### Computing Statistics Under Interval and Fuzzy Uncertainty

Hung T. Nguyen, Vladik Kreinovich, Berlin Wu and Gang Xiang User Rating

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- ISBN 9783642249044 / 3642249043
- Title Computing Statistics Under Interval and Fuzzy Uncertainty
- Author Hung T. Nguyen, Vladik Kreinovich, Berlin Wu and Gang Xiang
- Category Probability & Statistics

Maths For Scientists

Maths For Engineers

Mathematical Theory Of Computation - Format Hardcover
- Year 2011
- Pages 432
- Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
- Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K
- Language English
- Dimensions 156mm x 234mm x 25mm

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.Â 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.Â 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.

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.

**Review**

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 Nather, Zentralblatt MATH, Vol. 1238, 2012)

Nguyen, New Mexico State University, Las Cruces

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