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Uncertainty Theory

Author: Baoding Liu

Publisher: Springer

Published: 2007-09-14

Total Pages: 255

ISBN-13: 3540731652

This book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory. The purpose is to equip the readers with an axiomatic approach to deal with uncertainty. For this new edition the entire text has been totally rewritten. The chapters on chance theory and uncertainty theory are completely new. Mathematicians, researchers, engineers, designers, and students will find this work a stimulating and useful reference.

Uncertainty Theory

Author: Baoding Liu

Publisher: Springer Science & Business Media

Published: 2011-11-07

Total Pages: 350

ISBN-13: 3642139582

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Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Uncertainty is any concept that satisfies the axioms of uncertainty theory. Thus uncertainty is neither randomness nor fuzziness. It is also known from some surveys that a lot of phenomena do behave like uncertainty. How do we model uncertainty? How do we use uncertainty theory? In order to answer these questions, this book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory, including uncertain programming, uncertain risk analysis, uncertain reliability analysis, uncertain process, uncertain calculus, uncertain differential equation, uncertain logic, uncertain entailment, and uncertain inference. Mathematicians, researchers, engineers, designers, and students in the field of mathematics, information science, operations research, system science, industrial engineering, computer science, artificial intelligence, finance, control, and management science will find this work a stimulating and useful reference.

Decision Making Under Uncertainty

Author: Mykel J. Kochenderfer

Publisher: MIT Press

Published: 2015-07-24

Total Pages: 350

ISBN-13: 0262331713

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An introduction to decision making under uncertainty from a computational perspective, covering both theory and applications ranging from speech recognition to airborne collision avoidance. Many important problems involve decision making under uncertainty—that is, choosing actions based on often imperfect observations, with unknown outcomes. Designers of automated decision support systems must take into account the various sources of uncertainty while balancing the multiple objectives of the system. This book provides an introduction to the challenges of decision making under uncertainty from a computational perspective. It presents both the theory behind decision making models and algorithms and a collection of example applications that range from speech recognition to aircraft collision avoidance. Focusing on two methods for designing decision agents, planning and reinforcement learning, the book covers probabilistic models, introducing Bayesian networks as a graphical model that captures probabilistic relationships between variables; utility theory as a framework for understanding optimal decision making under uncertainty; Markov decision processes as a method for modeling sequential problems; model uncertainty; state uncertainty; and cooperative decision making involving multiple interacting agents. A series of applications shows how the theoretical concepts can be applied to systems for attribute-based person search, speech applications, collision avoidance, and unmanned aircraft persistent surveillance. Decision Making Under Uncertainty unifies research from different communities using consistent notation, and is accessible to students and researchers across engineering disciplines who have some prior exposure to probability theory and calculus. It can be used as a text for advanced undergraduate and graduate students in fields including computer science, aerospace and electrical engineering, and management science. It will also be a valuable professional reference for researchers in a variety of disciplines.

Toeplitz Approach to Problems of the Uncertainty Principle

Author: Alexei Poltoratski

Publisher: American Mathematical Soc.

Published: 2015-03-07

Total Pages: 216

ISBN-13: 1470420171

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The Uncertainty Principle in Harmonic Analysis (UP) is a classical, yet rapidly developing, area of modern mathematics. Its first significant results and open problems date back to the work of Norbert Wiener, Andrei Kolmogorov, Mark Krein and Arne Beurling. At present, it encompasses a large part of mathematics, from Fourier analysis, frames and completeness problems for various systems of functions to spectral problems for differential operators and canonical systems. These notes are devoted to the so-called Toeplitz approach to UP which recently brought solutions to some of the long-standing problems posed by the classics. After a short overview of the general area of UP the discussion turns to the outline of the new approach and its results. Among those are solutions to Beurling's Gap Problem in Fourier analysis, the Type Problem on completeness of exponential systems, a problem by Pólya and Levinson on sampling sets for entire functions, Bernstein's problem on uniform polynomial approximation, problems on asymptotics of Fourier integrals and a Toeplitz version of the Beurling-Malliavin theory. One of the main goals of the book is to present new directions for future research opened by the new approach to the experts and young analysts. A co-publication of the AMS and CBMS.

Theory of Decision Under Uncertainty

Author: Itzhak Gilboa

Publisher: Cambridge University Press

Published: 2009-03-16

Total Pages: 216

ISBN-13: 052151732X

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This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories. It focuses on the meaning of probability, discussing some definitions and surveying their scope of applicability. The behavioral definition of subjective probability serves as a way to present the classical theories, culminating in Savage's theorem. The limitations of this result as a definition of probability lead to two directions - first, similar behavioral definitions of more general theories, such as non-additive probabilities and multiple priors, and second, cognitive derivations based on case-based techniques.

Middle Range Theory for Nursing, Fourth Edition

Author: Mary Jane Smith, PhD, RN, FAAN

Publisher: Springer Publishing Company

Published: 2018-03-10

Total Pages: 424

ISBN-13: 0826159923

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Three-time recipient of the AJN Book of the Year Award! Praise for the third edition: “This is an outstanding edition of this book. It has great relevance for learning about, developing, and using middle range theories. It is very user friendly, yet scholarly." Score: 90, 4 Stars -Doody's Medical Reviews The fourth edition of this invaluable publication on middle range theory in nursing reflects the most current theoretical advances in the field. With two additional chapters, new content incorporates exemplars that bridge middle range theory to advanced nursing practice and research. Additional content for DNP and PhD programs includes two new theories: Bureaucratic Caring and Self-Care of Chronic Illness. This user-friendly text stresses how theory informs practice and research in the everyday world of nursing. Divided into four sections, content sets the stage for understanding middle range theory by elaborating on disciplinary perspectives, an organizing framework, and evaluation of the theory. Middle Range Theory for Nursing, Fourth Edition presents a broad spectrum of 13 middle range theories. Each theory is broken down into its purpose, development, and conceptual underpinnings, and includes a model demonstrating the relationships among the concepts, and the use of the theory in research and practice. In addition, concept building for research through the lens of middle range theory is presented as a rigorous 10-phase process that moves from a practice story to a conceptual foundation. Exemplars are presented clarifying both the concept building process and the use of conceptual structures in research design. This new edition remains an essential text for advanced practice, theory, and research courses. New to the Fourth Edition: Reflects new theoretical advances Two completely new chapters New content for DNP and PhD programs Two new theories: Bureaucratic Caring and Self-Care of Chronic Illness Two articles from Advances in Nursing Science documenting a historical meta-perspective on middle range theory development Key Features: Provides a strong contextual foundation for understanding middle range theory Introduces the Ladder of Abstraction to clarify the range of nursing’s theoretical foundation Presents 13 middle range theories with philosophical, conceptual, and empirical dimensions of each theory Includes Appendix summarizing middle range theories from 1988 to 2016

Elements for a Theory of Decision in Uncertainty

Author: Jaime Gil-Aluja

Publisher: Springer Science & Business Media

Published: 1999-11-30

Total Pages: 354

ISBN-13: 9780792359876

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This book provides tools for making decisions in an environment of uncertainty. In Chapter 1 the author explains the most important aspects of the concept of relation. From this start arise the other three concepts that cover practically all processes from which decisions stem. These three concepts are: attribution from which the concept of assignment arises; and grouping, which includes the concept of an original function. The techniques presented, as well as the models and algorithms developed, constitute an invaluable aid for those who must make decisions. Audience: Researchers and graduate students interested in mathematics applied to economics and management.

Uncertainty

Author: David Lindley

Publisher: Anchor

Published: 2008-02-12

Total Pages: 274

ISBN-13: 0307389480

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The gripping, entertaining, and vividly-told narrative of a radical discovery that sent shockwaves through the scientific community and forever changed the way we understand the world. Werner Heisenberg’s “uncertainty principle” challenged centuries of scientific understanding, placed him in direct opposition to Albert Einstein, and put Niels Bohr in the middle of one of the most heated debates in scientific history. Heisenberg’s theorem stated that there were physical limits to what we could know about sub-atomic particles; this “uncertainty” would have shocking implications. In a riveting and lively account, David Lindley captures this critical episode and explains one of the most important scientific discoveries in history, which has since transcended the boundaries of science and influenced everything from literary theory to television.

Uncertainty and Information

Author: George J. Klir

Publisher: John Wiley & Sons

Published: 2005-11-22

Total Pages: 499

ISBN-13: 0471755567

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Deal with information and uncertainty properly and efficientlyusing tools emerging from generalized information theory Uncertainty and Information: Foundations of Generalized InformationTheory contains comprehensive and up-to-date coverage of resultsthat have emerged from a research program begun by the author inthe early 1990s under the name "generalized information theory"(GIT). This ongoing research program aims to develop a formalmathematical treatment of the interrelated concepts of uncertaintyand information in all their varieties. In GIT, as in classicalinformation theory, uncertainty (predictive, retrodictive,diagnostic, prescriptive, and the like) is viewed as amanifestation of information deficiency, while information isviewed as anything capable of reducing the uncertainty. A broadconceptual framework for GIT is obtained by expanding theformalized language of classical set theory to include moreexpressive formalized languages based on fuzzy sets of varioustypes, and by expanding classical theory of additive measures toinclude more expressive non-additive measures of varioustypes. This landmark book examines each of several theories for dealingwith particular types of uncertainty at the following fourlevels: * Mathematical formalization of the conceived type ofuncertainty * Calculus for manipulating this particular type ofuncertainty * Justifiable ways of measuring the amount of uncertainty in anysituation formalizable in the theory * Methodological aspects of the theory With extensive use of examples and illustrations to clarify complexmaterial and demonstrate practical applications, generoushistorical and bibliographical notes, end-of-chapter exercises totest readers' newfound knowledge, glossaries, and an Instructor'sManual, this is an excellent graduate-level textbook, as well as anoutstanding reference for researchers and practitioners who dealwith the various problems involving uncertainty and information. AnInstructor's Manual presenting detailed solutions to all theproblems in the book is available from the Wiley editorialdepartment.

Uncertainty in Economics

Author: Peter Diamond

Publisher: Academic Press

Published: 2014-05-10

Total Pages: 569

ISBN-13: 1483264505

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Uncertainty in Economics: Readings and Exercises provides information pertinent to the fundamental aspects of the economics of uncertainty. This book discusses ho uncertainty affects both individual behavior and standard equilibrium theory. Organized into three parts encompassing 30 chapters, this book begins with an overview of the relevance of expected utility maximization for positive and normative theories of individual choice. This text then examines the biases in judgments, which reveal some heuristics of thinking under uncertainty. Other chapters consider the effect of restricting trade in contingent commodities to those trades that can be affected through the stock and bond markets. This book discusses as well the individual problem of sequential choice and equilibria, which are built around the notion of sequential choice. The final chapter deals with an entirely different aspect of the economics of information and reverts to the assumption that markets are perfect and costless. This book is a valuable resource for economists and students.