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- Includes supplementary material: sn.pub/extras
Part of the book series: SpringerBriefs in Applied Sciences and Technology (BRIEFSAPPLSCIENCES)
Part of the book sub series: SpringerBriefs in Computational Intelligence (BRIEFSINTELL)
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Table of contents (3 chapters)
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Front Matter
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Back Matter
About this book
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.
Reviews
“The book under review presents a mathematically based description of the theory of random sets and fuzzy random sets as representations of ill-observed random variables or partially known conditional probabilities. … This publication can be treated as a good introductory textbook for everyone who is interested in the theory of ill-observed random variables.” (Marek T. Malinowski, Mathematical Reviews, November, 2015)
Authors and Affiliations
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Departamento de Estadística e I.O. y D. M, Universidad de Oviedo, Oviedo, Spain
Inés Couso
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IRIT, CNRS, Université Paul Sabatier, Toulouse, France
Didier Dubois
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Departamento de Informática, Universidad de Oviedo, Oviedo, Spain
Luciano Sánchez
Bibliographic Information
Book Title: Random Sets and Random Fuzzy Sets as Ill-Perceived Random Variables
Book Subtitle: An Introduction for Ph.D. Students and Practitioners
Authors: Inés Couso, Didier Dubois, Luciano Sánchez
Series Title: SpringerBriefs in Applied Sciences and Technology
DOI: https://doi.org/10.1007/978-3-319-08611-8
Publisher: Springer Cham
eBook Packages: Engineering, Engineering (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2014
Softcover ISBN: 978-3-319-08610-1Published: 01 August 2014
eBook ISBN: 978-3-319-08611-8Published: 22 July 2014
Series ISSN: 2191-530X
Series E-ISSN: 2191-5318
Edition Number: 1
Number of Pages: VIII, 97
Number of Illustrations: 8 b/w illustrations
Topics: Computational Intelligence, Artificial Intelligence, Statistics for Engineering, Physics, Computer Science, Chemistry and Earth Sciences