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Fuzzy Set Theory
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Fuzzy Set Theory
Applications in the Social Sciences



April 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
 
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

Sample Materials & Chapters

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Chapter 3

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