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SpringerBriefs in Computational Intelligence

Random Sets and Random Fuzzy Sets as Ill-Perceived Random Variables

An Introduction for Ph.D. Students and Practitioners

Authors: Couso, Inés, Dubois, Didier, Sanchez, Luciano

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  • ISBN 978-3-319-08611-8
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Softcover $69.99
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  • ISBN 978-3-319-08610-1
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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)


Table of contents (3 chapters)

Table of contents (3 chapters)

Buy this book

eBook $54.99
price for USA in USD (gross)
  • ISBN 978-3-319-08611-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.99
price for USA in USD
  • ISBN 978-3-319-08610-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

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
Series Title
SpringerBriefs in Computational Intelligence
Copyright
2014
Publisher
Springer International Publishing
Copyright Holder
The Author(s)
eBook ISBN
978-3-319-08611-8
DOI
10.1007/978-3-319-08611-8
Softcover ISBN
978-3-319-08610-1
Series ISSN
2625-3704
Edition Number
1
Number of Pages
VIII, 97
Number of Illustrations
8 b/w illustrations
Topics