Uncertainty Theory

A Branch of Mathematics for Modeling Human Uncertainty

  • Baoding Liu

Part of the Studies in Computational Intelligence book series (SCI, volume 300)

Table of contents

  1. Front Matter
  2. Baoding Liu
    Pages 1-79
  3. Baoding Liu
    Pages 81-113
  4. Baoding Liu
    Pages 115-123
  5. Baoding Liu
    Pages 125-130
  6. Baoding Liu
    Pages 131-138
  7. Baoding Liu
    Pages 139-145
  8. Baoding Liu
    Pages 147-161
  9. Baoding Liu
    Pages 163-175
  10. Baoding Liu
    Pages 177-186
  11. Baoding Liu
    Pages 187-213
  12. Baoding Liu
    Pages 215-223
  13. Back Matter

About this book


Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Uncertainty is any concept that satisfies the axioms of uncertainty theory. Thus uncertainty is neither randomness nor fuzziness. It is also known from some surveys that a lot of phenomena do behave like uncertainty. How do we model uncertainty? How do we use uncertainty theory? In order to answer these questions, this book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory, including uncertain programming, uncertain risk analysis, uncertain reliability analysis, uncertain process, uncertain calculus, uncertain differential equation, uncertain logic, uncertain entailment, and uncertain inference. Mathematicians, researchers, engineers, designers, and students in the field of mathematics, information science, operations research, system science, industrial engineering, computer science, artificial intelligence, finance, control, and management science will find this work a stimulating and useful reference.


Credibility Theory Fuzzy Sets Random Fuzzy Theory Rough Sets Uncertainty Theory

Authors and affiliations

  • Baoding Liu
    • 1
  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-13959-8
  • Copyright Information Springer Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering
  • Print ISBN 978-3-642-13958-1
  • Online ISBN 978-3-642-13959-8
  • Series Print ISSN 1860-949X
  • Series Online ISSN 1860-9503
  • About this book