5 edition of **Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables (Theory and Decision Library B)** found in the catalog.

- 166 Want to read
- 38 Currently reading

Published
**October 31, 2002**
by Springer
.

Written in English

- Fuzzy set theory,
- Set theory,
- Probabilities,
- Mathematics,
- Science/Mathematics,
- Probability & Statistics - General,
- General,
- Mathematics / Logic,
- Limit theorems (Probability th,
- Limit theorems (Probability theory),
- Random variables

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 413 |

ID Numbers | |

Open Library | OL8370306M |

ISBN 10 | 1402009186 |

ISBN 10 | 9781402009181 |

The primary aim of the book is to provide a systematic development of the theory of metric spaces of normal, upper semicontinuous fuzzy convex fuzzy sets with compact support sets, mainly on the base space ℜ n. An additional aim is to sketch selected applications in which these metric space results and methods are essential for a thorough. Applications of Continuous Mathematics to Computer Science by Hung T. Nguyen, Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables. Shoumei Li. 06 Dec Paperback. US$ US$ Save US$ Add to basket.

Applications of Category Theory to Fuzzy Subsets by Stephen Ernest Rodabaugh, , available at Book Depository with free delivery worldwide. Abstract. We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors).Cited by: 8.

Fuzzy random variables (or fuzzy variables) generalize random variables and random vectors; they also generalize random sets [ The expected value of a fuzzy variable is a natural generalization of the integral of a set- valued function [2]. Kwakernaak [ introduced the notion of a fuzzy random variable as a. In this paper, with a new notion of exponential independence for random variables under an upper expectation, we establish a kind of strong laws of large numbers for capacities. Our limit theorems show that the cluster points of empirical averages not only lie in the interval between the upper expectation and the lower expectation with lower probability one, but such an interval also is Cited by: 4.

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: Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables (Theory and Decision Library B) (): Shoumei Li, Cited by: Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables (Theory and Decision Library B Book 43) - Kindle edition by Shoumei Li, Ogura, Y., Kreinovich, V.

Download it once and read it on your Kindle device, PC, phones or tablets. Use features like bookmarks, note taking and highlighting while reading Limit Theorems and Applications of Set Manufacturer: Springer. Over past 40 years there were many important works for set-valued and fuzzy set-valued random variables related to strong law of large numbers [5,14,41], center limit theorems [1, 26, 27] and.

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. ISBN: OCLC Number: Description: 1 online resource (xiii, pages) Contents: I Limit Theorems of Set-Valued and Fuzzy Set-Valued Random Variables The Space of Set-Valued Random Variables The Aumann Integral and the Conditional Expectation of a Set-Valued Random Variable Strong Laws of Large Numbers.

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.

ISBN: OCLC Number: Description: xii, pages ; 25 cm: Contents: Limit Theorems of Set-Valued and Fuzzy Set-Valued Random Variables --The Space of Set-Valued Random Variables --Hyperspaces of a Banach Space --The Hausdorff Metric in Hyperspaces and An Embedding Theorem --Convergences in Hyperspaces --Set.

Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables Shoumei Li, Yukio Ogura, Vladik Kreinovich (auth.) After the pioneering works by Robbins {, ) and Choquet (), the notation of a set-valued random variable (called a random closed set in literatures) was systematically introduced by Kendall { Li S., Ogura Y., Kreinovich V.

() Fuzzy Set-Valued Random Variables. In: Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables.

Theory and Decision Library (Series B: Mathematical and Statistical Methods), vol Author: Shoumei Li, Yukio Ogura, Vladik Kreinovich. We give central limit theorems for generalized set-valued random variables whose level sets are compact both in R d or in a Banach space under milder conditions than those obtained recently by the latter two authors.

Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables, Kluwer Academic ()Cited by: In this paper, we discuss fuzzy set-valued Gaussian processes based on the results of [S. Li, Y. Ogura, V. Kreinovich, Limit Theorems and Applications of Set.

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 : Shoumei Li; Y Ogura; V Kreinovich. All rights at reproduction in any form reserved.

PURI AND RALESCU Fuzzy random variables (or fuzzy variables) generalize random variables and random vectors; they also generalize random sets [15].

The expected value of a fuzzy variable is a natural generalization of the integral of a set- valued function [2].Cited by: Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables (Theory and Decision Library B) ( ed.

Edition) by Shoumei Li, Yukio Ogura, Vladik Kreinovich Hardcover, Pages, Published ISBN / ISBN / Need it Fast. 2 day shipping options After the pioneering Book Edition: Ed.

Edition. A decomposition theorem for fuzzy set-valued random variables. Authors: V., Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables. Kluwer Academic Publishers Group, Dordrecht. [7] Molchanov, I., Theory of Random Sets. by: 9. 2 Preliminaries on set-valued random variables Throughout this paper, we assume that (Ω,A,µ) is a nonatomic complete probability space, (X,∥∥) is a real separable Banach space, N is the set of nature numbers, K(X) is the familyof all nonempty closed subsets of X, and Kbc(X) is the family of all nonempty bounded closed convex subsets of X.

Let A and B be two nonempty subsets of X. Theory and Decision Library B Ser.: Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables 43 by V. Kreinovich, Y. Ogura, Shoumei Shoumei Li Unknown, Pages, Published Pages: The main mathematical model for fuzzy data is a fuzzy random variable.

A good theoretical treatment is in the Li-Ogura-Kreinovich book (Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables). A less mathematical, yet still theoretical book is Bandemer and Nather's Fuzzy Data Analysis (however note the date).

() Tools for fuzzy random variables: Embeddings and measurabilities. () A random approximation of set valued càdlàg functions. () Limit theorems for extremes with random sample size. Advances in Applied Probability() Limit theorems for extremes with random sample size.

Cited by: Theory of Probability & Its ApplicationsThe Concepts of Tightness for Fuzzy Set Valued Random Variables. International Journal of Fuzzy Logic and Intelligent SystemsSome limit theorems for independent random processes at random points in time and random elements defined by by:.

Full Description:" Strong Limit Theorems in Non-Commutative Probability gives motivation to analyze information and is also useful when criticizing plots; or it is a well-written section if the character is properly designed, if the narrative sounds innocent, etc.

If you ever have the opportunity to discuss the book with others, you will be able to clearly tell their views, as you .Vladik Kreinovich’s most popular book is Applications of Interval Computations. Limit Theorems and Applications of Set-Valued and Fuzzy Set-Valued Random Variables by.

Shoumei Li, Y. Ogura, Vladik Kreinovich.Applications of Random Set Theory in Econometrics 7 Random Sets The conventional theory of random sets deals with random closed sets.

An advan-tage of this approach is that random points (i.e. random sets that are singletons) are closed, and so the theory of random closed sets includes the classical caseFile Size: KB.