Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables: 43 (Theory and Decision Library B) - Hardcover

Li, Shoumei; Kreinovich, V.; Ogura, Y.

 
9781402009181: Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables: 43 (Theory and Decision Library B)
Hardcover
ISBN 10: 1402009186 ISBN 13: 9781402009181
Verlag: Springer, 2002

Inhaltsangabe

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.

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Críticas

From the reviews:

"The book under review is devoted to set-valued and fuzzy set-valued random variables which are generalizations of ordinary random variables ... . the book is a useful reference for mathematicians who are working on set-valued or fuzzy set-valued random variables and related topics. Here one can find in one place results that are scattered throughout the literature. All the theorems are proven and the historical comments give the reader a wider perspective." (Osmo Kaleva, Mathematical Reviews, Issue 2005 b)

Reseña del editor

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Springer
Erscheinungsdatum
2002
Sprache
Englisch
ISBN 10 
1402009186
ISBN 13 
9781402009181
Einband
Tapa dura
Anzahl der Seiten
412
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
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Hamburg
Deutschland

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