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.
General
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