Abstract
In Sect. 15.6 we have discussed how set theoretic operations like intersection, union, and complement can be generalized to fuzzy sets. This section 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
R.E. Moore, Interval Analysis (Prentice Hall, Englewood Cliffs, 1966)
R.E. Moore, Methods and Applications of Interval Analysis (Society for Industrial and Applied Mathematics, Philadelphia, 1979)
H.T. Nguyen, A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64, 369–380 (1978)
L.A. Zadeh, The concept of a lingustic variable and its application to approximate reasoning. Part I Inf. Sci. 8, 199–249 (1975a)
L.A. Zadeh, The concept of a lingustic variable and its application to approximate reasoning. Part II Inf. Sci. 8, 301–357 (1975b)
L.A. Zadeh, The concept of a lingustic variable and its application to approximate reasoning. Part III Inf. Sci. 9, 43–80 (1975c)
Author information
Authors and Affiliations
Corresponding authors
Rights and permissions
Copyright information
© 2016 Springer-Verlag London
About this chapter
Cite this chapter
Kruse, R., Borgelt, C., Braune, C., Mostaghim, S., Steinbrecher, M. (2016). The Extension Principle. In: Computational Intelligence. Texts in Computer Science. Springer, London. https://doi.org/10.1007/978-1-4471-7296-3_16
Download citation
DOI: https://doi.org/10.1007/978-1-4471-7296-3_16
Published:
Publisher Name: Springer, London
Print ISBN: 978-1-4471-7294-9
Online ISBN: 978-1-4471-7296-3
eBook Packages: Computer ScienceComputer Science (R0)