fuzzy Topological Spaces. International Journal of Neutrosophic Science. 2025;Volume 26(Issue 3):221-228. DOI: https://doi.org/10.54216/IJNS.260315

B. D., V. M., "W- Hausdorff Separation Axiom in Second Order Interval Valued Fuzzy Topological Spaces," International Journal of Neutrosophic Science, vol. Volume 26, no. Issue 3, pp. 221-228, 2025. DOI: https://doi.org/10.54216/IJNS.260315

Digital Archive Ready