Fuzzy Set Theory: Applications in the Social Sciences

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Overview

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.

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Editorial Reviews

Marinano Ruiz Espejo
"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
"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."
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Product Details

Meet the Author

Research Interests: Ignorance and Uncertainty, Risk, Decision Making, Statistical Methods for Psychological Research, Social Dilemmas, Fuzzy Logic, Philosophy and Social Psychology of Science

Teaching:

Introductory Graduate Statistics, Linear Models, Generalized Linear Models, Psychometrics, Item Response Theory

Research:

My research is focused on the intersection of statistics and behavioral science. I have done work in a number of areas.

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Table of Contents

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

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