Intuitionistic Fuzzy Sets Theory and Applications

In the beginning of 1983, I came across A. Kaufmann's book "Introduction to the theory of fuzzy sets" (Academic Press, New York, 1975). This was my first acquaintance with the fuzzy set theory. Then I tried to introduce a new component (which determines t

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Studies in Fuzziness and Soft Computing Editor-in-chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw, Poland E-mail: [email protected] Vol. 3. A. Geyer-Schulz Fuzzy Rule-Based Expert Systems and Genetic Machine Learning. 2nd ed. 1996 ISBN 3-7908-0964-0

Vol. 14. E. Hisdal Logical Structures for Representation of Knowledge and Uncertainty, 1998 ISBN 3-7908-1056-8

Vol. 4. T. Onisawa and J. Kacprzyk (Eds.) Reliability and Safety Analyses under Fuzziness. 1995 ISBN 3-7908-0837-7

Vol. 15. G.J. K1ir and M.J. Wiennan Uncertainty-Based Information, 1998 ISBN 3-7908-1073-8

Vol. 5. P. Bosc and J. Kacprzyk (Eds.) Fuzziness in Database Management Systems. 1995 ISBN 3-7908-0858-X Vol. 6. E. S. Lee and Q. Zhu Fuzzy and Evidence Reasoning. 1995 ISBN 3-7908-0880-6

Vol. 16. D. Driankov and R. Palm (Eds.) Advances in Fuzzy Control. 1998 ISBN 3-7908-1090-8 Vol. 17. L. Reznik, V. Dimitrov and J. Kacprzyk (Eds.) Fuzzy Systems Design. 1998 ISBN 3-7908-1118-1

Vol. 7. B.A. Juliano and W. Bandler Tracing Chains-of-Thought. 1996 ISBN 3-7908-0922-5

Vol. 18. L. Polkowski and A. Skowron (Eds.) Rough Sets in Knowledge Discovery 1. 1998, ISBN 3-7908-1119-X

Vol. S. F. Herrera and J. L. Verdegay (Eds.) Genetic Algorithms and Soft Computing. 1996. ISBN 3-790S-0956-X

Vol. 19. L. Polkowski and A. Skowron (Eds.) Rough Sets in Knowledge Discovery 2. 1998. ISBN 3-7908-1120-3

Vol. 9. M. Sato et aI. Fuzzy Clustering Models and Applications. 1997, ISBN 3-7908-1026-6

Vol. 20. J. N. Mordeson and P. S. Nair Fuzzy Mathematics. 1998 ISBN 3-7908-1121-1

Vol. 10. L.C. Jain (Ed.) Soft Computing Techniques in Knowledge-based Intelligent Engineering Systems. 1997. ISBN 3-790S-1035-5 Vol. II. W. Mielczarski (Ed.) Fuzzy Logic Techniques in Power Systems. 1998, ISBN 3-7908-1044-4 Vol. 12. B. Bouchon-Meunier (Ed.) Aggregation and Fusion of Imperfect Information. 1998 ISBN 3-7908-1048-7 Vol. 13. E. Ortowska (Ed.) Incomplete Information: Rough Set Analysis. 1998 ISBN 3-7908-1049-5

Vol. 21. L. C. Jain and T. Fukuda (Eds.) Soft Computing for Intelligent Robotic Systems. 1998 ISBN 3-7908-1147-5 Vol. 22. J. Cardoso and H. Camargo (Eds.) Fuzziness in Petri Nets. 1999 ISBN 3-7908-1158-0 Vol. 23. P. S. Szczepaniak (Ed.) Computational Intelligence and Applications, 1999 ISBN 3-7908-1161-0 Vol. 24. E. Ortowska (Ed.) Logic at Work. 1999 ISBN 3-7908-1164-5 continued on page 324

Krassimir T. Atanassov

Intuitionistic Fuzzy Sets Theory and Applications

With 121 Figures

Springer-Verlag Berlin Heidelberg GmbH

Prof. Krassimir T. Atanassov Centre of Biomedical Engineering Bulgarian Academy of Sciences ul. Acad. G. Bonchev, Bl. 105 Sofia-lI13 Bulgaria Email: [email protected]

ISBN 978-3-7908-2463-6 Cataloging-in-Publication Data applied for Die Deutsche Bibliothek - CIP-Einheitsaufnabme Atanasov, Krassimir T.: Intuitionistic fuzzy sets: theory and applications I Krassimir T. Atanassov. (Studies in fuzziness and soft computing; Vol. 35) ISBN 978-3-7908-2463-6 ISBN 978-3-7908-1870-3 (eBook) DOI 10.1007/978-