Fuzzy Set Theory

Applications in the Social Sciences
1. Auflage 2006
ISBN: 978-0-7619-2986-4
Verlag: Sage Publications, Inc

Buch, Englisch, Band 147, 112 Seiten, Format (B × H): 140 mm x 216 mm, Gewicht: 150 g

Reihe: Quantitative Applications in the Social Sciences

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

Autoren/Hrsg.

Smithson, Michael

Verkuilen, Jay

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Mathematische Logik
• Sozialwissenschaften Soziologie | Soziale Arbeit Soziologie Allgemein Demographie, Demoskopie
• Sozialwissenschaften Soziologie | Soziale Arbeit Soziologie Allgemein Empirische Sozialforschung, Statistik
• Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Forschungsmethodik, Wissenschaftliche Ausstattung

Inhaltsverzeichnis

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

Über Autor(innen)

Smithson, Michael
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, and Intergroup Aspects (1999). His other publications include more than 170 refereed journal articles and book chapters. His primary research interests are in judgment and decision making under ignorance and uncertainty, statistical methods for the social sciences, and applications of fuzzy set theory to the social sciences.

Verkuilen, Jay
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.