Uncertainty Modeling and Analysis in Engineering and the Sciences [Hardcover]

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
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