© 2015

Uncertainty Theory

  • The first book available on the research of human uncertainty

  • Covering three different main areas of uncertainty theory: uncertain variable, uncertain set and uncertain process

  • Presents applications of uncertainty theory in industrial engineering, automation and finance


Part of the Springer Uncertainty Research book series (SUR)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Baoding Liu
    Pages 1-8
  3. Baoding Liu
    Pages 9-28
  4. Baoding Liu
    Pages 29-103
  5. Baoding Liu
    Pages 105-125
  6. Baoding Liu
    Pages 127-135
  7. Baoding Liu
    Pages 137-149
  8. Baoding Liu
    Pages 151-155
  9. Baoding Liu
    Pages 157-167
  10. Baoding Liu
    Pages 169-175
  11. Baoding Liu
    Pages 177-220
  12. Baoding Liu
    Pages 221-246
  13. Baoding Liu
    Pages 247-258
  14. Baoding Liu
    Pages 259-282
  15. Baoding Liu
    Pages 283-302
  16. Baoding Liu
    Pages 303-318
  17. Baoding Liu
    Pages 319-345
  18. Baoding Liu
    Pages 347-363
  19. Back Matter
    Pages 365-487

About this book


When no samples are available to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degree that each event will happen. Perhaps some people think that the belief degree should be modeled by subjective probability or fuzzy set theory. However, it is usually inappropriate because both of them may lead to counterintuitive results in this case.

In order to rationally deal with belief degrees, uncertainty theory was founded in 2007 and subsequently studied by many researchers. Nowadays, uncertainty theory has become a branch of axiomatic mathematics for modeling belief degrees.

This is an introductory textbook on uncertainty theory, uncertain programming, uncertain statistics, uncertain risk analysis, uncertain reliability analysis, uncertain set, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation. This textbook also shows applications of uncertainty theory to scheduling, logistics, networks, data mining, control, and finance.


Chance Theory Fuzzy Theory Human Uncertainty Risk Analysis Uncertain Process Uncertain Set Uncertain Variable

Authors and affiliations

  1. 1.Department of Mathematical SciencesTsinghua UniversityBeijingChina

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