Skip to main content

My Personal View on Intuitionistic Fuzzy Sets Theory

  • Chapter

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 220))

Abstract

In this chapter, some remarks are given on the history, theory, applications and research on the extension of fuzzy sets model proposed by the author in 1983.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arieli, O., C. Cornelis, G. Deschrijver, E. Kerre, Relating intuitionistic fuzzy sets and interval-valued sets through bilattices. Proceedings of the 6th International FLINS Conference Applied Computational Intelligence, Blankenberge, 1–3 Sept. 2004, 57–64.

    Google Scholar 

  2. Asparoukhov, O., K. Atanassov, Intuitionistic fuzzy interpretation of confidencial intervals of criteria for decision making, Proc. of the First Workshop on Fuzzy Based Expert Systems (D. Lakov, Ed.), Sofia, Sept. 28–30, 1994, 56–58.

    Google Scholar 

  3. Atanassov, K. Generalized nets and their fuzzings, AMSE Review, Vol. 2 (1985), No. 3, 39–49.

    Google Scholar 

  4. Atanassov, K. Review and new results on intuitionistic fuzzy sets. Preprint IM-MFAIS-1-88, Sofia, 1988.

    Google Scholar 

  5. Atanassov, K. Temporal intuitionistic fuzzy sets. Comptes Rendus de l’Academie bulgare des Sciences, Tome 44, 1991, No. 7, 5–7.

    MATH  MathSciNet  Google Scholar 

  6. Atanassov, K. Intuitionistic Fuzzy Sets, Springer Physica-Verlag, Berlin, 1999.

    MATH  Google Scholar 

  7. Atanassov, K. On four intuitionistic fuzzy topological operators. Mathware & Soft Computing, Vol. 8, 2001, 65–70.

    Google Scholar 

  8. Atanassov, K. Open problems in intuitionistic fuzzy sets theory. Proceedings of 6-th Joint Conf. on Information Sciences, Research Triangle Park (North Carolina, USA), March 8-13, 2002, 113–116.

    Google Scholar 

  9. Atanassov, K. “Twenty years later" or some words about the intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, Vol. 9 (2003), No. 3, 1–3.

    Google Scholar 

  10. Atanassov, K. Intuitionistic fuzzy sets: past, present and future. Proc. of the Third Conf. of the European Society for Fuzzy Logic and Technology EUSFLAT’ 2003, Zittau, 10-12 Sept. 2003, 12–19.

    Google Scholar 

  11. Atanassov, K. Remarks on Intuitionistic fuzzy set theory. Soft Computing Foundations and Theoretical Aspects (K. Atanassov, O. Hryniewicz, J. Kacprzyk, Eds.), Academicka Oficyna Wydawnicza EXIT, Warszawa, 2004, 1–17.

    Google Scholar 

  12. Atanassov, K. On some types of intuitionistic fuzzy negations. Notes on Intuitionistic Fuzzy Sets, Vol. 11, 2005, No. 4, 170–172.

    Google Scholar 

  13. Atanassov, K. On some intuitionistic fuzzy negations. Notes on Intuitionistic Fuzzy Sets, Vol. 11, 2005, No. 6, 13–20.

    Google Scholar 

  14. Atanassov, K. On the implications and negations over intuitionistic fuzzy sets. Proceedings of the Free University of Burgas Conference, 9–11 June 2006 (in press).

    Google Scholar 

  15. Atanassov, K. On intuitionistic fuzzy negations and De Morgan’s laws. accepted for IPMU’2006, Paris, 2006.

    Google Scholar 

  16. Atanassov, K., A. Ban. On an operator over intuitionistic fuzzy sets. Comptes Rendus de l’Academie bulgare des Sciences, Tome 53, 2000, No. 5, 39–42.

    Google Scholar 

  17. Atanassov, K., G. Gargov. Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 31, 1989, No. 3, 343–349.

    Article  MATH  MathSciNet  Google Scholar 

  18. Atanassov, K., J. Kacprzyk, E. Szmidt, L. Todorova. On separability of intuitionistic fuzzy sets. Proc. of the 10-th Int. Fuzzy Systems Assoc. World Congress, Istanbul, June 30 - July 2, 2003, In:- Lecture Notes in Artificial Intelligence, Vol. 2715: Fuzzy Sets and Systems - IFSA 2003, Springer, Berlin, 2003, 285–292.

    Google Scholar 

  19. Atanassov, K., V. Kreinovich. Intuitionistic fuzzy interpretation of intetrval data, Notes on Intuitionistic Fuzzy Sets, Vol. 5 (1999), No. 1, 1–8.

    MATH  MathSciNet  Google Scholar 

  20. Atanassov, K., G. Pasi and R. Yager. Intuitionistic fuzzy interpretations of multi-criteria multi-person and multi-measurement tool decision making. International Journal of Systems Research, Vol. 36, 2005, No. 14, 859–868.

    Article  MathSciNet  Google Scholar 

  21. Atanassova, V. Strategies for decision making in the conditions of intuitionistic fuzziness. In: - Computational Intelligence, Theory and Applications (B. Reusch, Ed.), Springer, Berlin, 2005, 263–269.

    Google Scholar 

  22. Buhaescu, T. On the convexity of intuitionistic fuzzy sets, Itinerant Seminar of functional equations, approximation and convexity, Cluj-Napoca, 1988, 137–143.

    Google Scholar 

  23. Bustince, H., P. Burillo. Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 79, 1996, No. 3, 403–405.

    Article  MATH  MathSciNet  Google Scholar 

  24. čoker, D. Fuzzy rough sets are intuitionistic L-fuzzy sets, Fuzzy Sets and Systems, Vol. 96, 1998, No. 3, 381–383.

    Article  MathSciNet  Google Scholar 

  25. Cornelis, C. Tweezijdigheid in de Representatie en Verwerking van Imprecieze Informatie. Universiteit Gent, Faculteit Wetenschappen, 2004.

    Google Scholar 

  26. Deschrijver, G., E. Kerre. On the relationship between some extensions of fuzzy set theory. Fuzzy Sets and Systems, Vol. 133 (2003), No. 2, 227–235.

    Article  MATH  MathSciNet  Google Scholar 

  27. Cornelis C., M. De Cock, E. Kerre Intuitionistic fuzzy rough sets: at the crossroads of imperfect knowledge. Expert Systems, Vol. 20 (5) (2003), No. 2, 260–270.

    Google Scholar 

  28. Dubois, D., H. Prade. Fuzzy Sets and Systems: Theory and Applications, Acad. Press, New York, 1980.

    MATH  Google Scholar 

  29. Gehrke, M. C. Walker, E. Walker. Some comments on interval-valued fuzzy sets. International Journal of Intelligent Systems, Vol. 11 (1996), 751–5759.

    Article  MATH  Google Scholar 

  30. Georgiev, K. A simplification of the Neutrosophic Sets. Neutrosophic Logic and Intuitionistic Fuzzy Sets. Notes on Intuitionistic Fuzzy Sets, Vol. 11 (2005), 2, 28–31.

    Google Scholar 

  31. D. Gomez, J. Montero, H. Bustince “Sobre los conjuntos intuicionistas fuzzy de Atanassov”, XIII Congreso Español sobre Tecnologías y Lógica Fuzzy, ESTYLF’06 (In Spanish), Ciudad Real (Spain), September 2006.

    Google Scholar 

  32. Heyting, A. Intuitionism. An Introduction. North-Holland, Amsterdam, 1956.

    MATH  Google Scholar 

  33. Kaufmann, A. Introduction a la thèorie des sous-ensembles flous. Masson, Paris, 1977.

    Google Scholar 

  34. Kondakov, N. Logical Dictionary., Moskow, Nauka, 1971 (in Russian).

    Google Scholar 

  35. Koshelev, M., V. Kreinovich, B. Rachamreddy, H. Yasemis, K. Atanassov, Fundamental justification of intuitionistic fuzzy logic and interval-valued fuzzy methods. Proceedings of the Second International Conference on Intuitionistic Fuzzy Sets (J. Kacprzyk and K. Atanassov, Eds.), Vol. 1; Notes on Intuitionistic Fuzzy Sets, Vol. 4 (1998), No. 2, 42–46.

    Google Scholar 

  36. Kreinovich, V., M. Mukaidono, K. Atanassov. From fuzzy values to intuitionistic fuzzy values, to intuitionistic fuzzy intervals etc.: can we get an arbitrary ordering? Proceedings of the Third International Conference on Intuitionistic Fuzzy Sets (J. Kacprzyk and K. Atanassov, Eds.), Vol. 1; Notes on Intuitionistic Fuzzy Sets, Vol. 5 (1999), No. 3, 11–18.

    Google Scholar 

  37. Kreinovich, V., H. Nguyen, B. Wu, K. Atanassov, Fuzzy justification of heuristic methods in inverse problems and in numerical computations, with applications to detection of business cycles from fuzzy and intuitionistic fuzzy data. Proceedings of the Second International Conference on Intuitionistic Fuzzy Sets (J. Kacprzyk and K. Atanassov, Eds.), Vol. 2; Notes on Intuitionistic Fuzzy Sets, Vol. 4 (1998), No. 2, 47–56.

    Google Scholar 

  38. Maji, P.K., R. Biswas, A.R. Roy Intuitionistic fuzzy soft sets. The Journal of Fuzzy Mathematics, Vol. 9, 2001, No. 3, 677–692.

    MATH  MathSciNet  Google Scholar 

  39. J.M. Mendel, Robert I. Bob John, “Type-2 fuzzy sets made simple”, IEEE Transactions on Fuzzy Systems, 10(2) (2002), 117–127.

    Article  Google Scholar 

  40. J.M. Mendel, “Advances in type-2 fuzzy sets and systems”. Information Sciences, In Press, Available online 21 June 2006.

    Google Scholar 

  41. Nikolova, M., N. Nikolov, C. Cornelis, G. Deschrijver. Survey of the research on intuitionistic fuzzy sets. Advanced Studies in Contemporary Mathematics, Vol. 4, 2002, No. 2, 127–157.

    MATH  MathSciNet  Google Scholar 

  42. Pankowska, A., M. Wygdalak. Intuitionistic fuzzy sets - an alternative look. Proc. of the Third Conf. of the European Society for Fuzzy Logic and Technology EUSFLAT’ 2003, Zittau, 10–12 Sept. 2003, 135–140.

    Google Scholar 

  43. Rizvi, S., H.J. Naqvi, D. Nadeem. Rough intuitionistic fuzzy sets. Proceedings of 6-th Joint Conf. on Information Sciences, Research Triangle Park (North Carolina, USA), March 8-13, 2002, 101–104.

    Google Scholar 

  44. Rocha, L. M., V. Kreinovich, R. Baker Kearfott. Computing uncertainty in interval based sets, In: Applications of Interval Computations (R. Baker Kearfott and V. Kreinovich, Eds.), Kluwer Academic Publishers, Dordrecht, 1996, 337–380.

    Google Scholar 

  45. Samanta, S.K., T.K. Mondal. Intuitionistic fuzzy rough sets and rough intuitionistic fuzzy sets. The Journal of Fuzzy Mathematics, Vol. 9, 2001, No. 3, 561–582.

    MATH  MathSciNet  Google Scholar 

  46. Smarandache, F. Neutrosophic set - a generalization of the intuitionistic fuzzy set. International Journal of Pure and Applied Mathematics, Vol. 24, No. 3, 2005, 287–297.

    MATH  MathSciNet  Google Scholar 

  47. E. Szmidt. “Applications of Intuitionistic Fuzzy Sets in Decision Making”, D. Sc. dissertation Techn. Univ., Sofia, (2000).

    Google Scholar 

  48. I.K. Vlachos, G.D. Sergiadis “Inner product based entropy in the intuitionistic fuzzy setting”, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 14 (3), 351–367 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  49. Wang, G., He Y. Intuitionistic fuzzy sets and L-fuzzy sets, Fuzzy Sets and Systems, Vol. 110 (2000), No. 2, 271–274.

    Article  MATH  MathSciNet  Google Scholar 

  50. Zadeh, L. The Concept of a Linguistic Variable and its Application to Approximate Reasoning. American Elsevier Publ. Co., New York, 1973.

    Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Atanassov, K.T. (2008). My Personal View on Intuitionistic Fuzzy Sets Theory. In: Bustince, H., Herrera, F., Montero, J. (eds) Fuzzy Sets and Their Extensions: Representation, Aggregation and Models. Studies in Fuzziness and Soft Computing, vol 220. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73723-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-73723-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73722-3

  • Online ISBN: 978-3-540-73723-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics