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
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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.
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.
Atanassov, K. Generalized nets and their fuzzings, AMSE Review, Vol. 2 (1985), No. 3, 39–49.
Atanassov, K. Review and new results on intuitionistic fuzzy sets. Preprint IM-MFAIS-1-88, Sofia, 1988.
Atanassov, K. Temporal intuitionistic fuzzy sets. Comptes Rendus de l’Academie bulgare des Sciences, Tome 44, 1991, No. 7, 5–7.
Atanassov, K. Intuitionistic Fuzzy Sets, Springer Physica-Verlag, Berlin, 1999.
Atanassov, K. On four intuitionistic fuzzy topological operators. Mathware & Soft Computing, Vol. 8, 2001, 65–70.
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.
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.
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.
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.
Atanassov, K. On some types of intuitionistic fuzzy negations. Notes on Intuitionistic Fuzzy Sets, Vol. 11, 2005, No. 4, 170–172.
Atanassov, K. On some intuitionistic fuzzy negations. Notes on Intuitionistic Fuzzy Sets, Vol. 11, 2005, No. 6, 13–20.
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).
Atanassov, K. On intuitionistic fuzzy negations and De Morgan’s laws. accepted for IPMU’2006, Paris, 2006.
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.
Atanassov, K., G. Gargov. Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 31, 1989, No. 3, 343–349.
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.
Atanassov, K., V. Kreinovich. Intuitionistic fuzzy interpretation of intetrval data, Notes on Intuitionistic Fuzzy Sets, Vol. 5 (1999), No. 1, 1–8.
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.
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.
Buhaescu, T. On the convexity of intuitionistic fuzzy sets, Itinerant Seminar of functional equations, approximation and convexity, Cluj-Napoca, 1988, 137–143.
Bustince, H., P. Burillo. Vague sets are intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol. 79, 1996, No. 3, 403–405.
čoker, D. Fuzzy rough sets are intuitionistic L-fuzzy sets, Fuzzy Sets and Systems, Vol. 96, 1998, No. 3, 381–383.
Cornelis, C. Tweezijdigheid in de Representatie en Verwerking van Imprecieze Informatie. Universiteit Gent, Faculteit Wetenschappen, 2004.
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.
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.
Dubois, D., H. Prade. Fuzzy Sets and Systems: Theory and Applications, Acad. Press, New York, 1980.
Gehrke, M. C. Walker, E. Walker. Some comments on interval-valued fuzzy sets. International Journal of Intelligent Systems, Vol. 11 (1996), 751–5759.
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.
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.
Heyting, A. Intuitionism. An Introduction. North-Holland, Amsterdam, 1956.
Kaufmann, A. Introduction a la thèorie des sous-ensembles flous. Masson, Paris, 1977.
Kondakov, N. Logical Dictionary., Moskow, Nauka, 1971 (in Russian).
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.
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.
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.
Maji, P.K., R. Biswas, A.R. Roy Intuitionistic fuzzy soft sets. The Journal of Fuzzy Mathematics, Vol. 9, 2001, No. 3, 677–692.
J.M. Mendel, Robert I. Bob John, “Type-2 fuzzy sets made simple”, IEEE Transactions on Fuzzy Systems, 10(2) (2002), 117–127.
J.M. Mendel, “Advances in type-2 fuzzy sets and systems”. Information Sciences, In Press, Available online 21 June 2006.
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.
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.
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.
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.
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.
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.
E. Szmidt. “Applications of Intuitionistic Fuzzy Sets in Decision Making”, D. Sc. dissertation Techn. Univ., Sofia, (2000).
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).
Wang, G., He Y. Intuitionistic fuzzy sets and L-fuzzy sets, Fuzzy Sets and Systems, Vol. 110 (2000), No. 2, 271–274.
Zadeh, L. The Concept of a Linguistic Variable and its Application to Approximate Reasoning. American Elsevier Publ. Co., New York, 1973.
Editor information
Editors and Affiliations
Rights 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)