Bücher der Reihe Springer Uncertainty Research

Uncertainty Theory

This book introduces readers to the basic concepts of and latest findings in the area of differential equations with uncertain factors.

Its comprehensive and systematic treatment of renewal processes, renewal reward processes and the alternating renewal process is one of the book's major features, making it particularly valuable for readers who are interested in learning about renewal theory.

When no samples are available to estimate a probability distribution, we have to invite some domain experts to evaluate the belief degree that each event will happen. Perhaps some people think that the belief degree should be modeled by subjective probability or fuzzy set theory. However, it is usually inappropriate because both of them may lead to counterintuitive results in this case.In order to rationally deal with belief degrees, uncertainty theory was founded in 2007 and subsequently studied by many researchers. Nowadays, uncertainty theory has become a branch of axiomatic mathematics for modeling belief degrees.This is an introductory textbook on uncertainty theory, uncertain programming, uncertain statistics, uncertain risk analysis, uncertain reliability analysis, uncertain set, uncertain logic, uncertain inference, uncertain process, uncertain calculus, and uncertain differential equation. This textbook also shows applications of uncertainty theory to scheduling, logistics, networks, data mining, control, and finance.

This book introduces the theory and applications of uncertain optimal control, and establishes two types of models including expected value uncertain optimal control and optimistic value uncertain optimal control. These models, which have continuous-time forms and discrete-time forms, make use of dynamic programming. The uncertain optimal control theory relates to equations of optimality, uncertain bang-bang optimal control, optimal control with switched uncertain system, and optimal control for uncertain system with time-delay. Uncertain optimal control has applications in portfolio selection, engineering, and games.The book is a useful resource for researchers, engineers, and students in the fields of mathematics, cybernetics, operations research, industrial engineering, artificial intelligence, economics, and management science.

This first book focuses on uncertain graph and network optimization. It covers three different main contents: uncertain graph, uncertain programming and uncertain network optimization. It also presents applications of uncertain network optimization in a lot of real problems such as transportation problems, dispatching medical supplies problems and location problems.The book is suitable for researchers, engineers, teachers and students in the field of mathematics, information science, computer science, decision science, management science and engineering, artificial intelligence, industrial engineering, economics and operations research.