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Computing Statistics Under Interval and Fuzzy Uncertainty

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.
Computing Statistics Under Interval and Fuzzy Uncertainty
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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.
Nguyen, New Mexico State University, Las Cruces
Part I Computing Statistics under Interval and Fuzzy Uncertainty: Formulation of the Problem and an Overview of General Techniques Which Can Be Used for Solving this Problem.- Part II Algorithms for Computing Statistics Under Interval and Fuzzy Uncertainty.- Part III Towards Computing Statistics under Interval and Fuzzy Uncertainty: Gauging the Quality of the Input Data.- Part IV Applications.- Part V Beyond Interval and Fuzzy Uncertainty.
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)
Author
Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Series
Studies in Computational Intelligence
Year
2011
ISBN-10
3642249043
ISBN-13
9783642249044
Format
Hardcover
Imprint
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Place of Publication
Berlin
Country of Publication
Germany
DEWEY
006.3
Short Title
COMPUTING STATISTICS UNDER INT
Edition Description
2012
Language
English
Media
Book
Series Number
393
Residence
US
Birth
1944
Subtitle
Applications to Computer Science and Engineering
Publication Date
2011-11-02
Illustrations
biography
Pages
444
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