Fuzzy Semi Open Soft Sets Related Properties in Fuzzy Soft Topological Spaces

Volume 13, Issue 2, pp 94-114 http://dx.doi.org/10.22436/jmcs.013.02.01

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 3639 Downloads
• 5521 Views

Authors

A. Kandil - Mathematics Department, Faculty of Science, Helwan University, Helwan, Egypt. O. A. E. Tantawy - Mathematics Department, Faculty of Science, Zagazig University, Zagazig, Egypt. S. A. El-sheikh - Mathematics Department, Faculty of Education, Ain Shams University, Cairo, Egypt. A. M. Abd El-latif - Mathematics Department, Faculty of Education, Ain Shams University, Cairo, Egypt.

Abstract

In the present paper, we continue the study on fuzzy soft topological spaces and investigate the properties of fuzzy semi open (closed) soft sets, fuzzy semi soft interior (closure), fuzzy semi continuous (open) soft functions and fuzzy semi separation axioms which are important for further research on fuzzy soft topology. In particular, we study the relationship between fuzzy semi soft interior fuzzy semi soft closure. Moreover, we study the properties of fuzzy soft semi regular spaces and fuzzy soft semi normal spaces. This paper, not only can form the theoretical basis for further applications of topology on soft sets, but also lead to the development of information systems.

Share and Cite

Keywords

• Soft set
• Fuzzy soft set
• Fuzzy soft topological space
• Fuzzy semi soft interior
• Fuzzy semi soft closure
• Fuzzy semi open soft
• Fuzzy semi closed soft
• Fuzzy semi continuous soft functions
• Fuzzy soft semi separation axioms
• Fuzzy soft semi regular
• Fuzzy soft semi \(T_i\)-spaces (i =1،2،3،4)
• Fuzzy soft semi normal.

MSC

•  54A40
•  54A05
•  06D72

References

• [1] B. Ahmad, A. Kharal, Mappings of fuzzy soft classes , Adv. Fuzzy Syst. Art. ID 407890, (2009), 6 pages.
  • View Article
  • Google Scholar
  • MATH


• [2] B. Ahmad, A. Kharal , Mappings of soft classes, New Math. Nat. Comput., 7 (3) (2011), 471-481.
  • View Article
  • Google Scholar
  • MATH


• [3] B. Ahmad, A. Kharal, On fuzzy soft sets, Adv. Fuzzy Syst., (2009), 1-6.
  • View Article
  • Google Scholar


• [4] M. I. Ali, F. Feng, X. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications , 57 (2009), 1547-1553.
  • View Article
  • MathSciNet
  • Google Scholar


• [5] A. M. Aminpour, M. Seilani , Compact topological semigroups associated with oids , J. Math. Computer Sci. , 12 (3) (2014), 219-234.
  • Google Scholar


• [6] S. Atmaca, I.Zorlutuna , On fuzzy soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 5 (2013), 377-386.
  • Google Scholar


• [7] A. Aygunoglu, H. Aygun , Introduction to fuzzy soft groups, Computers and Mathematics with Applications , 58 (2009), 1279-1286.
  • View Article
  • MathSciNet
  • Google Scholar


• [8] Bakir Tanay, M. Burcl Kandemir , Topological structure of fuzzy soft sets, Computer and mathematics with applications, 61 (2011), 2952-2957.
  • View Article
  • MathSciNet
  • Google Scholar


• [9] N. Cagman, F. Citak, S. Enginoglu, Fuzzy parameterized fuzzy soft set theory and its applications, Turkish Journal of Fuzzy Systems, 1 (1) (2010), 21-35.


• [10] N. Cagman, S. Enginoglu, Soft set theory and uni-int decision making, European Journal of Operational Research , 207 (2010), 848-855.
  • View Article
  • Google Scholar


• [11] C. L. Change, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182-190.
  • Google Scholar


• [12] Eshagh Hosseinpour, T-rough fuzzy subgroups of groups, J. Math. Computer Sci. , 12 (3) (2014), 186-195.
  • Google Scholar


• [13] Haci Aktas, Naim Cagman, Soft sets and soft groups, Innformation science, 177 (2007), 2726-2735.
  • View Article
  • Google Scholar


• [14] M. Jain, M. P. S. Bhatia, A rough set based approach to classify node behavior in mobile ad hoc networks, J. Math. Computer Sci. , 10 (2) (2014), 64-78.
  • Google Scholar


• [15] Jianyu Xiao, Minming Tong, Qi Fan, Su Xiao, Generalization of Belief and Plausibility Functions to Fuzzy Sets, Applied Mathematics Information Sciences, 6 (2012), 697-703.
  • Google Scholar


• [16] A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. Abd El-latif, \(\gamma\)-operation and decompositions of some forms of soft continuity in soft topological spaces, Annals of Fuzzy Mathematics and Informatics , 7 (2014), 181-196.
  • MathSciNet
  • Google Scholar
  • MATH


• [17] A.Kandil, O. A. E. Tantawy, S. A. El-Sheikh, A. M. Abd El-latif, Soft semi separation axioms and irresolute soft functions, Annals of Fuzzy Mathematics and Informatics , 8 (2014), 305-318.
  • Google Scholar
  • MATH


• [18] D. V. Kovkov, V. M. Kolbanov, D. A. Molodtsov, Soft sets theory-based optimization , Journal of Computer and Systems Sciences Finternational , 46 (6) (2007), 872-880.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [19] F. Lin , Soft connected spaces and soft paracompact spaces, International Journal of Mathematical Science and Engineering, 7 (2) (2013), 1-7.
  • View Article
  • Google Scholar


• [20] J. Mahanta, P. K. Das, Results on fuzzy soft topological spaces, arXiv:1203.0634v1, (2012),
  • Google Scholar


• [21] P. K. Maji, R. Biswas, A. R. Roy, Fuzzy soft sets, Journal of Fuzzy Mathematics , 9 (3) (2001), 589-602.
  • Google Scholar


• [22] P. K. Maji, R. Biswas, A. R. Roy, intuitionistic fuzzy soft sets, Journal of Fuzzy Mathematics, 9 (3) (2001), 677-691.
  • Google Scholar


• [23] P. K. Maji, R. Biswas, A. R. Roy, Soft set theory, Computers and Mathematics with Applications , 45 (2003), 555-562.
  • View Article
  • Google Scholar


• [24] P. Majumdar, S. K. Samanta, Generalised fuzzy soft sets, Computers and Mathematics with Applications, 59 (2010), 1425-1432.
  • View Article
  • Google Scholar


• [25] D. A. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications , 37 (1999), 19-31.
  • View Article
  • MathSciNet
  • Google Scholar


• [26] D. Molodtsov, V. Y. Leonov, D. V. Kovkov, Soft sets technique and its application , Nechetkie Sistemy i Myagkie Vychisleniya , 1 (1) (2006), 8-39.
  • Google Scholar


• [27] A. Mukherjee, S. B. Chakraborty, On Intuitionistic fuzzy soft relations, Bulletin of Kerala Mathematics Association, 5 (1) (2008), 35-42.
  • MathSciNet
  • Google Scholar


• [28] B. Pazar Varol, H. Aygun, Fuzzy soft topology, Hacettepe Journal of Mathematics and Statistics, 41 (3) (2012), 407-419.
  • Google Scholar


• [29] D. Pei, D. Miao, From soft sets to information systems, in: X. Hu, Q. Liu, A. Skowron, T. Y. Lin, R. R. Yager, B. Zhang (Eds.), Proceedings of Granular Computing, in: IEEE, 2 (2005), 617-621.
  • View Article
  • Google Scholar


• [30] H. Rahimpoor, A. Ebadian, M. Eshaghi Gordji, A. Zohri , Fixed point theory for generalized quasi-contraction Maps in modular metric spaces, J. Math. Computer Sci. , 10 (1) (2014), 47-53.
  • Google Scholar


• [31] S. Roy, T. K. Samanta, A note on fuzzy soft topological spaces, Annals of Fuzzy Mathematics and informatics , 3 (2) (2012), 305-311.
  • MathSciNet
  • Google Scholar


• [32] S. Roy, T. K. Samanta, An introduction to open and closed sets on fuzzy topological spaces , Annals of Fuzzy Mathematics and Informatics, (2012)
  • MathSciNet
  • Google Scholar
  • MATH


• [33] M. Shabir, M. Naz, On soft topological spaces, Comput. Math. Appl. , 61 (2011), 1786-1799.
  • View Article
  • Google Scholar


• [34] J. K. Syed, L. A. Aziz , Fuzzy Inventory Model without Short-ages Using Signed Distance Method , Applied Mathematics Information Sciences, 1 (2007), 203-209.
  • Google Scholar


• [35] B. Tanay, M. B. Kandemir, Topological structure of fuzzy soft sets, Computer and Math. with appl. , 61 (2011), 2952--2957.
  • View Article
  • MathSciNet
  • Google Scholar


• [36] Won Keun Min, A note on soft topological spaces, Computers and Mathematics with Applications , 62 (2011), 3524-3528.
  • View Article
  • Google Scholar


• [37] Z. Xiao, L. Chen, B. Zhong, S. Ye, Recognition for soft information based on the theory of soft sets, in: J. Chen (Ed.), Proceedings of ICSSSM-05, 2 (2005), 1104-1106.
  • View Article
  • Google Scholar


• [38] Yong Chan Kim, Jung Mi Ko, Fuzzy G-closure operators , commun Korean Math. Soc., 18(2) (2008), 325-340.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [39] L. A. Zadeh, Fuzzy sets, Information and Control , 8 (1965), 338-353.


• [40] Y. Zou, Z. Xiao, Data analysis approaches of soft sets under incomplete information, Knowledge-Based Systems, 21 (2008), 941-945.
  • View Article
  • Google Scholar