Fuzzy probability and statistics /

Fuzzy probability and statistics /

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Bibliographic Details
Author / Creator:Buckley, James J., 1936-
Imprint:Berlin : Springer-Verlag, 2006.
Description:1 online resource (xiii, 270 pages) : illustrations.
Language:English
Series:Studies in fuzziness and soft computing, 1860-0808 ; v. 196
Studies in fuzziness and soft computing ; v. 196.
Subject:
Fuzzy mathematics.
Probabilities.
Fuzzy statistics.
Fuzzy mathematics.
Fuzzy statistics.
Probabilities.
Format: E-Resource Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/11068935
Hidden Bibliographic Details
ISBN:9783540331902
3540331905
3540308415
9783540308416
1280613092
9781280613098
Notes:Includes bibliographical references and index.
Print version record.
Summary: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: two chapters on fuzzy ANOVA (one-way and two-way); random fuzzy numbers with applications to fuzzy Monte Carlo studies; and a fuzzy nonparametric estimator for the median.
Other form:Print version: Buckley, James J., 1936- Fuzzy probability and statistics. Berlin : Springer-Verlag, 2006 3540308415 9783540308416
Table of Contents:
  • 1. Introduction
  • 1.1. Introduction
  • 1.2. Notation
  • 1.3. Previous Research
  • 1.4. Figures
  • 1.5. Maple/Solver Commands
  • 1.6. References
  • 2. Fuzzy Sets
  • 2.1. Introduction
  • 2.2. Fuzzy Sets
  • 2.2.1. Fuzzy Numbers
  • 2.2.2. Alpha-Cuts
  • 2.2.3. Inequalities
  • 2.2.4. Discrete Fuzzy Sets
  • 2.3. Fuzzy Arithmetic
  • 2.3.1. Extension Principle
  • 2.3.2. Interval Arithmetic
  • 2.3.3. Fuzzy Arithmetic
  • 2.4. Fuzzy Functions
  • 2.4.1. Extension Principle
  • 2.4.2. Alpha-Cuts and Interval Arithmetic
  • 2.4.3. Differences
  • 2.5. Ordering Fuzzy Numbers
  • 2.6. References
  • 3. Fuzzy Probability Theory
  • 3.1. Introduction
  • 3.2. Fuzzy Probabilities from Confidence Intervals
  • 3.3. Fuzzy Probabilities from Expert Opinion
  • 3.4. Restricted Fuzzy Arithmetic
  • 3.4.1. Probabilities
  • 3.4.2. Restricted Arithmetic: General
  • 3.4.3. Computing Fuzzy Probabilities
  • 3.5. Fuzzy Probability
  • 3.6. Fuzzy Conditional Probability
  • 3.7. Fuzzy Independence
  • 3.8. Fuzzy Bayes' Formula
  • 3.9. Applications
  • 3.9.1. Blood Types
  • 3.9.2. Resistance to Surveys
  • 3.9.3. Testing for HIV
  • 3.9.4. Color Blindness
  • 3.9.5. Fuzzy Bayes
  • 3.10. References
  • 4. Discrete Fuzzy Random Variables
  • 4.1. Introduction
  • 4.2. Fuzzy Binomial
  • 4.3. Fuzzy Poisson
  • 4.4. Applications
  • 4.4.1. Fuzzy Poisson Approximating Fuzzy Binomial
  • 4.4.2. Overbooking
  • 4.4.3. Rapid Response Team
  • 4.5. References
  • 5. Continuous Fuzzy Random Variables
  • 5.1. Introduction
  • 5.2. Fuzzy Uniform
  • 5.3. Fuzzy Normal
  • 5.4. Fuzzy Negative Exponential
  • 5.5. Applications
  • 5.5.1. Fuzzy Uniform
  • 5.5.2. Fuzzy Normal Approximation to Fuzzy Binomial
  • 5.5.3. Fuzzy Normal Approximation to Fuzzy Poisson
  • 5.5.4. Fuzzy Normal
  • 5.5.5. Fuzzy Negative Exponential
  • 5.6. References
  • 6. Estimate [mu], Variance Known
  • 6.1. Introduction
  • 6.2. Fuzzy Estimation
  • 6.3. Fuzzy Estimator of [mu]
  • 6.4. References
  • 7. Estimate [mu], Variance Unknown
  • 7.1. Fuzzy Estimator of [mu]
  • 7.2. References
  • 8. Estimate p, Binomial Population
  • 8.1. Fuzzy Estimator of p
  • 8.2. References
  • 9. Estimate [sigma superscript 2] from a Normal Population
  • 9.1. Introduction
  • 9.2. Biased Fuzzy Estimator
  • 9.3. Unbiased Fuzzy Estimator
  • 9.4. References
  • 10. Fuzzy Arrival/Service Rates
  • 10.1. Introduction
  • 10.2. Fuzzy Arrival Rate
  • 10.3. Fuzzy Service Rate
  • 10.4. References
  • 11. Fuzzy Uniform
  • 11.1. Introduction
  • 11.2. Fuzzy Estimators
  • 11.2.1. Details
  • 11.3. References
  • 12. Fuzzy Max Entropy Principle
  • 12.1. Introduction
  • 12.2. Maximum Entropy Principle
  • 12.2.1. Discrete Probability Distributions
  • 12.2.2. Continuous Probability Distributions
  • 12.3. Imprecise Side-Conditions
  • 12.3.1. Discrete Probability Distributions
  • 12.3.2. Continuous Probability Distributions
  • 12.4. Summary and Conclusions
  • 12.5. References
  • 13. Max Entropy: Crisp Discrete Solutions
  • 13.1. Introduction
  • 13.2. Max Entropy: Discrete Distributions
  • 13.3. Max Entropy: Imprecise Side-Conditions
  • 13.4. Summary and Conclusions
  • 13.5. References
  • 14. Max Entropy: Crisp Continuous Solutions
  • 14.1. Introduction
  • 14.2. Max Entropy: Probability Densities
  • 14.3. Max Entropy: Imprecise Side-Conditions
  • 14.4. E = [0, M]
  • 14.5. E = [0, [infinity])
  • 14.6. E = (-[infinity], [infinity])
  • 14.7. Summary and Conclusions
  • 14.8. References
  • 15. Tests on [mu], Variance Known
  • 15.1. Introduction
  • 15.2. Non-Fuzzy Case
  • 15.3. Fuzzy Case
  • 15.4. One-Sided Tests
  • 15.5. References
  • 16. Tests on [mu], Variance Unknown
  • 16.1. Introduction
  • 16.2. Crisp Case
  • 16.3. Fuzzy Model
  • 16.3.1. T[[alpha]] for Non-Positive Intervals
  • 16.4. References
  • 17. Tests on p for a Binomial Population
  • 17.1. Introduction
  • 17.2. Non-Fuzzy Test
  • 17.3. Fuzzy Test
  • 17.4. References
  • 18. Tests on [sigma superscript 2], Normal Population
  • 18.1. Introduction
  • 18.2. Crisp Hypothesis Test
  • 18.3. Fuzzy Hypothesis Test
  • 18.4. References
  • 19. Fuzzy Correlation
  • 19.1. Introduction
  • 19.2. Crisp Results
  • 19.3. Fuzzy Theory
  • 19.4. References
  • 20. Estimation in Simple Linear Regression
  • 20.1. Introduction
  • 20.2. Fuzzy Estimators
  • 20.3. References
  • 21. Fuzzy Prediction in Linear Regression
  • 21.1. Prediction
  • 21.2. References
  • 22. Hypothesis Testing in Regression
  • 22.1. Introduction
  • 22.2. Tests on a
  • 22.3. Tests on b
  • 22.4. References
  • 23. Estimation in Multiple Regression
  • 23.1. Introduction
  • 23.2. Fuzzy Estimators
  • 23.3. References
  • 24. Fuzzy Prediction in Regression
  • 24.1. Prediction
  • 24.2. References
  • 25. Hypothesis Testing in Regression
  • 25.1. Introduction
  • 25.2. Tests on b
  • 25.3. Tests on c
  • 25.4. References
  • 26. Fuzzy One-Way ANOVA
  • 26.1. Introduction
  • 26.2. Crisp Hypothesis Test
  • 26.3. Fuzzy Hypothesis Test
  • 26.4. References
  • 27. Fuzzy Two-Way ANOVA
  • 27.1. Introduction
  • 27.2. Crisp Hypothesis Tests
  • 27.3. Fuzzy Hypothesis Tests
  • 27.4. References
  • 28. Fuzzy Estimator for the Median
  • 28.1. Introduction
  • 28.2. Crisp Estimator for the Median
  • 28.3. Fuzzy Estimator
  • 28.4. Reference
  • 29. Random Fuzzy Numbers
  • 29.1. Introduction
  • 29.2. Random Fuzzy Numbers
  • 29.3. Tests for Randomness
  • 29.3.1. RNGenerator
  • 29.3.2. RNAnalysis
  • 29.4. Monte Carlo Study
  • 29.5. References
  • 30. Selected Maple/Solver Commands
  • 30.1. Introduction
  • 30.2. SOLVER
  • 30.2.1. Example 13.3.1
  • 30.2.2. Example 13.3.2
  • 30.2.3. Example 13.3.3
  • 30.2.4. Example 13.3.4
  • 30.2.5. Problems
  • 30.3. Maple
  • 30.3.1. Chapter 3
  • 30.3.2. Chapter 4
  • 30.3.3. Chapter 5
  • 30.3.4. Chapter 6
  • 30.3.5. Chapter 7
  • 30.3.6. Chapter 8
  • 30.3.7. Chapter 9
  • 30.3.8. Chapter 10
  • 30.3.9. Chapters 11-13
  • 30.3.10. Chapter 14
  • 30.3.11. Chapter 15
  • 30.3.12. Chapter 16
  • 30.3.13. Chapter 17
  • 30.3.14. Chapter 18
  • 30.3.15. Chapter 19
  • 30.3.16. Chapter 20
  • 30.3.17. Chapter 21
  • 30.3.18. Chapter 22
  • 30.3.19. Chapter 23
  • 30.3.20. Chapter 24
  • 30.3.21. Chapter 25
  • 30.3.22. Chapter 26
  • 30.3.23. Chapter 27
  • 30.3.24. Chapter 28
  • 30.3.25. Chapter 29
  • 30.4. References
  • 31. Summary and Future Research
  • 31.1. Summary
  • 31.2. Future Research
  • 31.2.1. Fuzzy Probability
  • 31.2.2. Unbiased Fuzzy Estimators
  • 31.2.3. Comparing Fuzzy Numbers
  • 31.2.4. No Decision Conclusion
  • 31.2.5. Fuzzy Uniform
  • 31.2.6. Interval Arithmetic
  • 31.2.7. Fuzzy Prediction
  • 31.2.8. Fuzzy ANOVA
  • 31.2.9. Nonparametric Statistics
  • 31.2.10. Randomness Tests Fuzzy Numbers
  • 31.2.11. Future
  • 31.3. References
  • Index
  • List of Figures
  • List of Tables

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