Uncertainty Modeling and Analysis in Engineering and the Sciences


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Grant General Conditions. Cooperative Agreement Conditions. Special Conditions. Federal Demonstration Partnership. Policy Office Website. The book is written to assist analyst and designers in understanding the fundamentals of knowledge and ignorance, how to model and analyze uncertainty, and how to select appropriate analytical tools for a particular problem.

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The authors adopt a more generalized approach to uncertainty analysis that includes both probabilistic and nonprobabilistic methods. The book begins with this quote from Stephen Hawking: "The greatest enemy of knowledge is not ignorance; it is the illusion of knowledge". This quote was deliberately chosen by the authors to set the tone for the discussion on the close connection between uncertainty, information, ignorance and knowledge.

The authors look at the meaning, nature, and hierarchy of knowledge and ignorance from a philosophical perspective; where the close connection between uncertainty and information as a pair, and ignorance and knowledge as another pair are carefully examined. The subject of Systems Framework is well treated, with emphasis on taxonomy of systems, complexity of systems, and systems knowledge. In order to quantify and analyze uncertainty, the data that contains or expresses the uncertainty in a system should be organized in a structured manner so that it can lend itself to mathematical or logical representation and analysis.

This leads the authors to explore methods of encoding data. The concept of Identification and Classification of Theories is used as a basis for defining a universal set based on closed-world and open-world assumptions, from which elements of the universal set precise or imprecise , and sets also precise or imprecise are developed. The fundamentals of classical set theory, probability theory, fuzzy sets, generalized measures, rough sets, and gray systems are presented as a formalized way of encoding data.

Uncertainty Modeling and Analysis in Engineering and the Sciences : Bilal M. Ayyub :

Numerical examples are used to explain the basic mathematical operations of fuzzy sets and rough sets. However, not much attention is paid to gray sets.


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In order to make appropriate decisions about a system, engineers and scientists need to synthesis data and information. This leads the authors to the subject of uncertainty and information synthesis. Here, measure theory and monotone measures, including possibility theory and the Dempster-Shafer theory of evidence are explained. They then compare and contrast these theories with some variations of probability theory, such as Bayesian probabilities, and interval probabilities.

Simple numerical problems are used to demonstrate how these methods can be used to aggregate expert opinion.

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The concept of aggregating expert opinion is further examined with demonstrative examples by utilizing minimum and maximum uncertainty criterion, and uncertainty invariance criterion. The book also presents methods for propagating uncertainty in input-output systems. The processes of eliciting expert opinions also receive a fair amount of coverage in the book. The authors demonstrate the applications of expert opinion elicitation with practical examples.

Techniques for visualizing uncertainty in information are also presented. Uncertainty Modeling and Analysis in Engineering and the Sciences presents a holistic view of understanding uncertainty in systems that are of relevance to engineers and scientists in practice, in a more generalized approach, and is a useful book that provides a fundamental understanding to analyzing uncertainty in engineering and scientific systems. The authors demonstrate a deep understanding of the subject matter and draw on real word examples to explain the concepts presented in the book.

A good book for students who follow the system engineering, but does not good for advance topics in uncertainties, especially for Math students. See all 11 reviews.


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