Intuitionistic Fuzzy Sets: Theory and Applications

"Intuitionistic Fuzzy Sets", subtitle: "Theory and Applications" is the title of a book by Krassimir Atanassov, published in Springer Physica-Verlag Publishing house in November 1999 under ISBN 3-7908-1228-5. It is featured in the series "Studies in Fuzziness and Soft Computing" under Volume 35.

The book introduces the basic definitions and properties of the intuitionistic fuzzy sets, which are substantial extensions of the ordinary fuzzy sets. The most important property of IFS not shared by the fuzzy sets is that modal operators can be defined over IFSs. The IFSs have essentially higher describing possibilities than fuzzy sets. The book discusses some of the IFS extensions (for example, interval-valued IFSs, temporal IFSs and others) and applications (e.g. intuitionistic fuzzy expert systems, intuitionistic fuzzy neural networks, intuitionistic fuzzy systems, intuitionistic fuzzy generalized nets, and other).

Table of Contents

Cover of the book

Foreword

Achnowledgments

Intuitionistic Fuzzy Sets: Past and Present

1. Intuitionistic Fuzzy Sets
   1. Definition of the Concept of an Intuitionistic Fuzzy Set - An Example
   2. Operations and Relations over Intuitionistic Fuzzy Sets. Properties
   3. Intuitionistic Fuzzy Sets of a Certain Level
   4. Cartesian Products over Intuitionistic Fuzzy Sets. Intuitionistic Fuzzy Relations
   5. "Necessity" and "Possibility" Operators on Intuitionistic Fuzzy Sets
   6. Topological Operators over Intuitionistic Fuzzy Sets
   7. Operators [math]\displaystyle{ D_{\alpha} }[/math] and [math]\displaystyle{ F_{\alpha, \beta} }[/math]
   8. Operator [math]\displaystyle{ G_{\alpha, \beta} }[/math]
   9. Operators [math]\displaystyle{ H_{\alpha, \beta} }[/math], [math]\displaystyle{ H^{*}_{\alpha, \beta} }[/math], [math]\displaystyle{ J_{\alpha, \beta} }[/math] and [math]\displaystyle{ J^{*}_{\alpha, \beta} }[/math]
   10. Relations between Operators Defined over Intuitionistic Fuzzy Sets
   11. Operator [math]\displaystyle{ X_{a,b,c,d,e,f} }[/math]
   12. Identifying and Unary Operators
   13. Level and Other Types of Operators
   14. Norms and Metrics over Intuitionistic Fuzzy Sets or Their Elements
   15. Intuitionistic Fuzzy Set Whose Universe is an Intuitionistic Fuzzy Set with Respect to Another Universe
2. Interval Valued Intuitionistic Fuzzy Sets
   1. Intuitionistic Fuzzy Sets and Interval Valued Fuzzy Sets
   2. Interval Valued Intuitionistic Fuzzy Sets: A Definition, Operrations and Relations on Them
   3. Operators over Interval Valued Intuitionistic Fuzzy Sets
   4. Norms and Metrics on Interval Valued Intuitionistic Fuzzy Sets
3. Other Extensions of Intuitionistic Fuzzy Sets
   1. Intuitionistic L- Fuzzy Sets
   2. Intuitionistic Fuzzy Sets over Different Universes
   3. Temporal Intuitionistic Fuzzy Sets
   4. Intuitionistic Fuzzy Sets of Second Type
   5. Some Future Extensions of Intuitionistic Fuzzy Sets
4. Elements of Intuitionistic Fuzzy Logics
   1. Intuitionistic Fuzzy Propositional Calculus
   2. Intuitionistic Fuzzy Predicate Logic
   3. Intuitionistic Fuzzy Modal Logic
   4. Extensions of Intuitionistic Fuzzy Modal Types of Operators
   5. Other Intuitionistic Fuzzy Modal Types of Operators
   6. Temporal Intuitionistic Fuzzy Logic
5. Applications of Intuitionistic Fuzzy Sets
   1. Intuitionistic Fuzzy Generalized Nets - Sample Applications
      1. Application of IFGN2 for the Modelling of Processes in a Petrochemical Firm
      2. Application ofIFGN2 for the Modelling of a Pneumatic Transportation Process
   2. Some Applications of Intuitionistic Fuzzy Generalized Nets in Medicine
   3. Intuitionistic Fuzzy Expert Systems and Intuitionistic Fuzzy Estimations of Expert Knowledge
   4. Intuitionistic Fuzzy Models of Neural Networks
   5. Intuitionistic Fuzzy Systems
   6. Intuitionistic Fuzzy Interpretation of Interval Data
   7. An Intuitionistic Fuzzy Model of Gravitational Potential

Open Problems in Intuitionistic Fuzzy Sets Theory

References

Index

Related books

• 2012 – On Intuitionistic Fuzzy Sets Theory, Krassimir Atanassov
• 2017 – Intuitionistic Fuzzy Logics, Krassimir Atanassov

See also

• Errata in "Intuitionistic Fuzzy Sets: Theory and Applications"
• Presentation on Springer website