Civil Engineering Contrast the pros and cons of using the theory of probability sets with more familiar theories, for example, the theory of random variables.
Theoretical Background takes an engineering rather than a mathematical approach, taking a convex probability distribution to describe the input data and/or final response of a system It deals with the mathematical theory of using sets of probability distributions to describe the input data and/or the final response of a system.
The authors’ particular focus is on applications to civil engineering problems, where the theory of random sets is employed as a basic and relatively simple model. However, the authors seek to clarify the relevance of the more general theory of in exact probabilities, Scholke capacity, fuzzy sets, p-boxes, convex sets of parametric probability distributions, and approximate inference in one dimension and in multiple dimensions with associated bound spaces.
Even though the choice of a theory of random sets may lead to a loss of generality, on the other hand, it allows for a self-contained selection of topics and a more unified presentation of theoretical content and algorithms. The book provides step-by-step explanations ofmorethan80 examples, which should help beginning students in the field (who may have difficulty wading through the vast and dispersed literature) in applying the described techniques to their own specific problems
The theory presented in the first part of this book summarizes the work that has been done over the past 30-40 years to try to overcome the limitations of classical probability theory, both in its objectivist interpretation (relative frequency of expected events) and in its subjective Bayesian or behavioral view, from various roots and pur poses The book is a summary of research that has attempted to overcome the limitations of classical probability theory, both in the relative frequency of events and in the subjective Bayesian or behavioral view.
The intended mission of this book is to provide a comprehensive presentation of all aspects of this subject. For an up-to-date and clear synthesis, the interested reader is referred, for example,to (Klir 2005).
The special perspective of the author concentrates on the mathematical theory, which can be referred to its application to civil engineering problems and to the general idea of a convex set of probability distributions describing the input data and/or the final response of a system.
In this respect, the theory of random sets has been employed as the most appropriate and relatively simple model for many typical problems. However, the authors seek to clarify the connection with the more general theory of imprecision probability.