1st Edition

Uncertainty Modeling and Analysis in Engineering and the Sciences

By Bilal M. Ayyub, George J. Klir Copyright 2006
    400 Pages 99 B/W Illustrations
    by Chapman & Hall

    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.

    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

    Biography

    Bilal M. Ayyub, George J. Klir