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Data uncertainty and important measures
The first part of the book defines the concept of uncertainties and the mathematical frameworks that will be used for uncertainty modeling. The application to system reliability assessment illustrates the concept. In the second part, evidential networks as a new tool to model uncertainty in reliability and risk analysis is proposed and described. Then it is applied on SIS performance assessment and in risk analysis of a heat sink. In the third part, Bayesian and evidential networks are used to deal with important measures evaluation in the context of uncertainties.-- Provided by Publisher.
Book
On the Entropy and the Maximum Entropy Principle of Uncertain Variables
A new variance formula is developed using the generalized inverse of an increasing function. Based on the variance formula, a new entropy formula for any uncertain variable is provided. Most of the entropy formulas in the literature are special cases of the new entropy formula. Using the new entropy formula, the maximum entropy distribution for unimodel entropy of uncertain variables is provided without using the Euler–Lagrange equation.
Journal Article
Research on the Optimization of Urban–Rural Passenger and Postal Integration Operation Scheduling Based on Uncertainty Theory
The integration of postal and passenger transport is an effective measure to enhance the utilization efficiency of passenger and freight transportation resources and to promote the sustainable development of urban–rural transit and logistics. This paper considers the uncertainty in passenger and freight demand as well as transit operation times, constructing an optimization model for integrated urban–rural transit and postal services based on uncertainty theory. Passenger and freight demand, along with the inverse uncertain distribution of events, serve as constraints, while minimizing passenger travel time and the cost for passenger transport companies are the optimization objectives. Taking into account the uncertainty of urban–rural bus travel time, the scheduling model is transformed into a robust form for scenarios involving single and multiple origin stations. The model is solved using an improved NSGA-II (Nondominated Sorting Genetic Algorithm II) to achieve effective coordinated scheduling of both passenger and freight services. Through a case study in Lotus County, Jiangxi Province, vehicle routing plans with varying levels of conservativeness were obtained. Comparing the results from different scenarios, it was found that when the total vehicle operating mileage increased from 1.96% to 62.26%, passenger transport costs rose from 2.95% to 62.66%, while the total passenger travel time decreased from 55.99% to 172.31%. In terms of optimizing costs and improving passenger travel efficiency, operations involving multiple starting stations for a single vehicle demonstrated greater advantages. Meanwhile, at a moderate level of robustness, it was easier to achieve a balance between operational costs and passenger travel time. The research findings provide theoretical support for improving travel conditions and resource utilization in rural areas, which not only helps enhance the operational efficiency of urban–rural transit but also contributes positively to promoting balanced urban–rural sustainable development and narrowing the urban–rural gap.
Journal Article
Residual analysis and parameter estimation of uncertain differential equations
All existing methods to estimate unknown parameters in uncertain differential equations are based on difference scheme, and do not work when the time intervals between observations are not short enough. In order to overcome this shortage, this paper presents a concept of residual. Afterwards, an algorithm is designed for calculating residuals of uncertain differential equation corresponding to observed data. In addition, this paper presents a method of moments based on residuals to estimate the unknown parameters in uncertain differential equations. Finally, some examples (including Alibaba stock price) are provided to illustrate the parameter estimation method.
Journal Article
Parameter estimation in uncertain differential equations
Parameter estimation is a critical problem in the wide applications of uncertain differential equations. The method of moments is employed for the first time as an approach for estimating the parameters in uncertain differential equations. Based on the difference form of an uncertain differential equation, a function of the parameters is proved to follow a standard normal uncertainty distribution. Setting the empirical moments of the functions of the parameters and the observed data equal to the moments of the standard normal uncertainty distribution, a system of equations about the parameters is obtained whose solutions are the estimates of the parameters. Analytic examples and numerical examples are given to illustrate the proposed method of moments.
Journal Article
Antifragile : things that gain from disorder
\"The acclaimed author of the influential bestseller The Black Swan, Nicholas Nassim Taleb takes a next big step with a deceptively simple concept: the \"antifragile.\" Like the Greek hydra that grows two heads for each one it loses, people, systems, and institutions that are antifragile not only withstand shocks, they benefit from them. In a modern world dominated by chaos and uncertainty, Antifragile is a revolutionary vision from one of the most subversive and important thinkers of our time. Praise for Nicholas Nassim Taleb \"[This] is the lesson of Taleb. and also the lesson of our volatile times. There is more courage and heroism in defying the human impulse, in taking the purposeful and painful steps to prepare for the unimaginable.\"--Malcolm Gladwell, author of The Tipping Point \"[Taleb writes] in a style that owes as much to Stephen Colbert as it does to Michel de Montaigne.\"--The Wall Street Journal \"The most prophetic voice of all. [Taleb is] a genuinely significant philosopher. someone who is able to change the way we view the structure of the world through the strength, originality and veracity of his ideas alone.\"--GQ \"Changed my view of how the world works.\"--Daniel Kahneman, Nobel laureate\"-- Provided by publisher.
Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science
Bayesian Networks \"This book should have a place on the bookshelf of every forensic scientist who cares about the science of evidence interpretation.\" Dr. Ian Evett, Principal Forensic Services Ltd, London, UK Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science Second Edition Continuing developments in science and technology mean that the amounts of information forensic scientists are able to provide for criminal investigations is ever increasing. The commensurate increase in complexity creates diffculties for scientists and lawyers with regard to evaluation and interpretation, notably with respect to issues of inference and decision. Probability theory, implemented through graphical methods, and specifically Bayesian networks, provides powerful methods to deal with this complexity. Extensions of these methods to elements of decision theory provide further support and assistance to the judicial system. Bayesian Networks for Probabilistic Inference and Decision Analysis in Forensic Science provides a unique and comprehensive introduction to the use of Bayesian decision networks for the evaluation and interpretation of scientific findings in forensic science, and for the support of decision-makers in their scientific and legal tasks. Includes self-contained introductions to probability and decision theory. Develops the characteristics of Bayesian networks, object-oriented Bayesian networks and their extension to decision models. Features implementation of the methodology with reference to commercial and academically available software. Presents standard networks and their extensions that can be easily implemented and that can assist in the reader's own analysis of real cases. Provides a technique for structuring problems and organizing data based on methods and principles of scientific reasoning. Contains a method for the construction of coherent and defensible arguments for the analysis and evaluation of scientific findings and for decisions based on them. Is written in a lucid style, suitable for forensic scientists and lawyers with minimal mathematical background. Includes a foreword by Ian Evett. The clear and accessible style of this second edition makes this book ideal for all forensic scientists, applied statisticians and graduate students wishing to evaluate forensic findings from the perspective of probability and decision analysis. It will also appeal to lawyers and other scientists and professionals interested in the evaluation and interpretation of forensic findings, including decision making based on scientific information.
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