Skip to main content
SpringerLink
Log in

On partially included intuitionistic fuzzy rough relations

  • Published:
Afrika Matematika Aims and scope Submit manuscript

Abstract

In this paper, we develop the idea of partially included intuitionistic fuzzy rough relation (briefly, PIIFR-relation) on a set in a different approach and study the effect of an Atanassov’s operator on the properties of PIIFR-relations. The new obtained class of relations contains the class of fuzzy rough relations and we establish sufficient conditions under which a PIIFR-relation is closed to Atanassov’s operator and composition operation. We determine sufficient conditions under which an intuitionistic fuzzy rough relation (briefly, IFR-relation) becomes a PIIFR-relation. Finally, we investigate semi-properties of IFR-relations, namely reflexivity, irreflexivity, asymmetry, transitivity, etc.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Atanassov, K.: Intutionistic fuzzy sets. Fuzzy Sets Syst. 64, 87–96 (1986)

    Article  MathSciNet  Google Scholar 

  2. Atanassov, K.: Intuitionistic Fuzzy Sets: Theory and Applications. Springer, New York (1999)

  3. Chakrabarty, K., Gedeon, T., Koczy, I.: Intuitionistic fuzzy rough sets. In: Proceeding of the Fourth Joint Conference of Information Sciences, Durham, pp. 211–214. JCTS (1998)

  4. Deschrijver, G., Kerre, E.E.: On the composition of intuitionistic fuzzy relations. Fuzzy Sets Syst. 136, 333–361 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fono, L.A., Njanpong, N.G.: Arrow-type results under intuitionistic fuzzy preferences. New Math. Nat. Comput. 9(1), 97–123 (2013). doi:10.1142/S1793005713500075

  6. Fono, L.A., Njanpong, N.G., Salles, M., Gwet, H.: A binary intuitionistic fuzzy relation: some new results, a general factorization and two properties of strict components. Int. J. Math. Math. Sci. 2009, 38 (2009). doi:10.1155/2009/580918. (Article ID 580918)

  7. Jana, S.P., Ghosh, S.K.: Intuitionistic fuzzy rough sets. Notes Intuit. Fuzzy Sets 8, 1–18 (2002)

    MathSciNet  MATH  Google Scholar 

  8. Li, D.-F.: Multiattribute decision making models and method using intuitionistic fuzzy sets. J. Comput. Syst. Sci. 70, 73–85 (2005)

    Article  MATH  Google Scholar 

  9. Lin, L., Yuan, X.H., Xia, Z.Q.: Multicriteria fuzzy decision-making methods based on intuitionistic fuzzy sets. J. Comput. Syst. Sci. 73, 84–88 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  10. Mukherjee, A., Das, A.K.: Intuitionistic fuzzy rough relations. Ann. Fuzzy Math. Inf. 6, 115–126 (2013)

    MathSciNet  MATH  Google Scholar 

  11. Nanda, S., Majumdar, S.: Fuzzy rough sets. Fuzzy Sets Syst. 45, 157–160 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  12. Pawlak, Z.: Rough sets. Int. J. Comput. Inform. Sci. 11, 341–356 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  14. Zadeh, L.A.: Similarity relations and fuzzy orderings. Inf. Sci. 3, 177–200 (1971)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors are very grateful and wish to thank the referees for their valuable comments as well as helpful suggestions in improving this research paper significantly.

Author information

Authors and Affiliations

  1. Department of Mathematics, ICV College, Belonia, 799155, Tripura, India

    Ajoy Kanti Das

Authors
  1. Ajoy Kanti Das
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ajoy Kanti Das.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Das, A.K. On partially included intuitionistic fuzzy rough relations. Afr. Mat. 27, 993–1001 (2016). https://doi.org/10.1007/s13370-016-0395-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13370-016-0395-2

Keywords

Mathematics Subject Classification

Search

Navigation