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2013 | OriginalPaper | Chapter

16. The Extension Principle

Authors : Rudolf Kruse, Christian Borgelt, Frank Klawonn, Christian Moewes, Matthias Steinbrecher, Pascal Held

Published in: Computational Intelligence

Publisher: Springer London

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Abstract

We have already discussed how set theoretic operations like intersection, union and complement can be generalized to fuzzy sets. This chapter is devoted to the issue of extending the concept of mappings or functions to fuzzy sets. These ideas allow us to define operations like addition, subtraction, multiplication, division or taking squares as well as set theoretic concepts like the composition of relations for fuzzy sets.

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previous chapter Fuzzy Sets and Fuzzy Logic
next chapter Fuzzy Relations
Literature
R.E. Moore. Interval Analysis. Prentice Hall, Englewood Cliffs, NJ, USA, 1966 MATH
R.E. Moore. Methods and Applications of Interval Analysis. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA, 1979 MATHCrossRef
L.A. Zadeh. The Concept of a Linguistic Variable and Its Application to Approximate Reasoning, Part I. Information Sciences 8:199–249, 1975a MathSciNetMATHCrossRef
L.A. Zadeh. The Concept of a Linguistic Variable and Its Application to Approximate Reasoning, Part II. Information Sciences 8:301–357, 1975b MathSciNetMATHCrossRef
L.A. Zadeh. The Concept of a Linguistic Variable and Its Application to Approximate Reasoning, Part III. Information Sciences 9:43–80, 1975c MathSciNetMATHCrossRef
Metadata
Title
The Extension Principle
Authors
Rudolf Kruse
Christian Borgelt
Frank Klawonn
Christian Moewes
Matthias Steinbrecher
Pascal Held
Copyright Year
2013
Publisher
Springer London
Book
Computational Intelligence

Print ISBN: 978-1-4471-5012-1

Electronic ISBN: 978-1-4471-5013-8

Copyright Year: 2013

DOI
https://doi.org/10.1007/978-1-4471-5013-8_16

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