This short book provides a unified view of the history and theory of random sets and fuzzy
random variables with special emphasis on its use for representing higher-order
non-statistical uncertainty about statistical experiments. The authors lay bare the existence
of two streams of works using the same mathematical ground but differing form their use of
sets according to whether they represent objects of interest naturally taking the form of sets
or imprecise knowledge about such objects. Random (fuzzy) sets can be used in many fields
ranging from mathematical morphology economics artificial intelligence information
processing and statistics per se especially in areas where the outcomes of random experiments
cannot be observed with full precision. This book also emphasizes the link between random sets
and fuzzy sets with some techniques related to the theory of imprecise probabilities. This
small book is intended for graduate and doctoral students in mathematics or engineering but
also provides an introduction for other researchers interested in this area. It is written from
a theoretical perspective. However rather than offering a comprehensive formal view of random
(fuzzy) sets in this context it aims to provide a discussion of the meaning of the proposed
formal constructions based on many concrete examples and exercises. This book should enable the
reader to understand the usefulness of representing and reasoning with incomplete information
in statistical tasks. Each chapter ends with a list of exercises.
