Ebook: Similarity and Compatibility in Fuzzy Set Theory: Assessment and Applications

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.

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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.

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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.
Content:
Front Matter....Pages I-XI
Introduction....Pages 1-2
Front Matter....Pages 3-3
The Nature of Similarity....Pages 5-7
Historic Assessment of Compatibility....Pages 9-16
Foundations of Fuzzy Set Theory....Pages 17-34
Compatibility in Fuzzy Inference....Pages 35-44
Compatibility in Approximate Reasoning....Pages 45-66
Front Matter....Pages 67-69
Set-Theoretic Measures....Pages 71-96
Proximity-Based Measures....Pages 97-132
Logic-Based Measures....Pages 133-137
Fuzzy-Valued Similarity Measures....Pages 139-142
Front Matter....Pages 143-145
Generic Classification Domain....Pages 147-151
Set-Theoretic Comparative Study....Pages 153-166
Proximity-Based Comparative Study....Pages 167-176
Logic-Based Comparative Study....Pages 177-181
Comparison Among the Three Classes....Pages 183-187
Back Matter....Pages 189-209

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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.
Content:
Front Matter....Pages I-XI
Introduction....Pages 1-2
Front Matter....Pages 3-3
The Nature of Similarity....Pages 5-7
Historic Assessment of Compatibility....Pages 9-16
Foundations of Fuzzy Set Theory....Pages 17-34
Compatibility in Fuzzy Inference....Pages 35-44
Compatibility in Approximate Reasoning....Pages 45-66
Front Matter....Pages 67-69
Set-Theoretic Measures....Pages 71-96
Proximity-Based Measures....Pages 97-132
Logic-Based Measures....Pages 133-137
Fuzzy-Valued Similarity Measures....Pages 139-142
Front Matter....Pages 143-145
Generic Classification Domain....Pages 147-151
Set-Theoretic Comparative Study....Pages 153-166
Proximity-Based Comparative Study....Pages 167-176
Logic-Based Comparative Study....Pages 177-181
Comparison Among the Three Classes....Pages 183-187
Back Matter....Pages 189-209
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