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International Conference on Rough Sets and Knowledge Technology

RSKT 2009: Rough Sets and Knowledge Technology pp 281–288Cite as

Closures of Intuitionistic Fuzzy Relations

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5589))

Abstract

The intuitionistic fuzzy set (IF set) theory, originated by Atanassov in 1986, has been used in a wide range of applications. In this paper we develop the concept of IF relation, and we discuss a variety of different properties that an IF relation may possess. Finally, we give Warshall’s algorithm for computing the transitive closure of an IF relation.

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References

  1. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets and Systems 20, 87–96 (1986)

    Article  MATH  Google Scholar 

  2. Atanassov, K.: More on intuitionistic fuzzy sets. Fuzzy Sets and Systems 33, 37–45 (1989)

    Article  MATH  Google Scholar 

  3. Atanassov, K.: New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems 61, 131–142 (1994)

    Article  MATH  Google Scholar 

  4. Atanassov, K.: Intuitionistic fuzzy logic: Theory and Application. Physica-Verlag, Heidelberg (1999)

    Book  MATH  Google Scholar 

  5. Baets, B.D., Meyer, H.D.: On the existence and construction of Ttransitive closures. Information Sciences 152, 167–179 (2003)

    Article  MATH  Google Scholar 

  6. Bandler, W., Kohout, L.: Special properties, closures and interiors of crisp and fuzzy relations. Fuzzy Sets and Systems 26, 317–331 (1988)

    Article  MATH  Google Scholar 

  7. Bustince, H., Burillo, P.: Structures on intuitionistic fuzzy relations. Fuzzy Sets and Systems 78, 293–303 (1996)

    Article  MATH  Google Scholar 

  8. Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems 79, 403–405 (1996)

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  10. De, S.K., Biswas, R., Roy, A.R.: An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems 117, 209–213 (2001)

    Article  MATH  Google Scholar 

  11. Grassmann, W.K., Tremblay, J.P.: Logic and discrete mathematics. A computer Science Perspective. Prentice-Hall, Englewood Cliffs (1996)

    Google Scholar 

  12. Liu, G.L.: The transitive closures of matrices over distributive lattices. In: The Proceedings of the IEEE International Conference on Granular Computing, pp. 63–66 (2006)

    Google Scholar 

  13. Naessens, H., Meyer, H.D., Baets, B.D.: Algorithms for the computation of T-transitive closures. IEEE Transactions on fuzzy system 10, 541–551 (2002)

    Article  Google Scholar 

  14. Pawlak, Z.: Rough sets. International Journal of Computer and Information Sciences 11, 341–356 (1982)

    Article  MATH  Google Scholar 

  15. Zadeh, L.A.: Fuzzy sets. Information and Control 8, 338–353 (1965)

    Article  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. School of Information Science, Beijing Language and Culture University, Beijing, 100083, China

    Guilong Liu

Authors
  1. Guilong Liu
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Editor information

Editors and Affiliations

  1. Faculty of Engineering and Surveying and Engineering, University of Southern Queensland, QLD 4350, Australia

    Peng Wen

  2. School of Information Technology, Queensland University of Technology, QLD 4001, Brisbane, Australia

    Yuefeng Li

  3. Institute of Mathematics, Warsaw University of Technology, Koszykowa 86, 02008, Warsaw, Poland

    Lech Polkowski

  4. Department of Computer Science, University of Regina, S4S 0A2, Regina, Saskatchewan, Canada

    Yiyu Yao

  5. Faculty of Medicine, Department of Medical Informatics, Shimane University, 89-1 Enya-cho, Izumo, 693-8501, Shimane, Japan

    Shusaku Tsumoto

  6. Institute of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing, China

    Guoyin Wang

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© 2009 Springer-Verlag Berlin Heidelberg

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Liu, G. (2009). Closures of Intuitionistic Fuzzy Relations. In: Wen, P., Li, Y., Polkowski, L., Yao, Y., Tsumoto, S., Wang, G. (eds) Rough Sets and Knowledge Technology. RSKT 2009. Lecture Notes in Computer Science(), vol 5589. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02962-2_35

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  • DOI: https://doi.org/10.1007/978-3-642-02962-2_35

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-02961-5

  • Online ISBN: 978-3-642-02962-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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