Titel: Fuzzy Probability and Statistics
Autor/en: James J. Buckley
Studies in Fuzziness and Soft Computing.
'Studies in Fuzziness and Soft Computing'.
78 schwarz-weiße Abbildungen, 27 schwarz-weiße Tabellen, Bibliographie.
21. Februar 2006 - gebunden - XIII
1.1 Introduction This book is written in the following divisions: (1) the introductory chapters consisting of Chapters 1 and 2; (2) introduction to fuzzy probability in Ch- ters3-5; (3)introductiontofuzzyestimationinChapters6-11; (4)fuzzy/crisp estimatorsofprobabilitydensity(mass)functionsbasedonafuzzymaximum entropyprincipleinChapters12-14; (5)introductiontofuzzyhypothesiste- ing in Chapters 15-18; (6) fuzzy correlation and regression in Chapters 19-25; (7) Chapters 26 and 27 are about a fuzzy ANOVA model; (8) a fuzzy esti- tor of the median in nonparametric statistics in Chapter 28; and (9) random fuzzy numbers with applications to Monte Carlo studies in Chapter 29. First we need to be familiar with fuzzy sets. All you need to know about fuzzy sets for this book comprises Chapter 2. For a beginning introduction to fuzzysetsandfuzzylogicsee. Oneotheritemrelatingtofuzzysets,needed infuzzyhypothesistesting, isalsoinChapter2: howwewilldeterminewhich of the following three possibilities is trueM N or M? N,for two fuzzy numbers M, N. TheintroductiontofuzzyprobabilityinChapters3-5isbasedonthebook  and the reader is referred to that book for more information, especially applications. Whatisnewhereis: (1)usinganonlinearoptimizationprogram in Maple  to solve certain optimization problems in fuzzy probability, where previously we used a graphical method; and (2) a new algorithm, suitable for using only pencil and paper, for solving some restricted fuzzy arithmetic problems. The introduction to fuzzy estimation is based on the book  and we refer the interested reader to that book for more about fuzzy estimators.
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.
From the reviews:
"The reviewed book is an interesting and well organized monograph on fuzzy statistics which can be recommended for specialists and non-specialists in the field of fuzzy sets research." (Krzysztof Piasecki, Zentralblatt MATH, Vol. 1095 (21), 2006)