Reasoning with uncertainty in order to cope with phenomena that are indeterminate and cannot be predicted exactly has become one of the major challenges in the 21st century, particularly when no samples are, or can, become available, and hence no probability theory can be applied. In such cases, one should rely on the beliefs of experts in an event as to whether it is likely or unlikely to happen. Instead of probability distributions, it is distributions of degrees of belief, that is, the variations of strength in beliefs about the likelihood of an event happening, that take center stage. Therefore, questions on how to obtain or to model degrees of belief rise from this domain of discourse.

Uncertainty theory is definitely one promising direction and has been well established since 2007. Unfortunately, uncertainty theory has been contrasted with probability theory to the extent that these two theories are being considered as two separate mathematical systems. It has been argued “that using uncertainty theory to model frequency may produce a crude result, while using probability theory to model [degrees of belief] may produce a big disaster.”

This is exactly the stepping-stone for writing and publishing this book. It is a thorough mathematical foundation of uncertainty theory and all associated concepts, for example, uncertainty measure, uncertain variables, uncertain programming, uncertain statistics and risk analysis, uncertain calculus, and many others. The book, in its almost 500 pages, is composed of ten sections devoted to chapters discussing all these related aspects of uncertainty theory, plus some appendices devoted to probability theory (probably as a contrast with uncertainty theory) and chance theory, though the latter is not discussed in the introduction of the book. The book is, nevertheless, a good read; however, it is mostly suitable for readers with a strong mathematical background or those keen on working with mathematical formalisms. The potential readership of the book is likely to be narrowed down even further to mathematicians or data scientists interested in analytics (perhaps big data analysis). Although it seems irrelevant for (big) data science, as this is a field with vast amounts of data available and is less about beliefs, there are many interesting lessons to be learned with regard to predictability and uncertain statistics.