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Über dieses Buch

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.



Chapter 1. Introduction

Chapter 2. Fuzzy Sets

Chapter 3. Fuzzy Probability Theory

Chapter 4. Discrete Fuzzy Random Variables

Chapter 5. Continuous Fuzzy Random Variables

Chapter 6. Estimate μ, Variance Known

Chapter 7. Estimate μ, Variance Unknown

Chapter 8. Estimate p, Binomial Population

Chapter 9. Estimate σ2 from a Normal Population

Chapter 10. Fuzzy Arrival/Service Rates

Chapter 11. Fuzzy Uniform

Chapter 12. Fuzzy Max Entropy Principle

We solved the maximum entropy principle with imprecise side-conditions, which were modeled as fuzzy sets, producing fuzzy probability distributions. It seems very natural if you start with a fuzzy mean, variance, etc, you need to end up with a fuzzy probability distribution. Fuzzy probability distributions produce fuzzy means, variances, etc. In the next two chapters we restrict the solutions to be crisp (not fuzzy).

Chapter 13. Max Entropy: Crisp Discrete Solutions

In this chapter we showed how to solve the maximum entropy problem with imprecise side-conditions for a crisp (non-fuzzy) discrete probability distribution. The next step would be to solve for a crisp continuous probability density. That is the topic of the next chapter.

Chapter 14. Max Entropy: Crisp Continuous Solutions

Chapter 15. Tests on μ, Variance Known

Chapter 16. Tests on μ, Variance Unknown

Chapter 17. Tests on p for a Binomial Population

Chapter 18. Tests on σ2, Normal Population

Chapter 19. Fuzzy Correlation

Chapter 20. Estimation in Simple Linear Regression

Chapter 21. Fuzzy Prediction in Linear Regression

Chapter 22. Hypothesis Testing in Regression

Chapter 23. Estimation in Multiple Regression

Chapter 24. Fuzzy Prediction in Regression

Chapter 25. Hypothesis Testing in Regression

Chapter 26. Fuzzy One-Way ANOVA

Chapter 27. Fuzzy Two-Way ANOVA

Chapter 28. Fuzzy Estimator for the Median

Chapter 29. Random Fuzzy Numbers

Chapter 30. Selected Maple/Solver Commands

Chapter 31. Summary and Future Research


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