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Similarity and Compatibility in Fuzzy Set Theory

Assessment and Applications

  • Book
  • © 2002

Overview

Authors:
  1. Valerie V. Cross

    1. Department of Computer Science and Engineering, University of South Carolina, Columbia, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Thomas A. Sudkamp

    1. Department of Computer Science, Wright State University, Dayton, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Overview of the fundamental role of the assessment of similarity and compatibility
  • Unified approach to quantifying similarity and compatibility
  • Examples of application

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 93)

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Table of contents (15 chapters)

  1. Front Matter

    Pages I-XI
    Download chapter PDF

  2. Introduction

    1. Introduction

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 1-2

  3. Similarity, Compatibility, and Fuzzy Set Theory

    1. Front Matter

      Pages 3-3
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    2. The Nature of Similarity

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 5-7

    3. Historic Assessment of Compatibility

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 9-16

    4. Foundations of Fuzzy Set Theory

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 17-34

    5. Compatibility in Fuzzy Inference

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 35-44

    6. Compatibility in Approximate Reasoning

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 45-66

  4. Taxonomy of Compatibility Measures

    1. Front Matter

      Pages 67-69
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    2. Set-Theoretic Measures

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 71-96

    3. Proximity-Based Measures

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 97-132

    4. Logic-Based Measures

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 133-137

    5. Fuzzy-Valued Similarity Measures

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 139-142

  5. Empirical Analysis of Compatibility Measures

    1. Front Matter

      Pages 143-145
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    2. Generic Classification Domain

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 147-151

    3. Set-Theoretic Comparative Study

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 153-166

    4. Proximity-Based Comparative Study

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 167-176

    5. Logic-Based Comparative Study

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 177-181

    6. Comparison Among the Three Classes

      • Valerie V. Cross, Thomas A. Sudkamp
      Pages 183-187

  6. Back Matter

    Pages 189-209
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Keywords

About this book

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.

Reviews

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)

Authors and Affiliations

  • Department of Computer Science and Engineering, University of South Carolina, Columbia, USA

    Valerie V. Cross

  • Department of Computer Science, Wright State University, Dayton, USA

    Thomas A. Sudkamp

Bibliographic Information

  • Book Title: Similarity and Compatibility in Fuzzy Set Theory

  • Book Subtitle: Assessment and Applications

  • Authors: Valerie V. Cross, Thomas A. Sudkamp

  • Series Title: Studies in Fuzziness and Soft Computing

  • DOI: https://doi.org/10.1007/978-3-7908-1793-5

  • Publisher: Physica Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2002

  • Hardcover ISBN: 978-3-7908-1458-3Published: 26 February 2002

  • Softcover ISBN: 978-3-7908-2507-7Published: 21 October 2010

  • eBook ISBN: 978-3-7908-1793-5Published: 05 June 2013

  • Series ISSN: 1434-9922

  • Series E-ISSN: 1860-0808

  • Edition Number: 1

  • Number of Pages: XI, 209

  • Topics: Discrete Mathematics, Artificial Intelligence, Data Structures and Information Theory

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