Uncertainty Modeling and Analysis in Engineering and the Sciences  book cover
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Uncertainty Modeling and Analysis in Engineering and the Sciences




ISBN 9781584886440
Published May 25, 2006 by Chapman and Hall/CRC
400 Pages 99 B/W Illustrations

 
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Book Description

Engineers and scientists often need to solve complex problems with incomplete information resources, necessitating a proper treatment of uncertainty and a reliance on expert opinions. Uncertainty Modeling and Analysis in Engineering and the Sciences prepares current and future analysts and practitioners to understand the fundamentals of knowledge and ignorance, how to model and analyze uncertainty, and how to select appropriate analytical tools for particular problems.

This volume covers primary components of ignorance and their impact on practice and decision making. It provides an overview of the current state of uncertainty modeling and analysis, and reviews emerging theories while emphasizing practical applications in science and engineering.

The book introduces fundamental concepts of classical, fuzzy, and rough sets, probability, Bayesian methods, interval analysis, fuzzy arithmetic, interval probabilities, evidence theory, open-world models, sequences, and possibility theory. The authors present these methods to meet the needs of practitioners in many fields, emphasizing the practical use, limitations, advantages, and disadvantages of the methods.

Table of Contents

Systems, Knowledge, and Ignorance
Data Abundance and Uncertainty
Systems Framework
Knowledge
Ignorance
From Data to Knowledge for Decision Making

Encoding Data and Expressing Information
Introduction
Identification and Classification of Theories
Crisp Sets and Operations
Fuzzy Sets and Operations
Generalized Measures
Rough Sets and Operations
Gray Systems and Operations

Uncertainty and Information Synthesis
Synthesis for a Goal
Knowledge, Systems, Uncertainty, and Information
Measure Theory and Classical Measures
Monotone Measures and Their Classification
Dempster-Shafer Evidence Theory
Possibility Theory
Probability Theory
Imprecise Probabilities
Fuzzy Measures and Fuzzy Integrals

Uncertainty Measures
Introduction
Uncertainty Measures: Definition and Types
Nonspecificity Measures
Entropy-Like Measures
Fuzziness Measure
Application: Combining Expert Opinions

Uncertainty-Based Principles and Knowledge Construction
Introduction
Construction of Knowledge
Minimum Uncertainty Principle
Maximum Uncertainty Principle
Uncertainty Invariance Principle
Methods for Open-World Analysis

Uncertainty Propagation for Systems
Introduction
Fundamental Methods for Propagating Uncertainty
Propagation of Mixed Uncertainty Types

Expert Opinions and Elicitation Methods
Introduction
Terminology
Classification of Issues, Study Levels, Experts, and Process Outcomes
Process Definition
Need Identification for Expert Opinion Elicitation
Selection of Study Level and Study Leader
Selection of Peer Reviewers and Experts
Identification, Selection, and Development of Technical Issues
Elicitation of Opinions
Documentation and Communication

Visualization of Uncertainty
Introduction
Visualization Methods
Criteria and Metrics for Assessing Visualization Methods
Intelligent Agents for Icon Selection, Display, and Updating
Ignorance Markup Language

Appendix A: Historical Perspectives on Knowledge

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