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On type-2 soft topologies

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

Sk. Nazmul

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

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
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.
AMA Nazmul S. On type-2 soft topologies. New Trends in Mathematical Sciences. October 2017;5(4):182-194.
Chicago Nazmul, Sk. “On Type-2 Soft Topologies”. New Trends in Mathematical Sciences 5, no. 4 (October 2017): 182-94.
EndNote Nazmul S (October 1, 2017) On type-2 soft topologies. New Trends in Mathematical Sciences 5 4 182–194.
IEEE S. Nazmul, “On type-2 soft topologies”, New Trends in Mathematical Sciences, vol. 5, no. 4, pp. 182–194, 2017.
ISNAD Nazmul, Sk. “On Type-2 Soft Topologies”. New Trends in Mathematical Sciences 5/4 (October2017), 182-194.
JAMA 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, 2017, pp. 182-94.
Vancouver Nazmul S. On type-2 soft topologies. New Trends in Mathematical Sciences. 2017;5(4):182-94.