Fuzzy set theory : applications in the social sciences

Abstract

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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