Fuzzy Set Theory

Michael Smithson - Australian National University
Jay Verkuilen - City University of New York, USA

Volume: 147

Series:
Quantitative Applications in the Social Sciences

February 2006 | 112 pages | SAGE Publications, Inc

Fuzzy set theory deals with sets or categories whose boundaries are blurry or, in other words, "fuzzy." This book presents an accessible introduction to fuzzy set theory, focusing on its applicability to the social sciences. Unlike most books on this topic, Fuzzy Set Theory: Applications in the Social Sciences provides a systematic, yet practical guide for researchers wishing to combine fuzzy set theory with standard statistical techniques and model-testing.

Key Features:

Addresses Basic Concepts: Fuzzy set theory is an analytic framework for handling concepts that are simultaneously categorical and dimensional. Starting with a rationale for fuzzy sets, this book introduces readers with an elementary knowledge of statistics to the necessary concepts and techniques of fuzzy set theory and fuzzy logic.
Introduces Novel Ways of Analyses: Researchers are shown alternative methods to conventional models, especially for testing theories that are expressed in set-wise terms. Issues of operationalizing graded membership in a fuzzy set and the measurement of the properties of such sets are a few of the topics addressed.
Illustrates Techniques and Applications: Real examples and data-sets from various disciplines in the social sciences are used to demonstrate the connections between fuzzy sets and other data analytic techniques, empirical applications of the technique, and the critiques of fuzzy set theory.

Intended Audience:
Ideal for researchers in the social sciences, education, and behavioral sciences; as well as graduate students in the applied social sciences

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Available Formats

ISBN: 9780761929864	Paperback	Suggested Retail Price: $46.00	Bookstore Price: $36.80
ISBN: 9781452212418	Electronic Version	Suggested Retail Price: $38.00	Bookstore Price: $30.40

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Series Editor’s Introduction

Acknowledgments

1. Introduction

2. An Overview of Fuzzy Set Mathematics

2.1 Set Theory

2.2 Why Fuzzy Sets?

2.3 The Membership Function

2.4 Operations of Fuzzy Set Theory

2.5 Fuzzy Numbers and Fuzzy Variables

2.6 Graphical Representations of Fuzzy Sets

3. Measuring Membership

3.1 Introduction

3.2 Methods for Constructing Membership Functions

3.3 Measurement Properties Required for Fuzzy Sets

3.4 Measurement Properties of Membership Functions

3.5 Uncertainty Estimates in Membership Assignment

4. Internal Structure and Properties of a Fuzzy Set

4.1 Cardinality: The Size of a Fuzzy Set

4.2 Probability Distributions for Fuzzy Sets

4.3 Defining and Measuring Fuzziness

5. Simple Relations Between Fuzzy Sets

5.1 Intersection, Union, and Inclusion

5.2 Detecting and Evaluating Fuzzy Inclusion

5.3 Quantifying and Modeling Inclusion: Ordinal Membership Scales

5.4 Quantified and Comparable Membership Scales

6. Multivariate Fuzzy Set Relations

6.1 Compound Set Indexes

6.2 Multiset Relations: Comorbidity, Covariation, and Co-Occurrence

6.3 Multiple and Partial Intersection and Inclusion

7. Concluding Remarks

References

Index

About the Authors

"I think that the book is a simple and accessible introduction to the theory of fuzzy sets and it includes many examples, formulae, figures, and tables which illustrate its contents. The presentation of the book and the academic content are very careful, which make for pleasant reading."

Marinano Ruiz Espejo

Universidad Nacional de Educacion a Distancia, Spain

Key features

Addresses issues of operationalizing graded membership in a fuzzy set and the measurement of the properties of such sets
Methods for exploring the relations among sets (e.g.. overlap and inclusion)
Advice regarding relevant software