Computing Statistics under Interval and Fuzzy Uncertainty
Applications to Computer Science and Engineering
Authors: Nguyen, H.T., Kreinovich, V., Wu, B., Xiang, G.
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- About this book
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In many practical situations, we are interested in statistics characterizing a population of objects: e.g. in the mean height of people from a certain area.
Most algorithms for estimating such statistics assume that the sample values are exact. In practice, sample values come from measurements, and measurements are never absolutely accurate. Sometimes, we know the exact probability distribution of the measurement inaccuracy, but often, we only know the upper bound on this inaccuracy. In this case, we have interval uncertainty: e.g. if the measured value is 1.0, and inaccuracy is bounded by 0.1, then the actual (unknown) value of the quantity can be anywhere between 1.0 - 0.1 = 0.9 and 1.0 + 0.1 = 1.1. In other cases, the values are expert estimates, and we only have fuzzy information about the estimation inaccuracy.
This book shows how to compute statistics under such interval and fuzzy uncertainty. The resulting methods are applied to computer science (optimal scheduling of different processors), to information technology (maintaining privacy), to computer engineering (design of computer chips), and to data processing in geosciences, radar imaging, and structural mechanics.
- Reviews
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From the reviews:
“This book is a research exposition by Kreinovich and coworkers. … The main goal is to present algorithms for computation of statistical characteristics (like variance) but under interval and fuzzy uncertainty of the available data. In this book, fuzzy uncertainty is reduced to interval uncertainty by alpha-cutwise consideration of (convex) fuzzy uncertainty. … For increase of readability, mathematical proofs are presented always at the end of the chapters.” (Wolfgang Näther, Zentralblatt MATH, Vol. 1238, 2012)
- Table of contents (47 chapters)
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Formulation of the Problem
Pages 3-8
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Computing Statistics under Probabilistic and Interval Uncertainty: A Brief Description
Pages 9-10
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Computing Statistics under Fuzzy Uncertainty: Formulation of the Problem
Pages 11-17
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Computing under Fuzzy Uncertainty Can Be Reduced to Computing under Interval Uncertainty
Pages 19-24
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Computing under Interval Uncertainty: Traditional Approach Based on Uniform Distributions
Pages 25-27
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Table of contents (47 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Computing Statistics under Interval and Fuzzy Uncertainty
- Book Subtitle
- Applications to Computer Science and Engineering
- Authors
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- Hung T. Nguyen
- Vladik Kreinovich
- Berlin Wu
- Gang Xiang
- Series Title
- Studies in Computational Intelligence
- Series Volume
- 393
- Copyright
- 2012
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-642-24905-1
- DOI
- 10.1007/978-3-642-24905-1
- Hardcover ISBN
- 978-3-642-24904-4
- Softcover ISBN
- 978-3-642-44570-5
- Series ISSN
- 1860-949X
- Edition Number
- 1
- Number of Pages
- XII, 432
- Topics
