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Probabilistic Analysis of Belief Functions

  • Book
  • © 2001

Overview

Authors:
  1. Ivan Kramosil

    1. Academy of Sciences of the Czech Republic, Prague, Czech Republic

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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Introduction

    • Ivan Kramosil
    Pages 1-7

  3. Preliminaries on Axiomatic Probability Theory

    • Ivan Kramosil
    Pages 9-20

  4. Probabilistic Model of Decision Making under Uncertainty

    • Ivan Kramosil
    Pages 21-31

  5. Basic Elements of Dempster-Shafer Theory

    • Ivan Kramosil
    Pages 33-44

  6. Elementary Properties of Belief Functions

    • Ivan Kramosil
    Pages 45-56

  7. Probabilistic Analysis of Dempster Combination Rule

    • Ivan Kramosil
    Pages 57-67

  8. Nonspecificity Degrees of Basic Probability Assignments

    • Ivan Kramosil
    Pages 69-82

  9. Belief Functions Induced by Partial Compatibility Relations

    • Ivan Kramosil
    Pages 83-99

  10. Belief Functions over Infinite State Spaces

    • Ivan Kramosil
    Pages 101-121

  11. Boolean Combinations of Set-Valued Random Variables

    • Ivan Kramosil
    Pages 123-129

  12. Belief Functions with Signed and Nonstandard Values

    • Ivan Kramosil
    Pages 131-155

  13. Jordan Decomposition of Signed Belief Functions

    • Ivan Kramosil
    Pages 157-168

  14. Monte-Carlo Estimations for Belief Functions

    • Ivan Kramosil
    Pages 169-184

  15. Boolean—Valued and Boolean—Like Processed Belief Functions

    • Ivan Kramosil
    Pages 185-205

  16. References

    • Ivan Kramosil
    Pages 207-212

  17. Back Matter

    Pages 213-214
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Keywords

About this book

Inspired by the eternal beauty and truth of the laws governing the run of stars on heavens over his head, and spurred by the idea to catch, perhaps for the smallest fraction of the shortest instant, the Eternity itself, man created such masterpieces of human intellect like the Platon's world of ideas manifesting eternal truths, like the Euclidean geometry, or like the Newtonian celestial me­ chanics. However, turning his look to the sub-lunar world of our everyday efforts, troubles, sorrows and, from time to time but very, very seldom, also our successes, he saw nothing else than a world full of uncertainty and tem­ porariness. One remedy or rather consolation was that of the deep and sage resignation offered by Socrates: I know, that I know nothing. But, happy or unhappy enough, the temptation to see and to touch at least a very small por­ tion of eternal truth also under these circumstances and behind phenomena charged by uncertainty was too strong. Probability theory in its most sim­ ple elementary setting entered the scene. It happened in the same, 17th and 18th centuries, when celestial mechanics with its classical Platonist paradigma achieved its greatest triumphs. The origins of probability theory were inspired by games of chance like roulettes, lotteries, dices, urn schemata, etc. and probability values were simply defined by the ratio of successful or winning results relative to the total number of possible outcomes.

Authors and Affiliations

  • Academy of Sciences of the Czech Republic, Prague, Czech Republic

    Ivan Kramosil

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