Intuitionistic Fuzzy Hypersoft Separation Axioms

Year 2022, , 66 - 73, 30.06.2022

Adem Yolcu , Elif Karataş , Taha Yasin Öztürk

https://doi.org/10.47000/tjmcs.920681

Cited By: 1

Abstract

In the present paper, we introduce the notion of $T_{i}$ $(i=0,1,2,3,4)$ separation axioms in intuitionistic fuzzy hypersoft topological spaces and discuss some of its properties. By using this notions, we also give some basic theorems of separation axioms in intuitionistic fuzzy hypersoft topological spaces. Finally, we present hereditary property of intuitionistic fuzzy hypersoft topological spaces.

Keywords

Hypersoft sets, hypersoft topology, intuitionistic fuzzy hypersoft sets, intuitionstic fuzzy hypersoft topology, separation axioms

References

• Abbas, M., Murtaza, G., Smarandache, F., Basic operation on hypersoft sets and hypersoft point, Neutrosophic sets and system, 35(2020), 407-421.
• Ali, M.I., A note on soft sets, rough soft sets and fuzzy soft sets, Appl. Soft Comput., 11(2011), 3329-3332.
• Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87-96
• Bera, T., Mahapatra, N.K., Introduction to neutrosophic soft topological space, Opsearch, 4(2017), 841-867.
• Broumi, S., Smarandache, F., Intuitionistic neutrosophic soft set, J. Inf. Comput. Sci., 8(2013), 130-140.
• Chang, C.L., Fuzzy topological spaces, Journal of mathematical Analysis and Applications, 1(1968), 182-190.
• Coker, D., An introduction to intuitionistic fuzzy topological spaces, Fuzzy Sets and Systems, 1(1997), 81-89.
• Molodtsov, D., Soft set theory-first results, Computers & Mathematics with Applications, 37(1999), 19-31.
• Maji, P.K., Biswas, R., Roy, A.R., Fuzzy soft sets, J. Fuzzy Math., 9(2001), 589-602.
• Maji, P.K., Biswas, R., Roy, A., Intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics, 3(2001), 677-692.
• Maji, P.K., Neutrosophic soft set, Ann. Fuzzy Math. Inform., 5(2013), 57-168.
• Majumdar, P. Samanta, S.K., Generalised fuzzy soft sets, Comput. Math. Appl., 59(2010), 1425-1432
• Pawlak, Z., Rough sets, Int. J. Inf. Comput. Sci., 11(1982), 341-356.
• Smarandache, F., Extension of soft set to hypersoft set, and then to plithogenic hypersoft set, Neutrosophic Sets and System, 22(2018), 168-170.
• Wang, F., Li, X., Chen, X., Hesitant fuzzy soft set and its applications in multicriteria decision making, J. Appl. Math., 2014(2014).
• Xiao, Z., Xia, S., Gong, K., Li, D., The trapezoidal fuzzy soft set and its application in MCDM, Appl. Math. Model., 36(2012), 5844-5855.
• Xu, W., Ma, J. Wang, S. Hao, G., Vague soft sets and their properties, Comput. Math. Appl., 59(2010), 787-794.
• Yang, X.B., Lin, T.Y., Yang, J.Y., Li, Y., Yu, D.Y., Combination of interval-valued fuzzy set and soft set, Comput. Math. Appl., 58(2009), 521-527.
• Yang, Y., Tan, X., Meng, C.C., The multi-fuzzy soft set and its application in decision making, Appl. Math. Model., 37(2013), 4915-4923.
• Yolcu, A., Smarandache F., Ozturk, T.Y, Intuitionistic fuzzy hypersoft sets, Communications Faculty of Sciences University of Ankara Series A Mathematics and Statistics, 70(2021), 443-455.
• Yolcu, A., Ozturk, T.Y., Fuzzy hypersoft sets and its application to decision-making, Theory and Application of Hypersoft Set, 50(2021).
• Yolcu, A., Intuitionistic fuzzy hypersoft topology and its application to multi-criteria decision making, Sigma Journal of Mathematics, In press.
• Yolcu, A., Ozturk T.Y., An introduction to fuzzy hypersoft topological spaces, Caucasian Journal of Science, In press.
• Zadeh, L.A, Fuzzy sets, Inf. Control, 8(1965), 338-353.