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On Intuitionistic Fuzzy Sets Theory

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On Intuitionistic Fuzzy Sets Theory is a monograph by Krassimir T. Atanassov, published in 2012 as Vol. 283 of the Studies in Fuzziness and Soft Computing Series, Springer, ISSN: 1434-9922, ISBN: 978-3-642-29126-5.

Book review

This book aims to be a comprehensive and accurate survey of state-of-art research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author´s previous book on Intuitionistic Fuzzy Sets, published by Springer in 1999 (Atanassov, Krassimir T., Intuitionistic Fuzzy Sets, Studies in Fuzziness and soft computing, ISBN 978-3-7908-1228-2, 1999). Since the aforementioned book has appeared, the research activity of the author within the area of intuitionistic fuzzy sets has been expanding into many directions. The results of the author´s most recent work covering the past 12 years as well as the newest general ideas and open problems in this field have been therefore collected in this new book.

“The volume is a comprehensive, carefully organized, in-depth treatise on intuitionistic fuzzy sets … . The material structured into 11 chapters is split into several main parts. The concepts of intuitionistic fuzzy sets (IFS) are motivated through a series of illustrative examples including those showing their geometric interpretations. … The exposure of the formal material is good with well thought-out arguments and a wealth of illustrative material. Overall, the book provides a very good reading for those interested in IFS.” (Witold Pedrycz, Zentralblatt MATH, Vol. 1247, 2012)


  1. On the Concept of Intuitionistic Fuzzy Sets
  2. Operations and Relations over IFSs
  3. Geometrical Interpretations of IFSs
  4. Modal and Topological Operators Defined over IFSs
  5. Extended Modal Operators
  6. Other Types of Operators
  7. Norms and Metrics over IFSs or Their Elements
  8. Intuitionistic Fuzzy Relations (IFRs)
  9. New Intuitionistic Fuzzy Operations
  10. On Two New Extensions of Intuitionistic Fuzzy Sets
  11. Concluding Remarks

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