Interval-valued neutrosophic soft sets and its decision making | International Journal of Machine Learning and Cybernetics Skip to main content

Advertisement

Log in

Interval-valued neutrosophic soft sets and its decision making

  • Original Article
  • Published:
International Journal of Machine Learning and Cybernetics Aims and scope Submit manuscript

Abstract

In this paper, the notion of the interval valued neutrosophic soft set (ivn-soft sets) is defined which is a combination of an interval valued neutrosophic set [35] and a soft set [29]. Our ivn-soft sets generalizes the concept of the soft set, fuzzy soft set, interval valued fuzzy soft set, intuitionistic fuzzy soft set, interval valued intuitionistic fuzzy soft set and neutrosophic soft set. Then, we introduce some definitions and operations on ivn-soft sets sets. Some properties of ivn-soft sets which are connected to operations have been established. Also, the aim of this paper is to investigate the decision making based on ivn-soft sets by level soft sets. Therefore, we develop a decision making methods and then give a example to illustrate the developed approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Acar U, Koyuncu F, Tanay B (2010) Soft sets and soft rings. Comput Math Appl 59:3458–3463

    Article  MathSciNet  MATH  Google Scholar 

  2. Aktaş H, Çağman N (2007) Soft sets and soft groups. Inf Sci 177:2726–2735

    Article  MathSciNet  MATH  Google Scholar 

  3. Atanassov K (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    Article  MathSciNet  MATH  Google Scholar 

  4. Awang MI, Rose ANM, Herawan T, Deris MM (2010) Soft set approach for selecting decision attribute in data clustering. In: Advanced data mining and applications lecture notes in computer science, vol 6441, pp 87–98

  5. Aygünoglu A, Aygün H (2009) Introduction to fuzzy soft groups. Comput Math Appl 58:1279–1286

    Article  MathSciNet  MATH  Google Scholar 

  6. Broumi S (2013) Generalized neutrosophic soft set. Int J Comput Sci Eng Inf Technol (IJCSEIT) 3/2. doi:10.5121/ijcseit.2013.3202

  7. Broumi S, Smarandache F (2013) Intuitionistic neutrosophic soft set. J Inf Comput Sci 8(2):130–140

    Google Scholar 

  8. Çağman, Karataş S, Enginoğlu S (2011) Soft topology. Comput Math Appl 62:351–358

  9. Çağman N, Erdoğan F, Enginoğlu S (2011) FP-soft set theory and its applications. Ann Fuzzy Math Inf 2(2):219–226

    MathSciNet  MATH  Google Scholar 

  10. Çağman N, Enginoğlu S (2010) Soft set theory and uni–int decision making. Eur J Oper Res 207:848–855

    Article  MathSciNet  MATH  Google Scholar 

  11. Çağman N, Deli I (2012) Means of FP-soft sets and its applications. Hacet J Math Stat 41(5):615–625

    MathSciNet  MATH  Google Scholar 

  12. Çağman N, Erdoğan F, Enginoğlu S (2011) FP-soft set theory and its applications. Ann Fuzzy Math Inf 2(2):219–226

    MathSciNet  MATH  Google Scholar 

  13. Çağman N, Enginoğlu S (2010) Soft set theory and uni–int decision making. Eur J Oper Res 207:848–855

    Article  MathSciNet  MATH  Google Scholar 

  14. Çağman N, Deli II (2013) Soft games. http://arxiv.org/abs/1302.4568

  15. Feng F, Li C, Davvaz B, Irfan Ali M (2010) Soft sets combined with fuzzy sets and rough sets: a tentative approach. Soft Comput 14:899–911

    Article  MATH  Google Scholar 

  16. Feng F, Jun YB, Liu X, Li L (2010) An adjustable approach to fuzzy soft sets based decision making. J Comput Appl Math 234:10–20

    Article  MathSciNet  MATH  Google Scholar 

  17. Jiang Y, Tang Y, Chen Q, Liu H, Tang J (2010) Interval-valued intuitionistic fuzzy soft sets and their properties. Comput Math Appl 60:906–918

    Article  MathSciNet  MATH  Google Scholar 

  18. Jiang Y, Tang Y, Chen Q (2011) An adjustable approach to intuitionistic fuzzy soft sets based decision making. Appl Math Model 35:824–836

    Article  MathSciNet  MATH  Google Scholar 

  19. Karaaslan F, Çağman N, Enginoğlu S (2012) Soft lattices. J New Results Sci 1:5–17

    Google Scholar 

  20. Kharal A (2010) Distance and similarity measures for soft sets. New Math Nat Comput 06:321. doi:10.1142/S1793005710001724

    Article  MathSciNet  MATH  Google Scholar 

  21. Kovkov DV, Kolbanov VM, Molodtsov DA (2007) Soft sets theory-based optimization. J Comput Syst Sci Int 46(6):872–880

    Article  MathSciNet  MATH  Google Scholar 

  22. Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602

    MathSciNet  MATH  Google Scholar 

  23. Maji PK, Roy AR, Biswas R (2004) On intuitionistic fuzzy soft sets. J Fuzzy Math 12(3):669–683

    MathSciNet  MATH  Google Scholar 

  24. Maji PK (2012) A neutrosophic soft set approach to a decision making problem. Ann Fuzzy Math Inf 3(2):313–319

    MathSciNet  MATH  Google Scholar 

  25. Maji PK (2013) Neutrosophic soft set. Comput Math Appl 45:555–562

    Article  MATH  Google Scholar 

  26. Maji PK, Roy AR (2002) An application of soft sets in a decision making problem. Comput Math Appl 44:1077–1083

    Article  MathSciNet  MATH  Google Scholar 

  27. Mamat R, Herawan T, Deris MM (2013) MAR: maximum attribute relative of soft set for clustering attribute selection. Knowl Based Syst 52:11–20

    Article  Google Scholar 

  28. Min WK (2011) A note on soft topological spaces. Comput Math Appl 62:3524–3528

    Article  MathSciNet  MATH  Google Scholar 

  29. Molodtsov DA (1999) Soft set theory-first results. Comput Math Appl 37:19–31

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  31. Nagarajan EKR, Meenambigai G (2011) An application of soft sets to lattices. Kragujev J Math 35(1):75–87

    MathSciNet  MATH  Google Scholar 

  32. Pawlak Z (1982) Rough sets. Int J Inf Comput Sci 11:341–356

    Article  MATH  Google Scholar 

  33. Smarandache F (2005) Neutrosophic set, a generalisation of the intuitionistic fuzzy sets. Int J Pure Appl Math 24:287–297

    MathSciNet  MATH  Google Scholar 

  34. Shabir M, Naz M (2011) On soft topological spaces. Comput Math Appl 61:1786–1799

    Article  MathSciNet  MATH  Google Scholar 

  35. Wang H, Smarandache F, Zhang YQ, Sunderraman R (2005) Interval Neutrosophic Sets and Logic: Theory and Applications in Computing. In: Neutrosophic book series, vol 5. Hexis, Arizona

  36. Wang H, Smarandache F, Zhang YQ, Sunderraman R (2010) Single valued neutrosophic sets. Multispace Multistructure 4:410–413

    MATH  Google Scholar 

  37. Şerife Yılmaz, Kazancı O (2013) Soft lattices(ideals, filters) related to fuzzy point. In: U.P.B. Scientific Bulletin, Series A, 75/ 3, pp 75–90

  38. Yüksel S, Dizman T, Yildizdan G, Sert U (2013) Application of soft sets to diagnose the prostate cancer risk. J Inequal Appl. doi:10.1186/1029-242X-2013-229

  39. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  40. Zhang Z, Wang C, Tian D, Li K (2014) A novel approach to interval-valued intuitionistic fuzzy soft set based decision making. Appl Math Model 38:1255–1270

    Article  MathSciNet  Google Scholar 

  41. Zhan J, Jun YB (2010) Soft BL-algebras based on fuzzy sets. Comput Math Appl 59:2037–2046

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Irfan Deli.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Deli, I. Interval-valued neutrosophic soft sets and its decision making. Int. J. Mach. Learn. & Cyber. 8, 665–676 (2017). https://doi.org/10.1007/s13042-015-0461-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13042-015-0461-3

Keywords

Navigation