SOME FEATURES OF FUZZY SOFT Α-T1 TOPOLOGICAL SPACES USING FUZZY SOFT POINTS

Authors:

Ruhul amin,Sumaiya Khatun Sumi,Hannan Miah,

DOI NO:

https://doi.org/10.26782/jmcms.2024.08.00006

Keywords:

Soft set,Fuzzy soft set,Fuzzy soft topological space,Quasi-coincidence,Fuzzy Soft T1 topological spaces,

Abstract

In this paper, we give new four notions of fuzzy soft α -T_1 topological space using the fuzzy soft points concept. We have discussed some implications and theorems, along with their proofs. Moreover, we have presented the hereditary, productive, and projective properties with proof. Finally, we have shown that our given notions are preserved under bijective, fuzzy soft open, and continuous mappings.

Refference:

I. Ahmad B., Kharal A. : On Fuzzy Soft Sets, Hindawi Publishing Corporation, Advances in Fuzzy Systems Article ID 586507, 2009.
II. Atmaca A. S., Zorlutuna I : On Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 5 (2), pp. 377-386, 2013.
III. Hannan Miah and Ruhul Amin : Some Features of Pairwise α-T_0 Spaces in Supra Fuzzy Bitopology, Journal of Mechanics of Continua and Mathematical Sciences, 15(11), pp. 1-11, 2020.
IV. Kandil A., Tantawy O. A. E., El-Sheikh S. A. and Abd El-latif A. M. : Some fuzzy soft topological properties based on fuzzy semi open soft sets, South Asian J. Math., 4 (4), pp. 154–169, 2014.
V. Kharal A. and Ahmad B.: Mappings on fuzzy soft classes, Hindawi Publishing Corporation, Adv. Fuzzy Syst., 2009.
VI. Mishra S. and Srivastava R. : On T_0 and T_1 Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 10 (4), pp. 591-605, 2015.
VII. Molodtsov D. : Soft Set Theory First Results, Comput. Math. Appl., 37 (4-5), pp 19-31, 1999.
VIII. Nazmul S. and Samanta S. K. : Soft Topological Groups, Kochi J. Math., 5, pp. 151-161, 2010.
IX. Pazar Varol B. and Aygun H. : Fuzzy soft topology, Hacettepe Journal of Mathematics and Statistics 41(3), pp. 407-419, 2012.
X. Roy S. and Samanta T. K. : A Note on Fuzzy Soft Topological Spaces, Ann. Fuzzy Math. Inform., 5 (2), pp. 305-311, 2012.
XI. Ruhul Amin and Raihanul Islam : New Concepts on R_1 Fuzzy Soft Topological Spaces, Ann. Fuzzy Math., 22 (2), (October), pp. 123-132, 2021.
XII. Ruhul Amin, Raihanul Islam, Sudipto Kumar Shaha and Saikh Shahjahan Miah : Some properties of T_0 fuzzy soft topological spaces in quasi-coincidence sense, Journal of Mechanics of Continua and Mathematical Sciences, 17(4), pp. 8-20, 2022.
XIII. Shabir M. and Naz M. : On Soft Topological Spaces, Comput. Math. Appl., 61, pp. 1786-1799, 2011.
XIV. Saleh S., Abd El-Latif A. M. and Al-Salemi A. : On Separation Axioms in Fuzzy Soft Topological Spaces, South Asian Journal of Mathematics, 8 (2), pp. 92-109, 2018.
XV. Tanay B. and Kandemir M. B. : Topological Structure of Fuzzy Soft Sets, Computer and Mathematics with Applications, 61, pp. 2952-2957, 2011.
XVI. Varol B. P. and Aygun H. : Fuzzy Soft Topology, Hacettepe Journal of Mathematics and Statistics, 41 (3), pp. 407-419, 2012.
XVII. Zadeh, L. A. : Fuzzy sets. Information and Control , 8, pp. 338-353, 1965.

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