Yao begins his book by stating that “uncertain differential equations” are a concept proposed by Liu in 2008. It appears, however, that what he calls uncertain differential equations are also known as stochastic differential equations, and various researchers have studied such equations since the early 20th century. The research of stochastic differential equations is a well-established field that did not begin in 2008. Yao’s book, however, does not seem to acknowledge the work of other researchers not connected to Liu or Yao. It is not clear what makes Liu’s approach so special and different that it deserves its own terminology. The author and his collaborators seem to work outside the stochastic differential equation research community. Interestingly, Yao and Liu are also the sole editors of the Springer book series on “Uncertainty Research,” in which this book is published. This raises even more questions, leading me to recommend any reader interested in stochastic differential equations to focus on the work of other authors and to avoid this book.

The book is organized in ten chapters that cover different aspects of the theory of uncertainty as introduced by Liu. Each chapter begins with a very short one-paragraph introduction, followed by a sequence of definitions, axioms, theorems, and proofs that contain little or no explanations.

It is very challenging to discuss the contributions of this book because it seems to have been conceived in an attempt to promote the work of the book’s editors. In addition, many of Liu’s papers on which this book is based appeared in online journals where Liu is also an editor. There appears to be an obvious conflict of interest, and it is not clear why Springer as the publisher decided to support such a project. More damning, the book appears in the Springer “Uncertainty Research” series, which so far contains two volumes, both of which are authored by either Liu or Yao, the two editors of the series.