Fuzzy Set Theory

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.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.

• Series Editor’s IntroductionAcknowledgments1. Introduction2. An Overview of Fuzzy Set Mathematics2.1 Set Theory2.2 Why Fuzzy Sets?2.3 The Membership Function2.4 Operations of Fuzzy Set Theory2.5 Fuzzy Numbers and Fuzzy Variables2.6 Graphical Representations of Fuzzy Sets3. Measuring Membership3.1 Introduction3.2 Methods for Constructing Membership Functions3.3 Measurement Properties Required for Fuzzy Sets3.4 Measurement Properties of Membership Functions3.5 Uncertainty Estimates in Membership Assignment4. Internal Structure and Properties of a Fuzzy Set4.1 Cardinality: The Size of a Fuzzy Set4.2 Probability Distributions for Fuzzy Sets4.3 Defining and Measuring Fuzziness5. Simple Relations Between Fuzzy Sets5.1 Intersection, Union, and Inclusion5.2 Detecting and Evaluating Fuzzy Inclusion5.3 Quantifying and Modeling Inclusion: Ordinal Membership Scales5.4 Quantified and Comparable Membership Scales6. Multivariate Fuzzy Set Relations6.1 Compound Set Indexes6.2 Multiset Relations: Comorbidity, Covariation, and Co-Occurrence6.3 Multiple and Partial Intersection and Inclusion7. Concluding RemarksReferencesIndexAbout 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."