Uncertainty Modeling and Analysis in Engineering and the Sciences: 1st Edition (Hardback) book cover

Uncertainty Modeling and Analysis in Engineering and the Sciences

1st Edition

By Bilal M. Ayyub, George J. Klir

Chapman and Hall/CRC

400 pages | 99 B/W Illus.

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pub: 2006-05-25
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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



From Data to Knowledge for Decision Making

Encoding Data and Expressing Information


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


Uncertainty Measures: Definition and Types

Nonspecificity Measures

Entropy-Like Measures

Fuzziness Measure

Application: Combining Expert Opinions

Uncertainty-Based Principles and Knowledge Construction


Construction of Knowledge

Minimum Uncertainty Principle

Maximum Uncertainty Principle

Uncertainty Invariance Principle

Methods for Open-World Analysis

Uncertainty Propagation for Systems


Fundamental Methods for Propagating Uncertainty

Propagation of Mixed Uncertainty Types

Expert Opinions and Elicitation Methods



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


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

About the Originator

Subject Categories

BISAC Subject Codes/Headings:
BUSINESS & ECONOMICS / Operations Research
MATHEMATICS / Probability & Statistics / General
TECHNOLOGY & ENGINEERING / Operations Research