Fuzzy Probability and Statistics

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.

Inhalt

Fuzzy Sets.- Fuzzy Probability Theory.- Discrete Fuzzy Random Variables.- Continuous Fuzzy Random Variables.- Estimate ?, Variance Known.- Estimate ?, Variance Unknown.- Estimate p, Binomial Population.- Estimate ?2 from a Normal Population.- Fuzzy Arrival/Service Rates.- Fuzzy Uniform.- Fuzzy Max Entropy Principle.- Max Entropy: Crisp Discrete Solutions.- Max Entropy: Crisp Continuous Solutions.- Tests on ?, Variance Known.- Tests on ?, Variance Unknown.- Tests on p for a Binomial Population.- Tests on ?2, Normal Population.- Fuzzy Correlation.- Estimation in Simple Linear Regression.- Fuzzy Prediction in Linear Regression.- Hypothesis Testing in Regression.- Estimation in Multiple Regression.- Fuzzy Prediction in Regression.- Hypothesis Testing in Regression.- Fuzzy One-Way ANOVA.- Fuzzy Two-Way ANOVA.- Fuzzy Estimator for the Median.- Random Fuzzy Numbers.- Selected Maple/Solver Commands.- Summary and Future Research.