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Soft Computing

, Volume 22, Issue 13, pp 4353–4360 | Cite as

The concept of \(\sigma \)-algebraic soft set

Foundations
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Abstract

In this paper, the concept of \(\sigma \)-algebraic soft set which can be used in decision-making process is introduced and some of its structural properties are studied. In order to compare the parameters in soft set theory, we give several characterizations using measurement on the initial universe. Then its applications are given.

Keywords

Soft set \(\sigma \)-Algebra Measurable set 

Notes

Acknowledgements

The author is very much grateful to referees and editor for their valuable comments and suggestions that helped in improving this paper.

Compliance with ethical standards

Conflict of interest

The author declares that they have no conflict of interests regarding the publication of this paper.

Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Aktaş H, Çağman N (2007) Soft sets and soft groups. Inf Sci 177:2726–2735MathSciNetCrossRefMATHGoogle Scholar
  2. Ali MI, Feng F, Liu XY, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57:1547–1553MathSciNetCrossRefMATHGoogle Scholar
  3. Babitha KV, Sunil JJ (2010) Soft set relations and functions. Comput Math Appl 60:1840–1849MathSciNetCrossRefMATHGoogle Scholar
  4. Chen D, Tsang ECC, Yeung DS, Wong X (2005) The parametrization reduction of soft sets and its applications. Comput Math Appl 49:757–763MathSciNetCrossRefMATHGoogle Scholar
  5. Emelyanov E (2007) Introduction to measure theory and Lebesgue integration. Middle East Technical University Press, AnkaraGoogle Scholar
  6. Feng F, Jun YB, Zhao X (2008) Soft semirings. Comput Math Appl 56:2621–2628MathSciNetCrossRefMATHGoogle Scholar
  7. Halmos PR (1950) Measure theory. D. Van Nostrand Company Inc., New York, p 314CrossRefGoogle Scholar
  8. Kharal A, Ahmad B (2009) Mappings on soft classes. New Math Nat Comput 7(3):471–481Google Scholar
  9. Li Z, Chen H, Gao N (2013) The topological structure on soft sets. J Comput Anal Appl 15(4):746–752MathSciNetMATHGoogle Scholar
  10. Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45:555–562MathSciNetCrossRefMATHGoogle Scholar
  11. Min WK (2012) Similarity in soft set theory. Appl Math Lett 25:310–314MathSciNetCrossRefMATHGoogle Scholar
  12. Min WK (2014) Soft sets over a common topological universe. J Intell Fuzzy Syst 26:2099–2106MathSciNetMATHGoogle Scholar
  13. Molodtsov D (1999) Soft set theory-First results. Comput Math Appl 37:19–31MathSciNetCrossRefMATHGoogle Scholar
  14. Pei D, Miao D (2005) From soft sets to information systems. In: Proceedings of IEEE international conference on granular computing 2:617–621Google Scholar
  15. Shabir M, Naz M (2011) On soft topological spaces. Comput Math Appl 61(7):1786–1799MathSciNetCrossRefMATHGoogle Scholar
  16. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353CrossRefMATHGoogle Scholar
  17. Zhu P, Wen Q (2010) Probabilistic soft sets. In: 2010 IEEE international conference on granular computing, pp 635–638Google Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of SciencesMugla Sitki Koçman UniversityMuglaTurkey

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