Intuitionistic Fuzzy Measures: Theory and Applications

Cover of the book

"Intuitionistic Fuzzy Measures: Theory and Applications" is the title of a book by Adrian Ban, published by Nova Science Publishers in 2006 under ISBN 1-59454-911-7.

The book is the outcome of about eight years of work performed by the author largely in the field of intuitionistic fuzzy set theory and more in depth on intuitionistic fuzzy measures presented from a point of view characteristic for pure mathematics. The purpose of the book is to present a continuation of studies conducted focusing mainly on measures that evaluate intuitionistic fuzzy sets by real values and crisp sets by intuitionistic fuzzy values.

Table of Contents

Preface

General Description of the Topic

CHAPTER 1. Intuitionistic Fuzzy Sets — pp, 1-57

• 1.1 Triangular Norms And Conorms
• 1.2 Intuitionistic Fuzzy Triangular Norms And Conorms
• 1.3 Operations, Operators And Relations On Intuitionistic Fuzzy Sets
• 1.4 Disjointness Of Intuitionistic Fuzzy Sets
• 1.5 Partitions Of Intuitionistic Fuzzy Sets
• 1.6 Discrete Intuitinistic Fuzzy Sets
• 1.7 Aproximation Of Intuitionistic Fuzzy Sets By Discrete Intuitionistic Fuzzy Sets
• 1.8 Bibliographical Remarks And Open Problems

CHAPTER 2. Measures on Intuitionistic Fuzzy Sets — pp, 59-165

• 2.1 Classes Of Intuitionistic Fuzzy Sets
• 2.2 Intuitionistic Fyzzy Set Functions
• 2.3 Variations Of Intuitionistic Fyzzy Set Functions
• 2.4 Measurable Functions
• 2.5 Fuzzy Measures On Intuitionistic Fuzzy Sets
• 2.6 Construction Of Decomposable Fuzzy Measures On Intuitionistic Fuzzy Sets
• 2.7 Intuitionistic Fuzzy Triangular Norm-Base Measures On Intuitionistic Fuzzy Sets
• 2.8 Other Measures On Intuitionistic Fuzzy Sets
• 2.9 Intuitionistic Fuzzy Entropies
• 2.10 Structural Characteristitics For Intuitionistic On TM-O-Algebras
• 2.11 Classical And Fuzzy Concepts Derived From Intuitionistic Fuzzy Concepts
• 2.12 Fuzzy Integrals On Intuitionistic Fuzzy Sets
• 2.13 Bibliographical Remarks And Open Ploblems

CHAPTER 3. Intuitionistic Fuzzy-Valued Measures and Integrals — pp, 167-229

• 3.1 Intuitionistic Fuzzy-Valued Fuzzy Measures: Definition And Construction
• 3.2 Properties Of Continuity And Duality Of The Intuiionistic Fuzzy-Valued Fuzzy-Measures
• 3.3 Structural Characteristic Of Intuitionistic Fuzzy-Valued Fuzzy Measures
• 3.4 Decomposable Intuitionistic Fuzzy-Valued Fuzzy Measures
• 3.5 A-Additive Intuitionistis Fuzy-Valued Fuzzy Measures
• 3.6 Quasi-Measures And Quasi-Fuzzy Measures
• 3.7 Intuitionistic Fuzzy- Valued Possibility And Necessity Measures
• 3.8 Measurable Funtions On Intuitionistic Fuzzy-Valued Measures Spaces
• 3.9 Sugeno Integral With Respect To Intuitionistic Fuzzy-Valued Fuzzy Measures
• 3.10 Set Fuctions Defined By Integrals With Respect To Intuitionistic Fuzzy-Valued Fuzzy Measures
• 3.11 Bibliographical Remarks And Open Problems

CHAPTER 4. Applications — pp, 231-249

• 4.1 Compositive Intuitionistic Fuzzy Information Measures
• 4.2 Measurable Entropy Intuitionistic Fuzzy Dinamical Systems
• 4.3 Synthetic Evaluation Of Objests
• 4.4 A Practical Interpretation Of Intuitionistic Fuzzy-Valued Fuzzy Measures And Integrals
• 4.5 Decision-Marking With Sugeno Integral With Respect To An Intuitionistic Fuzzy-Valued Fuzzy Measures
• 4.6 Intuitionistic Fuzzy Possibility And Necesary To Documentary Information Retrieval
• 4.7 Bibliographical Remarks And Open Problems

References

Index

See also

• Presentation of the book on the publisher website