Research Article
BibTex RIS Cite
Year 2019, Volume: 48 Issue: 3, 644 - 656, 15.06.2019

Abstract

References

  • A. Acikgoz and N. Tas, Binary soft set theory, Eur. J. Pure Appl. Math. 9 (4), 452–463, 2006.
  • B. Ahmad and S. Hussain, On some structures of soft topology, Mathematical Science, 64, 7 Pages, 2012.
  • M.I. Ali, F. Feng, X.Y. Liu, W.K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57, 1547–1553, 2009.
  • K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96, 1986.
  • K. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64, 159–174, 1994.
  • A. Aygunoglu and H. Aygun, Some notes on soft topological spaces, Neural Comput. Appl. 21, 113–119, 2012.
  • D. Chen, The parametrization reduction of soft sets and its applications, Comput. Math. Appl. 49, 757–763, 2005.
  • S. Hussain, A note on soft connectedness, J. Egyptian Math. Soc. 23 (1), 6–11, 2015.
  • S. Hussain, On some soft functions, Mathematical Science Letters, 4 (1), 55–61, 2015.
  • S. Hussain and B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl. 62, 4058–4067, 2011.
  • S. Hussain and B. Ahmad, Soft separation axioms in soft topological spaces, Hacet. J. Math. Stat. 44 (3), 559–568, 2015.
  • A. Kharal and B. Ahmad, Mappings on soft classes, New Math. Nat. Comput. 7 (3), 471–481, 2011.
  • B. Kostek, Soft set approach to subjective assesment of sound quality, IEEE Confer- ence I, 669–67, 1998.
  • Z. Kong, L. Gao, L. Wong and S. Li, The normal parameter reduction of soft sets and its algorithm, J. Comp. Appl. Math. 21, 941–945, 2008.
  • P.K. Maji, R. Biswas and A.R. Roy, An application of soft sets in a decision making problem, Comput. Math. Appl. 44, 1077–1083, 2002.
  • P.K. Maji, R. Biswas and A.R. Roy, Soft set theory, Comput. Math. Appl. 45, 555– 562, 2003.
  • D. Molodtsov, Soft set theory-First results, Comput. Math. Appl. 37 (4/5), 19–31, 1999.
  • D. Molodtsov, V.Y. Leonov and D.V. Kovkov, Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 1 (1), 8–39, 2006.
  • M. Mushrif, S. Sengupta and A.K. Ray, Texture classification using a novel, soft set theory based classification algorithm, Springer Berlin, Heidelberg, 254–264, 2006.
  • Z. Pawlak, Rough sets, Int. J. Comput. Sci. 11, 341–356, 1982.
  • D. Pie and D. Miao, From soft sets to information systems, Granular computing, IEEE Inter. Conf. 2, 617–621, (2005).
  • M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61, 1786– 1799, 2011.
  • Z. Xio, L. Chen, B. Zhong and S. Ye, Recognition for information based on the theory of soft sets, J. Chen(Ed.), Proceeding of ICSSSM-05, IEEE 2, 1104–1106, 2005.
  • L.A. Zadeh, Fuzzy sets, Inf. Comput. 8, 338–353, 1965.

On some structures of binary soft topological spaces

Year 2019, Volume: 48 Issue: 3, 644 - 656, 15.06.2019

Abstract

We initiate binary soft topological spaces which are, in fact, generalization of soft topological spaces in broader sense. The basic structures and concepts of binary soft topological spaces using binary soft points are studied and their fundamental properties are explored. Examples and counter examples are also provided to efficiently describe the presented notions and results. The results, discussed in this paper, are basic and provide an introductory platform but potentially useful research in theoretical as well as applicable directions.

References

  • A. Acikgoz and N. Tas, Binary soft set theory, Eur. J. Pure Appl. Math. 9 (4), 452–463, 2006.
  • B. Ahmad and S. Hussain, On some structures of soft topology, Mathematical Science, 64, 7 Pages, 2012.
  • M.I. Ali, F. Feng, X.Y. Liu, W.K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57, 1547–1553, 2009.
  • K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20, 87–96, 1986.
  • K. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, 64, 159–174, 1994.
  • A. Aygunoglu and H. Aygun, Some notes on soft topological spaces, Neural Comput. Appl. 21, 113–119, 2012.
  • D. Chen, The parametrization reduction of soft sets and its applications, Comput. Math. Appl. 49, 757–763, 2005.
  • S. Hussain, A note on soft connectedness, J. Egyptian Math. Soc. 23 (1), 6–11, 2015.
  • S. Hussain, On some soft functions, Mathematical Science Letters, 4 (1), 55–61, 2015.
  • S. Hussain and B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl. 62, 4058–4067, 2011.
  • S. Hussain and B. Ahmad, Soft separation axioms in soft topological spaces, Hacet. J. Math. Stat. 44 (3), 559–568, 2015.
  • A. Kharal and B. Ahmad, Mappings on soft classes, New Math. Nat. Comput. 7 (3), 471–481, 2011.
  • B. Kostek, Soft set approach to subjective assesment of sound quality, IEEE Confer- ence I, 669–67, 1998.
  • Z. Kong, L. Gao, L. Wong and S. Li, The normal parameter reduction of soft sets and its algorithm, J. Comp. Appl. Math. 21, 941–945, 2008.
  • P.K. Maji, R. Biswas and A.R. Roy, An application of soft sets in a decision making problem, Comput. Math. Appl. 44, 1077–1083, 2002.
  • P.K. Maji, R. Biswas and A.R. Roy, Soft set theory, Comput. Math. Appl. 45, 555– 562, 2003.
  • D. Molodtsov, Soft set theory-First results, Comput. Math. Appl. 37 (4/5), 19–31, 1999.
  • D. Molodtsov, V.Y. Leonov and D.V. Kovkov, Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya, 1 (1), 8–39, 2006.
  • M. Mushrif, S. Sengupta and A.K. Ray, Texture classification using a novel, soft set theory based classification algorithm, Springer Berlin, Heidelberg, 254–264, 2006.
  • Z. Pawlak, Rough sets, Int. J. Comput. Sci. 11, 341–356, 1982.
  • D. Pie and D. Miao, From soft sets to information systems, Granular computing, IEEE Inter. Conf. 2, 617–621, (2005).
  • M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61, 1786– 1799, 2011.
  • Z. Xio, L. Chen, B. Zhong and S. Ye, Recognition for information based on the theory of soft sets, J. Chen(Ed.), Proceeding of ICSSSM-05, IEEE 2, 1104–1106, 2005.
  • L.A. Zadeh, Fuzzy sets, Inf. Comput. 8, 338–353, 1965.
There are 24 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Sabir Hussain This is me 0000-0001-9191-8172

Publication Date June 15, 2019
Published in Issue Year 2019 Volume: 48 Issue: 3

Cite

APA Hussain, S. (2019). On some structures of binary soft topological spaces. Hacettepe Journal of Mathematics and Statistics, 48(3), 644-656.
AMA Hussain S. On some structures of binary soft topological spaces. Hacettepe Journal of Mathematics and Statistics. June 2019;48(3):644-656.
Chicago Hussain, Sabir. “On Some Structures of Binary Soft Topological Spaces”. Hacettepe Journal of Mathematics and Statistics 48, no. 3 (June 2019): 644-56.
EndNote Hussain S (June 1, 2019) On some structures of binary soft topological spaces. Hacettepe Journal of Mathematics and Statistics 48 3 644–656.
IEEE S. Hussain, “On some structures of binary soft topological spaces”, Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, pp. 644–656, 2019.
ISNAD Hussain, Sabir. “On Some Structures of Binary Soft Topological Spaces”. Hacettepe Journal of Mathematics and Statistics 48/3 (June 2019), 644-656.
JAMA Hussain S. On some structures of binary soft topological spaces. Hacettepe Journal of Mathematics and Statistics. 2019;48:644–656.
MLA Hussain, Sabir. “On Some Structures of Binary Soft Topological Spaces”. Hacettepe Journal of Mathematics and Statistics, vol. 48, no. 3, 2019, pp. 644-56.
Vancouver Hussain S. On some structures of binary soft topological spaces. Hacettepe Journal of Mathematics and Statistics. 2019;48(3):644-56.