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Computing Statistics under Interval and Fuzzy Uncertainty

Applications to Computer Science and Engineering

  • Hung T. Nguyen
  • Vladik Kreinovich
  • Berlin Wu
  • Gang Xiang

Part of the Studies in Computational Intelligence book series (SCI, volume 393)

Table of contents

  1. Front Matter
  2. 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

    1. Front Matter
      Pages 1-1
    2. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 3-8
    3. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 9-10
    4. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 11-17
    5. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 19-24
    6. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 25-27
    7. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 29-33
    8. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 35-45
    9. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 47-50
    10. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 55-58
  3. Algorithms for Computing Statistics under Interval and Fuzzy Uncertainty

    1. Front Matter
      Pages 59-59
    2. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 61-61
    3. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 63-63
    4. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 65-66
    5. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 67-78
    6. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 79-94
    7. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 95-117
    8. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 119-127
    9. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 129-151
    10. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 153-166
    11. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 169-171
    12. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 173-176
    13. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 177-180
    14. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 181-191
    15. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 193-209
    16. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 211-219
    17. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 221-224
    18. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 225-234
  4. Towards Computing Statistics under Interval and Fuzzy Uncertainty: Gauging the Quality of the Input Data

    1. Front Matter
      Pages 235-235
    2. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 237-242
    3. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 243-248
  5. Applications

    1. Front Matter
      Pages 249-249
    2. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 261-264
    3. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 265-275
    4. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 277-281
    5. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 283-287
    6. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 299-304
    7. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 305-316
    8. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 317-329
  6. Beyond Interval and Fuzzy Uncertainty

    1. Front Matter
      Pages 331-331
    2. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 333-334
    3. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 335-347
    4. Hung T. Nguyen, Vladik Kreinovich, Berlin Wu, Gang Xiang
      Pages 349-355

About this book

Introduction

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.

Keywords

Fuzziness Fuzzy Uncertainty Interval Uncertainty Soft Computing

Authors and affiliations

  • Hung T. Nguyen
    • 1
  • Vladik Kreinovich
    • 2
  • Berlin Wu
    • 3
  • Gang Xiang
    • 4
  1. 1.Department of EconomicsChiangMai UniversityChiangmaiThailand
  2. 2.Department of Computer ScienceUniversity of Texas at El PasoEl PasoUSA
  3. 3.Department of Mathematical SciencesNational Chengchi UniversityTaipeiTaiwan
  4. 4.Applied Biomathematics, Inc.SetauketUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-24905-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-24904-4
  • Online ISBN 978-3-642-24905-1
  • Series Print ISSN 1860-949X
  • Series Online ISSN 1860-9503
  • Buy this book on publisher's site