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Fuzzy Set Theory

Fuzzy Set Theory
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 provides a systematic, yet practical guide for researchers wishing to combine fuzzy set theory with standard statistical techniques and model-testing.
Series Editor’s Introduction
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
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

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Michael Smithson

Michael Smithson is a Professor in the Research School of Psychology at The Australian National University in Canberra, and received his PhD from the University of Oregon. He is the author of Confidence Intervals (2003), Statistics with Confidence (2000), Ignorance and Uncertainty (1989), and Fuzzy Set Analysis for the Behavioral and Social Sciences (1987), co-author of Fuzzy Set Theory: Applications in the Social Sciences (2006) and Generalized Linear Models for Categorical and Limited Dependent Variables (2014), and co-editor of Uncertainty and Risk: Multidisciplinary Perspectives (2008) and Resolving Social Dilemmas: Dynamic, Structural... More About Author

Jay Verkuilen

Jay Verkuilen, PhD, is an associate professor of educational psychology at the City University of New York Graduate Center. His methodological research work is primarily in the area of psychometrics and statistics. His empirical work focuses on measurement in education and clinical psychology, and statistical analysis of rehabilitation medicine, particularly in the area of aphasia. He is the author of several publications regarding fuzzy set theory in behavioral science. More About Author

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ISBN: 9780761929864
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