Interval-Valued Intuitionistic Fuzzy Sets

1. Front Matter

   Pages i-xi

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2. On Brouwer’s Intuitionism and Intuitionistic Fuzziness

   • Krassimir T. Atanassov

   Pages 1-7

3. On Interval Valued Intuitionistic Fuzzy Sets

   • Krassimir T. Atanassov

   Pages 9-25

4. Relations and Operations over IVIFSs

   • Krassimir T. Atanassov

   Pages 27-51

5. Operators over IVIFSs

   • Krassimir T. Atanassov

   Pages 53-122

6. Interval Valued Intuitionistic Fuzzy Pairs

   • Krassimir T. Atanassov

   Pages 123-129

7. Applications of IVIFSs

   • Krassimir T. Atanassov

   Pages 131-194

8. Conclusion and Remarks on Future Research

   • Krassimir T. Atanassov

   Pages 195-197

9. Back Matter

   Pages 199-200

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The book offers a comprehensive survey of interval-valued intuitionistic fuzzy sets. It reports on cutting-edge research carried out by the founder of the intuitionistic fuzzy sets, Prof. Krassimir Atanassov, giving a special emphasis to the practical applications of this extension. A few interesting case studies, such as in the area of data mining, decision making and pattern recognition, among others, are discussed in detail.


The book offers the first comprehensive guide on interval-valued intuitionistic fuzzy sets. By providing the readers with a thorough survey and important practical details, it is expected to support them in carrying out applied research and to encourage them to test the theory behind the sets for new advanced applications. The book is a valuable reference resource for graduate students and researchers alike.

• Intuitionistic Fuzzy Sets
• Intuitionistic Fuzzy Logic
• Interval Valued Intuitionistic Fuzzy Sets
• Interval Valued Intuitionistic Fuzzy Logic
• Interval Valued Intuitionistic Fuzzy Modal Operators
• Interval Valued Intuitionistic Fuzzy Graphs
• Interval Data
• Applications of Interval-valued Intuitionistic Fuzzy Sets
• Knowledge Discovery from Data
• Intuitionistic Fuzzy Inductive Reasoning
• Intercriteria Decision Making
• Intuitionistic Fuzzy Expert Systems
• Index Matrices

• Department of Bioinformatics and Mathematical Modelling, Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences, Sofia, Bulgaria

  Krassimir T. Atanassov

Krassimir Atanassov is a Professor and the Head of the Department of “Bioinformatics and Mathematical Modelling” at the Bulgarian Academy of Sciences. In 2013 he received the Award “Pythagoras” from the Ministry of Education, Youth and Science of Bulgaria, as an established researcher in the area of Technical sciences. Since the same year, he has also been fellow of the International Fuzzy Systems Association. His research interests cover the areas of Petri Nets, Fuzzy Sets and Number Theory. In the field of fuzzy sets, he developed the theory of intuitionistic fuzzy sets and showed their applications to artificial intelligence, systems theory, medicine, etc.


He has been serving as E-i-C of different journals. He is the author of numerous monographs, including the book Intuitionistic Fuzzy Logics (Springer, 2017).

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