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On type-2 soft topologies

Year 2017, Volume: 5 Issue: 4, 182 - 194, 01.10.2017

Sk. Nazmul

https://izlik.org/JA42RK85XN

Abstract

In the present paper, a notion of type-2 soft topology is introduced and some of its important properties are studied. For this we have defined product of type-2 soft sets, type-2 soft product spaces, type-2 soft continuous mappings etc. and their topological behaviours are examined.

Keywords

Soft sets soft mappings soft topologies type-2 soft sets type-2 soft mappings

References

  • Aktas, H. and Cagman, N., Soft sets and soft groups, Inform. Sci., 177 (2007) 2726–2735.
  • Bhabitha, K. V. and Sunil, J. J., Soft relations and functions, Comput. Math. Appl., 60 (2010) 1840–1849.
  • Cagman, N., Karatas, S. and Enginoglu, S., Soft topology, Comput. Math. Appl., 62 (2011) 351—358.
  • Chatterjee, R., Majumda, P. and Samanta, S. K., Type-2 soft sets, J. Intell. & Fuzzy Systems, 29 (2015) 885–898.
  • Hazra, H., Majumdar, P. and Samanta, S. K., Soft topology, Fuzzy Inform. Eng., 4(1) (2012) 105–115.
  • Hussain, S. and Ahmad, B., Some properties of soft topological spaces, Comput. Math. Appl. 62 (2011) 4058–4067.
  • Kharal, A. and Ahmad, B., Mappings on soft classes, New Math. Nat. Comput., 7(3) 471–481.
  • Maji, P. K. and Roy, A. R., An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002) 1077-1083.
  • Majumdar, P. and Samanta, S. K., On soft mappings, Comput. Math. Appl. 60 (2010) 2666–2672.
  • Majumdar, P. and Samanta, S. K., Similarity measure of soft sets, New Math. Nat. Comput., 4(1) (2008), 1–12.
  • Molodtsov, D., Soft Set Theory-First Results, Comput. Math. Appl., 37 (1999) 19-31.
  • Nazmul, Sk. and Samanta, S. K., Neighbourhood properties of soft topological spaces, Annl. Fuzzy Math. Inform., 6(1) (2013) 1–15.
  • Nazmul, Sk. and Samanta, S. K., Soft topological soft groups, Mathematical Sciences, 6:66 (2012) 1–10.
  • Nazmul, Sk. and Samanta, S. K., Generalized group soft topology, Annl. Fuzzy Math. Inform., 9(5) (2015) 783–800.
  • Nazmul, Sk. and Samanta, S. K., Some properties of soft groups and fuzzy soft groups under soft mappings, accepted at PJM, on December, 2016.
  • Nazmul, Sk., Type-2 soft groups, Communicated at Mathematical Sciences, Springer on September, 2016.
  • Shabir, M. and Naz, M., On soft toplogical spaces, Comput. Math. Appl., 61(7) (2011) 1786–1799.
  • Zadeh, L. A., Fuzzy sets, Inform. And Control, 8 (1965), 338–353.
  • Zadeh, L. A., The concept of linguistic variable and its application to approximate reasoning-I, Inform. Sci.(1975), 199-245.

Year 2017, Volume: 5 Issue: 4, 182 - 194, 01.10.2017

Sk. Nazmul

https://izlik.org/JA42RK85XN

Abstract

References

  • Aktas, H. and Cagman, N., Soft sets and soft groups, Inform. Sci., 177 (2007) 2726–2735.
  • Bhabitha, K. V. and Sunil, J. J., Soft relations and functions, Comput. Math. Appl., 60 (2010) 1840–1849.
  • Cagman, N., Karatas, S. and Enginoglu, S., Soft topology, Comput. Math. Appl., 62 (2011) 351—358.
  • Chatterjee, R., Majumda, P. and Samanta, S. K., Type-2 soft sets, J. Intell. & Fuzzy Systems, 29 (2015) 885–898.
  • Hazra, H., Majumdar, P. and Samanta, S. K., Soft topology, Fuzzy Inform. Eng., 4(1) (2012) 105–115.
  • Hussain, S. and Ahmad, B., Some properties of soft topological spaces, Comput. Math. Appl. 62 (2011) 4058–4067.
  • Kharal, A. and Ahmad, B., Mappings on soft classes, New Math. Nat. Comput., 7(3) 471–481.
  • Maji, P. K. and Roy, A. R., An application of soft sets in a decision making problem, Comput. Math. Appl., 44 (2002) 1077-1083.
  • Majumdar, P. and Samanta, S. K., On soft mappings, Comput. Math. Appl. 60 (2010) 2666–2672.
  • Majumdar, P. and Samanta, S. K., Similarity measure of soft sets, New Math. Nat. Comput., 4(1) (2008), 1–12.
  • Molodtsov, D., Soft Set Theory-First Results, Comput. Math. Appl., 37 (1999) 19-31.
  • Nazmul, Sk. and Samanta, S. K., Neighbourhood properties of soft topological spaces, Annl. Fuzzy Math. Inform., 6(1) (2013) 1–15.
  • Nazmul, Sk. and Samanta, S. K., Soft topological soft groups, Mathematical Sciences, 6:66 (2012) 1–10.
  • Nazmul, Sk. and Samanta, S. K., Generalized group soft topology, Annl. Fuzzy Math. Inform., 9(5) (2015) 783–800.
  • Nazmul, Sk. and Samanta, S. K., Some properties of soft groups and fuzzy soft groups under soft mappings, accepted at PJM, on December, 2016.
  • Nazmul, Sk., Type-2 soft groups, Communicated at Mathematical Sciences, Springer on September, 2016.
  • Shabir, M. and Naz, M., On soft toplogical spaces, Comput. Math. Appl., 61(7) (2011) 1786–1799.
  • Zadeh, L. A., Fuzzy sets, Inform. And Control, 8 (1965), 338–353.
  • Zadeh, L. A., The concept of linguistic variable and its application to approximate reasoning-I, Inform. Sci.(1975), 199-245.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Sk. Nazmul This is me

Publication Date October 1, 2017
IZ https://izlik.org/JA42RK85XN
Published in Issue Year 2017 Volume: 5 Issue: 4

Cite

APA Nazmul, S. (2017). On type-2 soft topologies. New Trends in Mathematical Sciences, 5(4), 182-194. https://izlik.org/JA42RK85XN
AMA 1.Nazmul S. On type-2 soft topologies. New Trends in Mathematical Sciences. 2017;5(4):182-194. https://izlik.org/JA42RK85XN
Chicago Nazmul, Sk. 2017. “On Type-2 Soft Topologies”. New Trends in Mathematical Sciences 5 (4): 182-94. https://izlik.org/JA42RK85XN.
EndNote Nazmul S (October 1, 2017) On type-2 soft topologies. New Trends in Mathematical Sciences 5 4 182–194.
IEEE [1]S. Nazmul, “On type-2 soft topologies”, New Trends in Mathematical Sciences, vol. 5, no. 4, pp. 182–194, Oct. 2017, [Online]. Available: https://izlik.org/JA42RK85XN
ISNAD Nazmul, Sk. “On Type-2 Soft Topologies”. New Trends in Mathematical Sciences 5/4 (October 1, 2017): 182-194. https://izlik.org/JA42RK85XN.
JAMA 1.Nazmul S. On type-2 soft topologies. New Trends in Mathematical Sciences. 2017;5:182–194.
MLA Nazmul, Sk. “On Type-2 Soft Topologies”. New Trends in Mathematical Sciences, vol. 5, no. 4, Oct. 2017, pp. 182-94, https://izlik.org/JA42RK85XN.
Vancouver 1.Sk. Nazmul. On type-2 soft topologies. New Trends in Mathematical Sciences [Internet]. 2017 Oct. 1;5(4):182-94. Available from: https://izlik.org/JA42RK85XN