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
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Author : Shoumei Li
language : en
Publisher:
Release Date : 2014-01-15
Limit Theorems And Applications Of Set Valued And Fuzzy Set Valued Random Variables written by Shoumei Li and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Limit Theorems And Applications Of Set Valued And Fuzzy Set Valued Random Variables
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Author : Shoumei Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Limit Theorems And Applications Of Set Valued And Fuzzy Set Valued Random Variables written by Shoumei Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
Limit Theorems And Applications Of Set Valued And Fuzzy Set Valued Random Variables
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Author : Shoumei Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-10-31
Limit Theorems And Applications Of Set Valued And Fuzzy Set Valued Random Variables written by Shoumei Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-10-31 with Mathematics categories.
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 Hölmander'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.
Theory Of Random Sets
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Author : Ilya Molchanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-05-11
Theory Of Random Sets written by Ilya Molchanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-05-11 with Mathematics categories.
This is the first systematic exposition of random sets theory since Matheron (1975), with full proofs, exhaustive bibliographies and literature notes Interdisciplinary connections and applications of random sets are emphasized throughout the book An extensive bibliography in the book is available on the Web at http://liinwww.ira.uka.de/bibliography/math/random.closed.sets.html, and is accompanied by a search engine
Nonlinear Mathematics For Uncertainty And Its Applications
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Author : Shoumei Li
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-21
Nonlinear Mathematics For Uncertainty And Its Applications written by Shoumei Li and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-21 with Technology & Engineering categories.
This volume is a collection of papers presented at the international conference on Nonlinear Mathematics for Uncertainty and Its Applications (NLMUA2011), held at Beijing University of Technology during the week of September 7--9, 2011. The conference brought together leading researchers and practitioners involved with all aspects of nonlinear mathematics for uncertainty and its applications. Over the last fifty years there have been many attempts in extending the theory of classical probability and statistical models to the generalized one which can cope with problems of inference and decision making when the model-related information is scarce, vague, ambiguous, or incomplete. Such attempts include the study of nonadditive measures and their integrals, imprecise probabilities and random sets, and their applications in information sciences, economics, finance, insurance, engineering, and social sciences. The book presents topics including nonadditive measures and nonlinear integrals, Choquet, Sugeno and other types of integrals, possibility theory, Dempster-Shafer theory, random sets, fuzzy random sets and related statistics, set-valued and fuzzy stochastic processes, imprecise probability theory and related statistical models, fuzzy mathematics, nonlinear functional analysis, information theory, mathematical finance and risk managements, decision making under various types of uncertainty, and others.
Mathematical Theory Of Fuzzy Sets
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Author : Hsien-Chung Wu
language : en
Publisher: CRC Press
Release Date : 2024-12-13
Mathematical Theory Of Fuzzy Sets written by Hsien-Chung Wu and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-13 with Mathematics categories.
Mathematical Theory of Fuzzy Sets presents the mathematical theory of non-normal fuzzy sets such that it can be rigorously used as a basic tool to study engineering and economic problems under a fuzzy environment. It may also be used as a textbook at the graduate level, or as a reference for researchers. The book explores the current state of affairs in set operations of fuzzy sets, arithmetic operations of fuzzy interval, and fuzzification of crisp functions, which are frequently adopted to model engineering and economic problems with fuzzy uncertainty. In particular, the concepts of gradual sets and gradual elements are presented in order to cope with the difficulty of considering elements of fuzzy sets like considering elements of crisp sets. Features Many extensions and equivalences for the essence of non-normal fuzzy sets Generalization of extension principle Presentation of the concepts of gradual sets and gradual elements
Soft Methods For Handling Variability And Imprecision
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Author : Didier Dubois
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-01
Soft Methods For Handling Variability And Imprecision written by Didier Dubois and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-01 with Mathematics categories.
Probability theory has been the only well-founded theory of uncertainty for a long time. It was viewed either as a powerful tool for modelling random phenomena, or as a rational approach to the notion of degree of belief. During the last thirty years, in areas centered around decision theory, artificial intelligence and information processing, numerous approaches extending or orthogonal to the existing theory of probability and mathematical statistics have come to the front. The common feature of those attempts is to allow for softer or wider frameworks for taking into account the incompleteness or imprecision of information. Many of these approaches come down to blending interval or fuzzy interval analysis with probabilistic methods. This book gathers contributions to the 4th International Conference on Soft methods in Probability and Statistics. Its aim is to present recent results illustrating such new trends that enlarge the statistical and uncertainty modeling traditions, towards the handling of incomplete or subjective information. It covers a broad scope ranging from philosophical and mathematical underpinnings of new uncertainty theories, with a stress on their impact in the area of statistics and data analysis, to numerical methods and applications to environmental risk analysis and mechanical engineering. A unique feature of this collection is to establish a dialogue between fuzzy random variables and imprecise probability theories.
Combining Soft Computing And Statistical Methods In Data Analysis
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Author : Christian Borgelt
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-10-12
Combining Soft Computing And Statistical Methods In Data Analysis written by Christian Borgelt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-12 with Technology & Engineering categories.
Over the last forty years there has been a growing interest to extend probability theory and statistics and to allow for more flexible modelling of imprecision, uncertainty, vagueness and ignorance. The fact that in many real-life situations data uncertainty is not only present in the form of randomness (stochastic uncertainty) but also in the form of imprecision/fuzziness is but one point underlining the need for a widening of statistical tools. Most such extensions originate in a "softening" of classical methods, allowing, in particular, to work with imprecise or vague data, considering imprecise or generalized probabilities and fuzzy events, etc. About ten years ago the idea of establishing a recurrent forum for discussing new trends in the before-mentioned context was born and resulted in the first International Conference on Soft Methods in Probability and Statistics (SMPS) that was held in Warsaw in 2002. In the following years the conference took place in Oviedo (2004), in Bristol (2006) and in Toulouse (2008). In the current edition the conference returns to Oviedo. This edited volume is a collection of papers presented at the SMPS 2010 conference held in Mieres and Oviedo. It gives a comprehensive overview of current research into the fusion of soft methods with probability and statistics.
Advances In Natural Computation Fuzzy Systems And Knowledge Discovery
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Author : Quan Xie
language : en
Publisher: Springer Nature
Release Date : 2022-01-04
Advances In Natural Computation Fuzzy Systems And Knowledge Discovery written by Quan Xie and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-04 with Technology & Engineering categories.
This book consists of papers on the recent progresses in the state of the art in natural computation, fuzzy systems and knowledge discovery. The book can be useful for researchers, including professors, graduate students, as well as R & D staff in the industry, with a general interest in natural computation, fuzzy systems and knowledge discovery. The work printed in this book was presented at the 2021 17th International Conference on Natural Computation, Fuzzy Systems and Knowledge Discovery (ICNC-FSKD 2021, 24–26 July 2021, Guiyang, China). All papers were rigorously peer-reviewed by experts in the areas.
Soft Methods For Integrated Uncertainty Modelling
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Author : Jonathan Lawry
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-10-08
Soft Methods For Integrated Uncertainty Modelling written by Jonathan Lawry and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-10-08 with Computers categories.
The idea of soft computing emerged in the early 1990s from the fuzzy systems c- munity, and refers to an understanding that the uncertainty, imprecision and ig- rance present in a problem should be explicitly represented and possibly even - ploited rather than either eliminated or ignored in computations. For instance, Zadeh de?ned ‘Soft Computing’ as follows: Soft computing differs from conventional (hard) computing in that, unlike hard computing, it is tolerant of imprecision, uncertainty and partial truth. In effect, the role model for soft computing is the human mind. Recently soft computing has, to some extent, become synonymous with a hybrid approach combining AI techniques including fuzzy systems, neural networks, and biologically inspired methods such as genetic algorithms. Here, however, we adopt a more straightforward de?nition consistent with the original concept. Hence, soft methods are understood as those uncertainty formalisms not part of mainstream s- tistics and probability theory which have typically been developed within the AI and decisionanalysiscommunity.Thesearemathematicallysounduncertaintymodelling methodologies which are complementary to conventional statistics and probability theory.