Some Notes on Soft Topological Concepts and an Application Method

Yıl 2020, Cilt: 8 Sayı: 1, 105 - 116, 20.03.2020

Mustafa Burç Kandemir

https://doi.org/10.36753/mathenot.632024

Öz

In this paper, using the concept of soft topology given in \cite{Mbk} i.e. with our new perspective of soft topology, we give some basic topological concepts such as open soft set, closed soft set, interior and closure of a soft set. We then give the concept of soft continuity of a given function between soft topological spaces, and from here we also define the concept of soft homeomorphism and argue the all obtained results. At the end of the article, we propose a decision-making method using soft topological concepts.

Anahtar Kelimeler

Soft set, Soft topological space, continuity, interior, closure

Kaynakça

• Acar, U. and Koyuncu, F. and Tanay, B., Soft sets and soft rings. Comput. Math. Appl. 59 (11) (2010) 3458-3463.
• Aktaş, H. and Çağman, N., Soft sets and soft groups. Inform. Sci. 177 (13) (2007) 2726-2735.
• Ali, M.I. and Feng, F. and Liu, X. and Min, W.K. and Shabir, M., On some new operations in soft set theory. Comput. Math. Appl. 57 (2009) 1547-1553.
• Aygüoğlu, A. and Aygün, H., Some notes on soft topological spaces, Neural Comput. & Applic. 21 (1) (2012) 113-119.
• Çağman, N. and Enginoğlu, S., Soft set theory and $uni-int$ decision making, European J. Oper. Res. 207 (2) (2010) 848-855.
• Çetkin, V. and Aygüoğlu, A. and Aygün, H., A new approach in handling soft decision making problems, J. Nonlinear Sci. Appl. 9 (2016) 231-239.
• Hussain, S. and Ahmad, B., Some properties of soft topological spaces, Comput. Math. Appl. 62 (11) (2011) 4058-4067.
• Kandemir, M.B., A new perspective on soft topology. Hittite J. Sci. Eng. 5 (2) (2018) 105-113.
• Kandemir, M.B., The concept of $\sigma$-algebraic soft set, Soft Comput. 22 (13) (2018) 4353-4360.
• Kandemir, M.B., Monotonic soft sets and its applications, Ann. Fuzzy Math. Inform. 12 (2) (2016) 295-307.
• Maji, P.K. and Biswas, R. and Roy, A.R., Soft set theory. Comput. Math. Appl. 45 (2003) 555-562.
• Maji, P.K. and Roy, A.R. and Biswas, R., An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (8-9) (2002) 1077-1083.
• Molodtsov, D., Soft set theory - first results. Comput. Math. Appl., 37 (1999), 19-31.
• Munkres, J.R., Topology. 2nd, edition. Prentice Hall, Inc. 2000.
• Qin, K. and Yang, J. and Zhang, X., Soft set approaches to decision making problems. In. T. Li et al. (eds) Rough Sets and Knowledge Technology RSTK 2012. Lecture Notes in Computer Science, vol. 7414, Springer (2012) 456-464.
• Shabir, M. and Naz, M., On soft topological spaces. Comput. Math. Appl. 61 (7) (2011) 1786-1799.
• Yüksel, Ş., General topology. 5th, extended edition. Eğitim Kitabevi Yayınları, 2006 (In Turkish).