Fuzzy Probability and Statistics (Studies in Fuzziness and Soft Computing, 196) 2006th Edition by James J. Buckley (PDF)

Description

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.

User’s Reviews

Editorial Reviews: Review 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) From the Back Cover 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐By way of motivating example, Buckley proposes a population containing two groups. When polled, some percentage of each group says that they would participate in a survey. Question: Given that information, what is the chance that a person picked at random would participate? Since all of the percentages involved are subject to some uncertainty themselves, the inputs can all be phrased as fuzzy numbers.This book does a great job of rewriting common kinds of statistical inference where traditional (or “crisp”) probabilities are replaced by fuzzy ones, reflecting the fundamental uncertainty in the entire process. As with other Springer “yellow books,” this covers its topic thoroughly, but requires a well-prepared reader with time and energy to devote to extracting this book’s value. That reader has a solid foundation in traditional probability, some understanding of fuzzy numbers, and a willingness to hold on tight during some of the developments.Although clear and well written, I don’t see that I’ll be using these concepts any time soon. The uncertainty already inherent in traditional stats suits most of my needs. I use interval arithmetic even more often. That’s a crude form of fuzzy numbers well suited to worst-case analysis, and is the special case that arises every time an ‘alpha cut’ appears in fuzzy explanations – which happens often. Yet other times, I need to reason in terms of exact PDFs, where the distribution of the sum of two random numbers is the convolution of their PDFs. Fuzzy probabilities seem to lie somewhere in the middle, between the coarseness of interval arithmetic and the heavy mechanism of handling exact PDFs. In other words, tools already available to me bracket this territory adequately.Anyone with a serious interest in soft logics should consider learning more about fuzzy probability. Buckley’s presentation gets the concepts and techniques across clearly, for anyone willing to put the time in. I just don’t see that it meets a need that I really have.– wiredweird

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