Ayyub / Klir Uncertainty Modeling and Analysis in Engineering and the Sciences

Erscheinungsjahr 2010
ISBN: 978-1-4200-1145-6
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 400 Seiten

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.

Zielgruppe

Engineers, financial analysts, economists, scientists, risk analysts, statisticians, and decision and policy makers.

Autoren/Hrsg.

Ayyub, Bilal M.

Klir, George J.

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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