On Fuzzy Hypersoft Topological Spaces

Year 2022, Volume: 9 Issue: 1, 1 - 19, 30.06.2022

Adem Yolcu , Taha Yasin Öztürk

https://doi.org/10.48138/cjo.970818

Cited By: 4

Abstract

This paper is aimed at constructing a topology on fuzzy hypersoft sets. The concepts of fuzzy hypersoft topology, fuzzy hypersoft open(closed) sets, fuzzy hypersoft interior, fuzzy hypersoft closure, fuzzy hypersoft base and fuzzy hypersoft subspace topology are also introduced here and some important theorems have been established.

Keywords

Fuzzy hypersoft set, Fuzzy hypersoft topology, fuzzy hypersoft basis, fuzzy hypersoft subspace

References

• Ahmad, B. & Kharal, A. (2009). On fuzzy soft sets. Advances in fuzzy systems, 2009.
• Aktaş, H., & Çağman, N. (2007). Soft sets and soft groups. Information sciences, 177(13), 2726-2735.
• Ali, M.I., Feng, X.Y. Liu, X.Y., Min, W.K. & Shabir, M. (2009). On some new operations in soft set theory. Computers and Mathematics with Applications, 57, 1547–1553.
• Chen, D., Tsang, E.C.C., Yeung, D.S. & Wong, X. (2005). The parametrization reduction of soft sets and its applicaitons. Computers and Mathematics with Applications, 49, 757–763.
• Feng, F., Jun, Y.B., & Zhao, X. (2008). Soft semirings. Computers and Mathematics with Applications, 56(10), 2621–2628.
• Gayen, S., Smarandache, F., Jha, S., Singh, M.K., Broumi, S. & Kumar, R. (2020). Introduction to plithogenic hypersoft subgroup. Neutrosophic Sets and Systems, 33(1), 14.
• Kharal, A. & Ahmad, B. (2009). Mappings on fuzzy soft classes. Adv. Fuzzy Syst., 2009.
• Martin, N. & Smarandache, F. (2020). Concentric Plithogenic Hypergraph based on Plithogenic Hypersoft sets–A Novel Outlook. Neutrosophic Sets and Systems, 33(1).
• Maji, P.K., Biswas, R. & Roy, A.R., (2003). Soft set theory. Comput. Math. Appl., 45, 555–562.
• Maji, P.K., Biswas, R. & Roy, A.R., (2001). Fuzzy soft sets. J. Fuzzy Math, 9, 589–602.
• Molodtsov, D. (1999). Soft set theory-first results. Computers and Mathematics with Applications, vol. 37, no. 4-5, pp. 19-31.
• Ozturk, T.Y. & Bayramov, S. (2014). Soft mappings space. The Scientific World Journal, 2014.
• Pei, D. & Miao, D. (2005). From soft sets to information systems. Proc. IEEE Int. Conf. Granular Comput. vol.2, pp.617–621.
• Pawlak, Z. (1982). Rough sets. International Journal of Computer and Information Sciences, vol. 11, no. 5, pp. 341–356.
• Rana, S., Qayyum, M., Saeed, M., Smarandache, F. & Khan, B. (2019). Plithogenic Fuzzy Whole Hypersoft Set, Construction of Operators and their Application in Frequency Matrix Multi Attribute Decision Making Technique. Neutrosophic Sets and Systems, vol.28, no.1.
• Roy, A.R. & Maji, P.K. (2007). A fuzzy soft set theoretic approach to decision making problems. Journal of computational and Applied Mathematics, vol.203 no.2 pp.412-418.
• Roy, S. & Samanta, T. K. (2012). A note on fuzzy soft topological spaces. Ann. Fuzzy Math. Inform. vol.3, pp.305–311.
• Saeed, M., Ahsan, M., Siddique, M.K. & Ahmad, M.R. (2020). A Study of The Fundamentals of Hypersoft Set Theory. International Journal of Scientific & Engineering Research, vol.11, no.1.
• Saqlain, M., Jafar, N., Moin, S., Saeed, M. & Broumi, S. (2020a). Single and Multi-valued Neutrosophic Hypersoft set and Tangent Similarity Measure of Single valued Neutrosophic Hypersoft Sets. Neutrosophic Sets and Systems, vol.32, no.1, pp.20.
• Smarandache, F. (2018). Extension of Soft Set to Hypersoft Set, and then to Plithogenic Hypersoft Set. Neutrosophic sets and system, vol.22, pp.168-170, 2018.
• Tanay, B. & Kandemir, M.B. (2011). Topological structure of fuzzy soft sets. Comput. Math. Appl., vol.61 pp.2952–2957.
• Yang, X., Lin, T.Y., Yang, J., Li, Y. & Yu, D. (2009). Combination of interval-valued fuzzy set and soft set Computers and Mathematics with Applications, vol. 58, no. 3, pp. 521–527.
• Yolcu, A. & Ozturk, T.Y. (2021). Fuzzy Hypersoft Sets and its application to decision-making. Theory and Application of Hypersoft Set, Pons Publishing House, pp. 50-64.
• Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338–353.