Overview

This title 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 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 H""olmander'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.

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9781402009181

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From the reviews: <p> The book under review is devoted to set-valued and fuzzy set-valued random variables which are generalizations of ordinary random variables a ] . 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)

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