Soft set theory and topology

D. N. Georgiou, A. C. Megaritis
DOI: https://doi.org/10.4995/agt.2014.2268

Abstract

In this paper we study and discuss the soft set theory giving new definitions, examples, new classes of soft sets, and properties for mappings between different classes of soft sets. Furthermore, we investigate the theory of soft topological spaces and we present new definitions, characterizations, and properties concerning the soft closure, the soft interior, the soft boundary, the soft continuity, the soft open and closed maps, and the soft homeomorphism.

Keywords

Soft set theory; Soft topology.

Subject classification

54A05; 06D72.

Full Text:

PDF

References

H. Aktas and N. Çagman, Soft sets and soft groups, Information Sciences 177 (2007), 2726-2735.

(http://dx.doi.org/10.1016/j.ins.2006.12.008)

M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), 1547-1553.

(http://dx.doi.org/10.1016/j.camwa.2008.11.009)

A. Aygunoglu and H. Aygun, Some notes on soft topological spaces, Neural. Comput. Appl. 21 (2011), 113-119.

(http://dx.doi.org/10.1007/s00521-011-0722-3)

N. Çagman and S. Enginoglu, Soft set theory and uni-int decision making, European J. Oper. Res. 207 (2010), 848-855.

(http://dx.doi.org/10.1016/j.ejor.2010.05.004)

N. Çagman and S. Enginoglu, Soft matrix theory and its decision making, Comput. Math. Appl. 59 (2010), 3308-3314.

(http://dx.doi.org/10.1016/j.camwa.2010.03.015)

N. Çagman, S. Karatas and S. Enginoglu, Soft topology, Comput. Math. Appl. 62 (2011), 351-358.

(http://dx.doi.org/10.1016/j.camwa.2011.05.016)

D. Chen, E. C. C. Tsang, D. S. Yeung and X. Wang, The parametrization reduction of soft sets and its applications, Comput. Math. Appl. 49 (2005), 757-763.

(http://dx.doi.org/10.1016/j.camwa.2004.10.036)

F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Computers & Mathematics with Applications 56, no. 10 (2008), 2621-2628.

(http://dx.doi.org/10.1016/j.camwa.2008.05.011)

S. Hussain and B. Ahmad, Some properties of soft topological spaces, Comput. Math. Appl. 62 (2011), 4058-4067.

(http://dx.doi.org/10.1016/j.camwa.2011.09.051)

O. Kazanci, S. Yilmaz and S. Yamak, Soft Sets and Soft BCH-Algebras, Hacettepe Journal of Mathematics and Statistics 39, no. 2 (2010), 205-217.

A. Kharal and B. Ahmad, Mappings of soft classes, New Math. Nat. Comput. 7, no. 3 (2011), 471-481.

(http://dx.doi.org/10.1142/S1793005711002025)

P. K. Maji, A. R. Roy and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002), 1077-1083.

(http://dx.doi.org/10.1016/S0898-1221(02)00216-X)

P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003), 555-562.

(http://dx.doi.org/10.1016/S0898-1221(03)00016-6)

P. K. Maji, R. Biswas and A. R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9, no. 3 (2001), 589-602.

P. Majumdar and S.K. Samanta, Similarity measure of soft sets, New Math. Nat. Comput. 4, no. 1 (2008), 1-12.

(http://dx.doi.org/10.1142/S1793005708000908)

W. K. Min, A note on soft topological spaces, Comput. Math. Appl. 62 (2011), 3524-3528.

(http://dx.doi.org/10.1016/j.camwa.2011.08.068)

D. A. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999), 19-31.

(http://dx.doi.org/10.1016/S0898-1221(99)00056-5)

D. A. Molodtsov, The description of a dependence with the help of soft sets, J. Comput. Sys. Sc. Int. 40, no. 6 (2001), 977-984.

D. A. Molodtsov, The theory of soft sets (in Russian), URSS Publishers, Moscow, 2004.

D. A. Molodtsov, V. Y. Leonov and D. V. Kovkov, Soft sets technique and its application, Nechetkie Sistemy i Myagkie Vychisleniya 1, no. 1 (2006), 8-39.

D. Pei and D. Miao, From soft sets to information systems, In: X. Hu, Q. Liu, A. Skowron, T. Y. Lin, R. R. Yager, B. Zhang, eds., Proceedings of Granular Computing, IEEE, 2 (2005), 617-621.

M. Shabir and M. Naz, On soft topological spaces, Comput. Math. Appl. 61 (2011), 1786-1799.

(http://dx.doi.org/10.1016/j.camwa.2011.02.006)

Y. Shao and K. Qin, The lattice structure of the soft groups, Procedia Engineering 15 (2011), 3621-3625.

(http://dx.doi.org/10.1016/j.proeng.2011.08.678)

I. Zorlutuna, M. Akdag, W. K. Min and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics 3, no. 2 (2012), 171-185.

Y. Zou and Z. Xiao, Data analysis approaches of soft sets under incomplete information, Knowl. Base. Syst. 21 (2008), 941-945.

(http://dx.doi.org/10.1016/j.knosys.2008.04.004)

Abstract Views

5184
Metrics Loading ...

Metrics powered by PLOS ALM


Bookmark and Share

 

Cited-By (articles included in Crossref)

This journal is a Crossref Cited-by Linking member. This list shows the references that citing the article automatically, if there are. For more information about the system please visit Crossref site

1. A New Approach to Hausdorff Space Theory via the Soft Sets
Güzide Şenel
Mathematical Problems in Engineering  vol: 2016  first page: 1  year: 2016  
doi: 10.1155/2016/2196743



Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt