On type-2 soft topologies

Yıl 2017, Cilt: 5 Sayı: 4, 182 - 194, 01.10.2017

Sk. Nazmul

Öz

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.

Anahtar Kelimeler

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

Kaynakça

• 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.