Overview
This book presents a clear, systematic treatment of convergence theorems of set-valued random variables (random sets) and fuzzy set-valued random variables (random fuzzy sets). Topics such as strong laws of large numbers and central limit theorems, including new results in connection with the theory of empirical processes are covered. The author's own recent developments on martingale convergence theorems and their applications to data processing are also included. The mathematical foundations along with a clear explanation such as Holmander's embedding theorem, notions of various convergence of sets and fuzzy sets, Aumann integrals, conditional expectations, selection theorems, measurability and integrability arguments for both set-valued and fuzzy set-valued random variables and newly obtained optimizations techniques based on invariant properties are also given.
Full Product Details
Author: Shoumei Li ,
Y. Ogura ,
V. Kreinovich
Publisher: Springer
Imprint: Springer
Edition: Softcover reprint of hardcover 1st ed. 2002
Volume: 43
Dimensions:
Width: 16.00cm
, Height: 2.10cm
, Length: 24.00cm
Weight: 0.710kg
ISBN: 9789048161393
ISBN 10: 9048161398
Pages: 394
Publication Date: 06 December 2010
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: Out of stock
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.
Reviews
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)
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)
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)
