Observations of uncertainty in measured data with time improves forecasting capability in a wide range of fields in engineering. This book provides an introduction to uncertainty forecasting based on fuzzy time series. It details descriptive, modeling, and forecasting methods for fuzzy time series. Coverage places emphasis on forecasting based on fuzzy random processes as well as forecasting involving fuzzy neuronal networks.

This report is the summary of a workshop conducted by the National Research Council in order to learn from both forecast makers and forecast users about improvements that can be made in understanding the markets for doctoral scientists and engineers. The workshop commissioned papers examined (1) the history and problems with models of demand and supply for scientists and engineers, (2) objectives and approaches to forecasting models, (3) margins of adjustment that have been neglected in models, especially substitution and quality, (4) the presentation of uncertainty, and (5) whether these forecasts of supply and demand are worthwhile, given all their shortcomings. The focus of the report was to provide guidance to the NSF and to scholars in this area on how models and the forecasts derived from them might be improved, and what role NSF should play in their improvement. In addition, the report examined issues of reporting forecasts to policymakers.

Uncertainty is a fundamental characteristic of weather, seasonal climate, and hydrological prediction, and no forecast is complete without a description of its uncertainty. Effective communication of uncertainty helps people better understand the likelihood of a particular event and improves their ability to make decisions based on the forecast. Nonetheless, for decades, users of these forecasts have been conditioned to receive incomplete information about uncertainty. They have become used to single-valued (deterministic) forecasts (e.g., "the high temperature will be 70 degrees Farenheit 9 days from now") and applied their own experience in determining how much confidence to place in the forecast. Most forecast products from the public and private sectors, including those from the National Oceanographic and Atmospheric Administration's National Weather Service, continue this deterministic legacy. Fortunately, the National Weather Service and others in the prediction community have recognized the need to view uncertainty as a fundamental part of forecasts. By partnering with other segments of the community to understand user needs, generate relevant and rich informational products, and utilize effective communication vehicles, the National Weather Service can take a leading role in the transition to widespread, effective incorporation of uncertainty information into predictions. "Completing the Forecast" makes recommendations to the National Weather Service and the broader prediction community on how to make this transition.

This report is the summary of a workshop conducted by the National Research Council in order to learn from both forecast makers and forecast users about improvements that can be made in understanding the markets for doctoral scientists and engineers. The workshop commissioned papers examined (1) the history and problems with models of demand and supply for scientists and engineers, (2) objectives and approaches to forecasting models, (3) margins of adjustment that have been neglected in models, especially substitution and quality, (4) the presentation of uncertainty, and (5) whether these forecasts of supply and demand are worthwhile, given all their shortcomings. The focus of the report was to provide guidance to the NSF and to scholars in this area on how models and the forecasts derived from them might be improved, and what role NSF should play in their improvement. In addition, the report examined issues of reporting forecasts to policymakers.

This textbook teaches the essential background and skills for understanding and quantifying uncertainties in a computational simulation, and for predicting the behavior of a system under those uncertainties. It addresses a critical knowledge gap in the widespread adoption of simulation in high-consequence decision-making throughout the engineering and physical sciences. Constructing sophisticated techniques for prediction from basic building blocks, the book first reviews the fundamentals that underpin later topics of the book including probability, sampling, and Bayesian statistics. Part II focuses on applying Local Sensitivity Analysis to apportion uncertainty in the model outputs to sources of uncertainty in its inputs. Part III demonstrates techniques for quantifying the impact of parametric uncertainties on a problem, specifically how input uncertainties affect outputs. The final section covers techniques for applying uncertainty quantification to make predictions under uncertainty, including treatment of epistemic uncertainties. It presents the theory and practice of predicting the behavior of a system based on the aggregation of data from simulation, theory, and experiment. The text focuses on simulations based on the solution of systems of partial differential equations and includes in-depth coverage of Monte Carlo methods, basic design of computer experiments, as well as regularized statistical techniques. Code references, in python, appear throughout the text and online as executable code, enabling readers to perform the analysis under discussion. Worked examples from realistic, model problems help readers understand the mechanics of applying the methods. Each chapter ends with several assignable problems. Uncertainty Quantification and Predictive Computational Science fills the growing need for a classroom text for senior undergraduate and early-career graduate students in the engineering and physical sciences and supports independent study by researchers and professionals who must include uncertainty quantification and predictive science in the simulations they develop and/or perform.

This book is written for all technologists and engineers. To those unfamiliar with forecasting it may appear a somewhat esoteric activity with little relevance to the everyday technical concerns of the reader. This is not so. The aim of this book is to show how forecasting can improve the quality of technical decision making. Furthermore, this can be accomplished without the use of highly sophisticated techniques which can only be applied by specialists. The approaches described in this book can be easily understood and used by all its readers.

Uncertainty has been of concern to engineers, managers and . scientists for many centuries. In management sciences there have existed definitions of uncertainty in a rather narrow sense since the beginning of this century. In engineering and uncertainty has for a long time been considered as in sciences, however, synonymous with random, stochastic, statistic, or probabilistic. Only since the early sixties views on uncertainty have ~ecome more heterogeneous and more tools to model uncertainty than statistics have been proposed by several scientists. The problem of modeling uncertainty adequately has become more important the more complex systems have become, the faster the scientific and engineering world develops, and the more important, but also more difficult, forecasting of future states of systems have become. The first question one should probably ask is whether uncertainty is a phenomenon, a feature of real world systems, a state of mind or a label for a situation in which a human being wants to make statements about phenomena, i. e. , reality, models, and theories, respectively. One cart also ask whether uncertainty is an objective fact or just a subjective impression which is closely related to individual persons. Whether uncertainty is an objective feature of physical real systems seems to be a philosophical question. This shall not be answered in this volume.