Introduction / 1: |
Notation / 1.1: |
Previous Research / 1.3: |
Figures / 1.4: |
Maple/Solver Commands / 1.5: |
References / 1.6: |
Fuzzy Sets / 2: |
Fuzzy Numbers / 2.1: |
Alpha-Cuts / 2.2.2: |
Inequalities / 2.2.3: |
Discrete Fuzzy Sets / 2.2.4: |
Fuzzy Arithmetic / 2.3: |
Extension Principle / 2.3.1: |
Interval Arithmetic / 2.3.2: |
Fuzzy Functions / 2.3.3: |
Alpha-Cuts and Interval Arithmetic / 2.4.1: |
Differences / 2.4.3: |
Ordering Fuzzy Numbers / 2.5: |
Fuzzy Probability Theory / 2.6: |
Fuzzy Probabilities from Confidence Intervals / 3.1: |
Fuzzy Probabilities from Expert Opinion / 3.3: |
Restricted Fuzzy Arithmetic / 3.4: |
Probabilities / 3.4.1: |
Restricted Arithmetic: General / 3.4.2: |
Computing Fuzzy Probabilities / 3.4.3: |
Fuzzy Probability / 3.5: |
Fuzzy Conditional Probability / 3.6: |
Fuzzy Independence / 3.7: |
Fuzzy Bayes' Formula / 3.8: |
Applications / 3.9: |
Blood Types / 3.9.1: |
Resistance to Surveys / 3.9.2: |
Testing for HIV / 3.9.3: |
Color Blindness / 3.9.4: |
Fuzzy Bayes / 3.9.5: |
Discrete Fuzzy Random Variables / 3.10: |
Fuzzy Binomial / 4.1: |
Fuzzy Poisson / 4.3: |
Fuzzy Poisson Approximating Fuzzy Binomial / 4.4: |
Overbooking / 4.4.2: |
Rapid Response Team / 4.4.3: |
Continuous Fuzzy Random Variables / 4.5: |
Fuzzy Uniform / 5.1: |
Fuzzy Normal / 5.3: |
Fuzzy Negative Exponential / 5.4: |
Fuzzy Normal Approximation to Fuzzy Binomial / 5.5: |
Fuzzy Normal Approximation to Fuzzy Poisson / 5.5.3: |
Estimate [mu], Variance Known / 5.5.4: |
Fuzzy Estimation / 6.1: |
Fuzzy Estimator of [mu] / 6.3: |
Estimate [mu], Variance Unknown / 6.4: |
Estimate p, Binomial Population / 7.1: |
Fuzzy Estimator of p / 8.1: |
Estimate [sigma superscript 2] from a Normal Population / 8.2: |
Biased Fuzzy Estimator / 9.1: |
Unbiased Fuzzy Estimator / 9.3: |
Fuzzy Arrival/Service Rates / 9.4: |
Fuzzy Arrival Rate / 10.1: |
Fuzzy Service Rate / 10.3: |
Fuzzy Estimators / 10.4: |
Details / 11.2.1: |
Fuzzy Max Entropy Principle / 11.3: |
Maximum Entropy Principle / 12.1: |
Discrete Probability Distributions / 12.2.1: |
Continuous Probability Distributions / 12.2.2: |
Imprecise Side-Conditions / 12.3: |
Summary and Conclusions / 12.3.1: |
Max Entropy: Crisp Discrete Solutions / 12.5: |
Max Entropy: Discrete Distributions / 13.1: |
Max Entropy: Imprecise Side-Conditions / 13.3: |
Max Entropy: Crisp Continuous Solutions / 13.4: |
Max Entropy: Probability Densities / 14.1: |
E = [0, M] / 14.3: |
E = [0, [infinity]) / 14.5: |
E = (-[infinity], [infinity]) / 14.6: |
Tests on [mu], Variance Known / 14.7: |
Non-Fuzzy Case / 15.1: |
Fuzzy Case / 15.3: |
One-Sided Tests / 15.4: |
Tests on [mu], Variance Unknown / 15.5: |
Crisp Case / 16.1: |
Fuzzy Model / 16.3: |
T[[alpha]] for Non-Positive Intervals / 16.3.1: |
Tests on p for a Binomial Population / 16.4: |
Non-Fuzzy Test / 17.1: |
Fuzzy Test / 17.3: |
Tests on [sigma superscript 2], Normal Population / 17.4: |
Crisp Hypothesis Test / 18.1: |
Fuzzy Hypothesis Test / 18.3: |
Fuzzy Correlation / 18.4: |
Crisp Results / 19.1: |
Fuzzy Theory / 19.3: |
Estimation in Simple Linear Regression / 19.4: |
Fuzzy Prediction in Linear Regression / 20.1: |
Prediction / 21.1: |
Hypothesis Testing in Regression / 21.2: |
Tests on a / 22.1: |
Tests on b / 22.3: |
Estimation in Multiple Regression / 22.4: |
Fuzzy Prediction in Regression / 23.1: |
Tests on c / 24.1: |
Fuzzy One-Way ANOVA / 25.4: |
Fuzzy Two-Way ANOVA / 26.1: |
Crisp Hypothesis Tests / 27.1: |
Fuzzy Hypothesis Tests / 27.3: |
Fuzzy Estimator for the Median / 27.4: |
Crisp Estimator for the Median / 28.1: |
Fuzzy Estimator / 28.3: |
Reference / 28.4: |
Random Fuzzy Numbers / 29: |
Tests for Randomness / 29.1: |
RNGenerator / 29.3.1: |
RNAnalysis / 29.3.2: |
Monte Carlo Study / 29.4: |
Selected Maple/Solver Commands / 29.5: |
SOLVER / 30.1: |
Example 13.3.1 / 30.2.1: |
Example 13.3.2 / 30.2.2: |
Example 13.3.3 / 30.2.3: |
Example 13.3.4 / 30.2.4: |
Problems / 30.2.5: |
Maple / 30.3: |
Chapter 3 / 30.3.1: |
Chapter 4 / 30.3.2: |
Chapter 5 / 30.3.3: |
Chapter 6 / 30.3.4: |
Chapter 7 / 30.3.5: |
Chapter 8 / 30.3.6: |
Chapter 9 / 30.3.7: |
Chapter 10 / 30.3.8: |
Chapters 11-13 / 30.3.9: |
Chapter 14 / 30.3.10: |
Chapter 15 / 30.3.11: |
Chapter 16 / 30.3.12: |
Chapter 17 / 30.3.13: |
Chapter 18 / 30.3.14: |
Chapter 19 / 30.3.15: |
Chapter 20 / 30.3.16: |
Chapter 21 / 30.3.17: |
Chapter 22 / 30.3.18: |
Chapter 23 / 30.3.19: |
Chapter 24 / 30.3.20: |
Chapter 25 / 30.3.21: |
Chapter 26 / 30.3.22: |
Chapter 27 / 30.3.23: |
Chapter 28 / 30.3.24: |
Chapter 29 / 30.3.25: |
Summary and Future Research / 30.4: |
Summary / 31.1: |
Future Research / 31.2: |
Unbiased Fuzzy Estimators / 31.2.1: |
Comparing Fuzzy Numbers / 31.2.3: |
No Decision Conclusion / 31.2.4: |
Fuzzy Prediction / 31.2.5: |
Fuzzy ANOVA / 31.2.8: |
Nonparametric Statistics / 31.2.9: |
Randomness Tests Fuzzy Numbers / 31.2.10: |
Future / 31.2.11: |
Index / 31.3: |
List of Figures |
List of Tables |