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Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables: 43 (Theory and Decision Library B) - Hardcover
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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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"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)
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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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Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables (Theory and Decision Library B, 43)
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Zustand: Fine. 407 pp., hardcover, LIKE NEW. - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country. Bestandsnummer des Verkäufers ZB1302351
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Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables
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Hardcover. Zustand: Fine. Signed. First Edition. No DJ. Signed and inscribed to previous owner by Vladik Kreinovich. Previous owner was Dr. Lofti A. Zadeh, Professor, University of California, Berkeley. No other markings in book. Lightly read. Lotfi Zadeh is credited, along with John R. Ragazzini, in 1952, with having pioneered the development of the z-transform method in discrete time signal processing and analysis. These methods are now standard in digital signal processing, digital control, and other discrete-time systems used in industry and research. He is an editor of International Journal of Computational Cognition. 391pp. Bestandsnummer des Verkäufers 3007733
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Limit Theorems And Applications Of Set-valued And Fuzzy Set-valued Random Variables (theory And Decision Library B:)
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Limit Theorems And Applications Of Set-valued And Fuzzy Set-valued Random Variables (theory And Decision Library B:)
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Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables (Theory and Decision Library B, 43)
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Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables (Theory and Decision Library B, 43)
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Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables
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Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables (Theory and Decision Library B, 43)
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Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables (Hardcover)
Verlag:
Kluwer Academic Publishers, New York, NY, 2002
ISBN 10: 1402009186
ISBN 13: 9781402009181
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Hardcover. Zustand: new. Hardcover. 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. 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). Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9781402009181
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Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables
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