Similarity and Compatibility in Fuzzy Set Theory

Assessment and Applications

Valerie V. Cross, Thomas A. Sudkamp (Autoren)

Buch | Softcover

XI, 209 Seiten

2010
Physica (Verlag)
978-3-7908-2507-7 (ISBN)

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Assessing the degree to which two objects, an object and a query, or two concepts are similar or compatible is a fundamental component of human reasoning and consequently is critical in the development of automated diagnosis, classification, information retrieval and decision systems. The assessment of similarity has played an important role in such diverse disciplines such as taxonomy, psychology, and the social sciences. Each discipline has proposed methods for quantifying similarity judgments suitable for its particular applications. This book presents a unified approach to quantifying similarity and compatibility within the framework of fuzzy set theory and examines the primary importance of these concepts in approximate reasoning. Examples of the application of similarity measures in various areas including expert systems, information retrieval, and intelligent database systems are provided.

1. Introduction.- 2. The Nature of Similarity.- 3. Historic Assessment of Compatibility.- 4. Foundations of Fuzzy Set Theory.- 5. Compatibility in Fuzzy Inference.- 6. Compatibility in Approximate Reasoning.- 7. Set-Theoretic Measures.- 8. Proximity-Based Measures.- 9. Logic-Based Measures.- 10. Fuzzy-Valued Similarity Measures.- 11. Generic Classification Domain.- 12. Set-Theoretic Comparative Study.- 13. Proximity-Based Comparative Study.- 14. Logic-Based Comparative Study.- 15. Comparison Among the Three Classes.- Index of Notation.- References.

From the reviews:

"The present book is a monograph devoted to exploring the fuzzy approach to modeling the similarity phenomenon. ... I think the attempt to provide a link between the earlier approaches to modeling of similarity ... and the current approaches being developed in the framework of fuzzy set theory is a very fortunate one. ... the book collects important material which was needed. I believe it will become a useful source for researchers and practitioners involved in fuzzy modeling and modeling of similarity." (Radim Belohlavek, International Journal of General Systems; Methodology, Applications, Education, Vol. 32 (6), 2003)

"This book presents various types of techniques for compatibility assessment in applications of fuzzy set theory and approximate reasoning. ... The book will be useful for researchers in the fields of pattern recognition, classification and intelligent systems." (Robert Fullér, Mathematical Reviews, 2003 b)

"This book provides a pioneering review of compatibility measures in fuzzy set theory and related areas. As a result, this book is likely to be valuable for all researchers working in this area. ... By any criterion, this book can be regarded as being successful in providing a comprehensive understanding of compatibility measures that will be worthwhile for any researcher." (Christian Setzkorn, Expert Update, Vol. 5 (3), 2002)

Erscheint lt. Verlag	21.10.2010
Reihe/Serie	Studies in Fuzziness and Soft Computing
Zusatzinfo	XI, 209 p.
Verlagsort	Heidelberg
Sprache	englisch
Maße	155 x 235 mm
Gewicht	337 g
Themenwelt	Mathematik / Informatik ► Informatik
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	Approximate Reasoning • classification • Compatibility • Expert System • fuzzy • Fuzzy Inference • Fuzzy set theory • set theory • Similarity
ISBN-10	3-7908-2507-7 / 3790825077
ISBN-13	978-3-7908-2507-7 / 9783790825077
Zustand	Neuware