Some information and knowledge are usually represented by human language
like “about 100km”, “approximately 39 ?C”, “roughly 80kg”, “low speed”,
“middle age”, and “big size”. Perhaps some people think that they are subjective
probability or they are fuzziness. However, a lot of surveys showed
that those imprecise quantities behave neither like randomness nor like fuzziness.
How do we understand them? How do we model them? These questions
provide a motivation to invent another mathematical tool to model those imprecise
quantities. In order to do so, an uncertainty theory was founded and
became a branch of axiomatic mathematics. Since then, uncertainty theory
has been developed steadily and applied widely.
Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Uncertainty is any concept that satisfies the axioms of uncertainty theory. Thus uncertainty is neither randomness nor fuzziness. It is also known from some surveys that a lot of phenomena do behave like uncertainty. How do we model uncertainty? How do we use uncertainty theory? In order to answer these questions, this book provides a self-contained, comprehensive and up-to-date presentation of uncertainty theory, including uncertain programming, uncertain risk analysis, uncertain reliability analysis, uncertain process, uncertain calculus, uncertain differential equation, uncertain logic, uncertain entailment, and uncertain inference. Mathematicians, researchers, engineers, designers, and students in the field of mathematics, information science, operations research, system science, industrial engineering, computer science, artificial intelligence, finance, control, and management science will find this work a stimulating and useful reference.