Valerie Cross and Thomas Sudkamp
Studies in Fuzziness and Soft Computing,
Number 93,
Physica-Verlag, 2002
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. try
Table of Contents:
Chapter
1. Introduction
Part
I Similarity, Compatibility, and Fuzzy Set Theory
Chapter
2. The Nature of Similarity
2.1
Dissimilarity, an opposite of similarity
2.2 Is
similarity symmetric?
2.3
Multidimensional vs. multi-attribute
2.4 Is
similarity relative?
Chapter
3. Historic assessment of compatibility
3.1
Taxonomy
3.2
Psychology
3.3
Statistical similarity
Chapter
4. Foundations of Fuzzy Set Theory
4.1
Representation and properties of fuzzy sets
4.2 Fuzzy
set operators
4.3
Aggregation
4.4 Fuzzy
logic as infinite-valued logic
4.5 Fuzzy
relations
4.6
Measuring uncertainty
Chapter
5. Fuzzy Set Theory in Approximate Reasoning
5.1
Compositional rule of inference
5.2
Compatibility-modification inference
5.3 Fuzzy
analogical and interpolation inference
Chapter
6. Applications of Compatibility Measures
6.1 Fuzzy
expert systems
6.2 Fuzzy
logic control
6.3
Information retrieval
6.4 Fuzzy
relational databases
-- 6.4.1
Notation and history
-- 6.4.2
Relational algebra extensions
6.5
Ranking fuzzy numbers
6.6
Similarity assessment experiments
Part
II Taxonomy of Compatibility Measures
Chapter
7. Set-Theoretic Measures
7.1
Inclusion indices
-- 7.1.1
Requirements
-- 7.1.2
Ordering of inclusion indices
-- 7.1.3 Reflexivity,
transitivity, and nesting
7.2
Partial matching indices
-- 7.2.1
Requirements
-- 7.2.2
Ordering of partial matching indices
-- 7.2.3
Ordering between inclusion and partial matching
-- 7.2.4
Reflexivity, transitivity, and nesting
7.3
Similarity indices
--7.3.1
Symmetric difference
-- 7.3.2
Similarity measure generatio
-- 7.3.3
Reflexivity, transitivity, and nesting
-- 7.3.4
Ordering within classes of similarity indices
-- 7.3.5
Ordering between classes of similarity indices
7.4
Ordering between set-theoretic classes
Chapter
8. Proximity Based Measures
8.1
Notation and terminology
8.2 Minkowski compatibility measures
-- 8.2.1
Metrics from symmetric difference
-- 8.2.2
Ordering of Minkowski measures
8.3
Angular coefficients as compatibility
8.4
Interval based compatibility measures
-- 8.4.1
Ordering of interval measures
-- 8.4.2
Relative distances
8.5
Linguistic approximation distance measures
Chapter
9. Logic-Based Measures
9.1 Fuzzy
truth values and compatibility
9.2
Similarity relations from co-implication
9.3
Ordering of logic based measures
Chapter
10. Fuzzy-Valued Similarity Measures
Part
III Empirical Analysis of Compatibility Measures
Chapter
11. Generic Classification Domain
11.1
Overview
11.2
Domain and evidential knowledge representation
11.3
Testing methodology
Chapter
12. Set-Theoretic Comparative Study
12.1 T3 aggregator
12.2 T1 aggregator
12.3 T2 aggregator
12.4
Modified mean aggregator
12.5
Summary of set-theoretic aggregator study
Chapter
13. Proximity-Based Comparative Study
13.1 T3 aggregator
13.2 G1,m
aggregator
13.3 T2 aggregator
Chapter
14. Logic-Based Comparative Study
14.1 T3 aggregator
14.2 G1,m
aggregator
14.3 T2 aggregator
Chapter
15. Comparison Among the Three Classes
15.1
Correlated domain knowledge
Index of
Notation
References