Fuzzy Probability and Statistics / Edition 1

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Overview

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.
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Editorial Reviews

From the Publisher
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)

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Product Details

  • ISBN-13: 9783540308416
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 4/11/2006
  • Series: Studies in Fuzziness and Soft Computing Series , #196
  • Edition description: 2006
  • Edition number: 1
  • Pages: 270
  • Product dimensions: 6.10 (w) x 9.40 (h) x 0.80 (d)

Table of Contents

1 Introduction 1
2 Fuzzy sets 7
3 Fuzzy probability theory 21
4 Discrete fuzzy random variables 51
5 Continuous fuzzy random variables 61
6 Estimate [mu], variance known 75
7 Estimate [mu], variance unknown 81
8 Estimate p, binomial population 85
9 Estimate [sigma][superscript 2] from a normal population 89
10 Fuzzy arrival/service rates 95
11 Fuzzy uniform 101
12 Fuzzy max entropy principle 107
13 Max entropy : crisp discrete solutions 115
14 Max entropy : crisp continuous solutions 125
15 Tests on [mu], variance known 143
16 Tests on [mu], variance unknown 151
17 Tests on p for a binomial population 159
18 Tests on [sigma][superscript 2], normal population 163
19 Fuzzy correlation 167
20 Estimation in simple linear regression 171
21 Fuzzy prediction in linear regression 177
22 Hypothesis testing in regression 181
23 Estimation in multiple regression 187
24 Fuzzy prediction in regression 193
25 Hypothesis testing in regression 197
26 Fuzzy one-way ANOVA 203
27 Fuzzy two-way ANOVA 209
28 Fuzzy estimator for the median 219
29 Random fuzzy numbers 223
30 Selected maple/solver commands 235
31 Summary and future research 253
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