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Fuzzy Probability and Statistics

  • Book
  • © 2006

Overview

Authors:
  1. James J. Buckley

    1. Department of Mathematics, University of Alabama at Birmingham, Birmingham, USA

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  • Clear and didactic book about fuzzy probabilities and statistics useful for students and researchers

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 196)

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Table of contents (31 chapters)

  1. Front Matter

    Pages i-xiii
    Download chapter PDF

  2. Introduction

    Pages 1-6

  3. Fuzzy Sets

    Pages 7-19

  4. Fuzzy Probability Theory

    Pages 21-49

  5. Discrete Fuzzy Random Variables

    Pages 51-60

  6. Continuous Fuzzy Random Variables

    Pages 61-74

  7. Estimate μ, Variance Known

    Pages 75-79

  8. Estimate μ, Variance Unknown

    Pages 81-83

  9. Estimate p, Binomial Population

    Pages 85-87

  10. Estimate σ2 from a Normal Population

    Pages 89-94

  11. Fuzzy Arrival/Service Rates

    Pages 95-99

  12. Fuzzy Uniform

    Pages 101-105

  13. Fuzzy Max Entropy Principle

    Pages 107-114

  14. Max Entropy: Crisp Discrete Solutions

    Pages 115-124

  15. Max Entropy: Crisp Continuous Solutions

    Pages 125-141

  16. Tests on μ, Variance Known

    Pages 143-149

  17. Tests on μ, Variance Unknown

    Pages 151-157

  18. Tests on p for a Binomial Population

    Pages 159-162

  19. Tests on σ2, Normal Population

    Pages 163-166

  20. Fuzzy Correlation

    Pages 167-170
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Keywords

About this book

This book combines material from our previous books FP (Fuzzy Probabilities: New Approach and Applications,Physica-Verlag, 2003) and FS (Fuzzy Statistics, Springer, 2004), plus has about one third new results. From FP we have material on basic fuzzy probability, discrete (fuzzy Poisson,binomial) and continuous (uniform, normal, exponential) fuzzy random variables. From FS we included chapters on fuzzy estimation and fuzzy hypothesis testing related to means, variances, proportions, correlation and regression. New material includes fuzzy estimators for arrival and service rates, and the uniform distribution, with applications in fuzzy queuing theory. Also, new to this book, is three chapters on fuzzy maximum entropy (imprecise side conditions) estimators producing fuzzy distributions and crisp discrete/continuous distributions. Other new results are: (1) two chapters on fuzzy ANOVA (one-way and two-way); (2) random fuzzy numbers with applications to fuzzy Monte Carlo studies; and (3) a fuzzy nonparametric estimator for the median.

Reviews

From the reviews:

"The reviewed book is an interesting and well organized monograph on fuzzy statistics which can be recommended for specialists and non-specialists in the field of fuzzy sets research." (Krzysztof Piasecki, Zentralblatt MATH, Vol. 1095 (21), 2006)

Authors and Affiliations

  • Department of Mathematics, University of Alabama at Birmingham, Birmingham, USA

    James J. Buckley

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