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Fuzzy Probabilities

New Approach and Applications

  • Book
  • © 2005

Overview

Authors:
  1. James J. Buckley

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

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  • New method of dealing with imprecise probabilities, most of which not published before

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 115)

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Table of contents (16 chapters)

  1. Front Matter

    Pages i-xi
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  2. Introduction

    Pages 1-6

  3. Fuzzy Sets

    Pages 7-30

  4. Fuzzy Probability Theory

    Pages 31-49

  5. Discrete Fuzzy Random Variables

    Pages 51-60

  6. Fuzzy Queuing Theory

    Pages 61-69

  7. Fuzzy Markov Chains

    Pages 71-83

  8. Fuzzy Decisions Under Risk

    Pages 85-93

  9. Continuous Fuzzy Random Variables

    Pages 95-108

  10. Fuzzy Inventory Control

    Pages 109-113

  11. Joint Fuzzy Probability Distributions

    Pages 115-123

  12. Applications of Joint Distributions

    Pages 125-132

  13. Functions of a Fuzzy Random Variable

    Pages 133-137

  14. Functions of Fuzzy Random Variables

    Pages 139-144

  15. Law of Large Numbers

    Pages 145-146

  16. Sums of Fuzzy Random Variables

    Pages 147-150

  17. Conclusions and Future Research

    Pages 151-155

  18. Back Matter

    Pages 157-166
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Keywords

About this book

In probability and statistics we often have to estimate probabilities and parameters in probability distributions using a random sample. Instead of using a point estimate calculated from the data we propose using fuzzy numbers which are constructed from a set of confidence intervals. In probability calculations we apply constrained fuzzy arithmetic because probabilities must add to one. Fuzzy random variables have fuzzy distributions. A fuzzy normal random variable has the normal distribution with fuzzy number mean and variance. Applications are to queuing theory, Markov chains, inventory control, decision theory and reliability theory.

Authors and Affiliations

  • Mathematics Department, University of Alabama at Birmingham, Birmingham

    James J. Buckley

Bibliographic Information

  • Book Title: Fuzzy Probabilities

  • Book Subtitle: New Approach and Applications

  • Authors: James J. Buckley

  • Series Title: Studies in Fuzziness and Soft Computing

  • DOI: https://doi.org/10.1007/3-540-32388-0

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2005

  • Hardcover ISBN: 978-3-540-25033-3Published: 11 March 2005

  • Softcover ISBN: 978-3-642-42133-4Published: 23 November 2014

  • eBook ISBN: 978-3-540-32388-4Published: 07 July 2006

  • Series ISSN: 1434-9922

  • Series E-ISSN: 1860-0808

  • Edition Number: 1

  • Number of Pages: XI, 168

  • Topics: Probability Theory and Stochastic Processes, Artificial Intelligence

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