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Uncertainty Theory

  • Book
  • © 2007

Overview

Authors:
  1. Dr. Baoding Liu

    1. Uncertainty Theory Laboratory Department of Mathematical Sciences, Tsinghua University, China

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  • Completely rewritten second edition
  • Self contained, comprehensive and up-to-date presentation of uncertainty theory
  • Axiomatic approach to equip the reader to deal with uncertainty

Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 154)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-X
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  2. Prerequisites

    • Dr. Baoding Liu
    Pages 1-18

  3. Probability Theory

    • Dr. Baoding Liu
    Pages 19-80

  4. Credibility Theory

    • Dr. Baoding Liu
    Pages 81-156

  5. Chance Theory

    • Dr. Baoding Liu
    Pages 157-204

  6. Uncertainty Theory

    • Dr. Baoding Liu
    Pages 205-234

  7. Supplements

    • Dr. Baoding Liu
    Pages 235-236

  8. Back Matter

    Pages 237-255
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Keywords

About this book

It was generally believed that the study of probability theory was started by Pascal and Fermat in 1654 when they succeeded in deriving the exact probabilitiesforcertaingamblingproblem. Greatprogresswasachievedwhen VonMisesinitializedtheconceptofsamplespace, and?lledthegapebetween probability theory and measure theory in 1931. An axiomatic foundation of probabilitytheorywasgivenbyKolmogoro?inhisFoundationsofProbability Theory of 1933. Since then, probability theory has been developed steadily and has been widely applied in science and engineering. Probability theory will be introduced in Chapter 2. Fuzzy set was initiated by Zadeh via membership function in 1965, and was well developed and applied in a wide variety of real problems. In order to measure a fuzzy event, Zadeh proposed the concept of possibility measure in 1978. Although possibility measure has been widely used, it has no se- duality property. However, a self-dual measure is absolutely needed in both theory and practice. In order to de?ne a self-dual measure, Liu and Liu gave the concept of credibility measure in 2002. Credibility theory is a branch of mathematics that studies the behavior of fuzzy phenomena. An axiomatic foundation of credibility theory was given by Liu in his Uncertainty Theory of 2004. Chapter 3 will provide the credibility theory. Sometimes, fuzziness and randomness simultaneously appear in a system.

Authors and Affiliations

  • Uncertainty Theory Laboratory Department of Mathematical Sciences, Tsinghua University, China

    Dr. Baoding Liu

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