Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables

  • Shoumei Li
  • Yukio Ogura
  • Vladik Kreinovich

Part of the Theory and Decision Library book series (TDLB, volume 43)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Limit Theorems of Set-Valued and Fuzzy Set-Valued Random Variables

    1. Front Matter
      Pages xiii-xiii
    2. Shoumei Li, Yukio Ogura, Vladik Kreinovich
      Pages 1-39
    3. Shoumei Li, Yukio Ogura, Vladik Kreinovich
      Pages 41-85
    4. Shoumei Li, Yukio Ogura, Vladik Kreinovich
      Pages 87-115
    5. Shoumei Li, Yukio Ogura, Vladik Kreinovich
      Pages 117-160
    6. Shoumei Li, Yukio Ogura, Vladik Kreinovich
      Pages 161-190
    7. Shoumei Li, Yukio Ogura, Vladik Kreinovich
      Pages 191-219
    8. Shoumei Li, Yukio Ogura, Vladik Kreinovich
      Pages 221-234
  3. Practical Applications of Set-Valued Random Variables

    1. Front Matter
      Pages 251-251
    2. Shoumei Li, Yukio Ogura, Vladik Kreinovich
      Pages 253-293
    3. Shoumei Li, Yukio Ogura, Vladik Kreinovich
      Pages 295-354
    4. Shoumei Li, Yukio Ogura, Vladik Kreinovich
      Pages 355-372
  4. Back Matter
    Pages 387-394

About this book

Introduction

After the pioneering works by Robbins {1944, 1945) and Choquet (1955), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall {1974) and Matheron {1975). It is well known that the theory of set-valued random variables is a natural extension of that of general real-valued random variables or random vectors. However, owing to the topological structure of the space of closed sets and special features of set-theoretic operations ( cf. Beer [27]), set-valued random variables have many special properties. This gives new meanings for the classical probability theory. As a result of the development in this area in the past more than 30 years, the theory of set-valued random variables with many applications has become one of new and active branches in probability theory. In practice also, we are often faced with random experiments whose outcomes are not numbers but are expressed in inexact linguistic terms.

Keywords

Martingal Martingale Random variable fuzzy optimization

Authors and affiliations

  • Shoumei Li
    • 1
  • Yukio Ogura
    • 2
  • Vladik Kreinovich
    • 3
  1. 1.Beijing Polytechnic UniversityBeijingThe Peoples Republic of China
  2. 2.Saga UniversitySagaJapan
  3. 3.University of Texas El PasoEl PasoUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-015-9932-0
  • Copyright Information Springer Science+Business Media B.V. 2002
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-90-481-6139-3
  • Online ISBN 978-94-015-9932-0
  • About this book
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