Uncertainty Modeling and Analysis in Engineering and the Sciences

Based on the authors' first-hand experiences, Uncertainty Modeling and Analysis in Engineering and the Sciences serves as a single-source reference and text on the theory, background, and history of the subject. This book provides guidance on the use of uncertainty modeling and analysis methods by presenting the historical, theoretical, and philosophical bases behind suggested methods. It offers critical reviews, advantages, disadvantages, and limitations of the methods discussed. Presenting broad and comprehensive coverage of the subject, the text also includes numerous case studies, examples, problems, figures, and tables as well as an extensive reference list.

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 KnowledgeIgnoranceFrom Data to Knowledge for Decision MakingEncoding 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 GoalKnowledge, Systems, Uncertainty, and InformationMeasure Theory and Classical Measures Monotone Measures and Their Classification Dempster-Shafer Evidence Theory Possibility Theory Probability Theory Imprecise ProbabilitiesFuzzy Measures and Fuzzy Integrals Uncertainty Measures Introduction Uncertainty Measures: Definition and Types Nonspecificity Measures Entropy-Like MeasuresFuzziness Measure Application: Combining Expert OpinionsUncertainty-Based Principles and Knowledge Construction Introduction Construction of Knowledge Minimum Uncertainty Principle Maximum Uncertainty Principle Uncertainty Invariance Principle Methods for Open-World AnalysisUncertainty Propagation for Systems Introduction Fundamental Methods for Propagating Uncertainty Propagation of Mixed Uncertainty TypesExpert Opinions and Elicitation Methods Introduction Terminology Classification of Issues, Study Levels, Experts, and Process OutcomesProcess Definition Need Identification for Expert Opinion ElicitationSelection of Study Level and Study LeaderSelection of Peer Reviewers and ExpertsIdentification, Selection, and Development of Technical IssuesElicitation of OpinionsDocumentation and Communication Visualization of Uncertainty Introduction Visualization MethodsCriteria and Metrics for Assessing Visualization MethodsIntelligent Agents for Icon Selection, Display, and Updating Ignorance Markup Language Appendix A: Historical Perspectives on Knowledge