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Fuzzy Set Theory


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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

About 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.


"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

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