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Type-2 fuzzy alpha-cuts

Hamrawi, Hussam; Coupland, Simon; John, Robert


Hussam Hamrawi

Simon Coupland

Robert John


Type-2 fuzzy logic systems make use of type-2 fuzzy sets. To be able to deliver useful type-2 fuzzy logic applications we need to be able to perform meaningful operations on these sets. These operations should also be practically tractable. However, type-2 fuzzy sets suffer the shortcoming of being complex by definition. Indeed, the third dimension, which is the source of extra parameters, is in itself the origin of extra computational cost. The quest for a representation that allow practical systems to be implemented is the motivation for our work. In this paper we define the alpha-cut decomposition theorem for type- 2 fuzzy sets which is a new representation analogous to the alpha-cut representation of type-1 fuzzy sets and the extension principle. We show that this new decomposition theorem forms a methodology for extending mathematical concepts from crisp sets to type-2 fuzzy sets directly. In the process of developing this theory we also define a generalisation that allows us to extend operations from interval type-2 fuzzy sets or interval valued fuzzy sets to type-2 fuzzy sets. These results will allow for the more applications of type-2 fuzzy sets by expiating the parallelism that the research here affords.


Hamrawi, H., Coupland, S., & John, R. (2017). Type-2 fuzzy alpha-cuts. IEEE Transactions on Fuzzy Systems, 25(3),

Journal Article Type Article
Acceptance Date Apr 15, 2016
Online Publication Date Jun 1, 2016
Publication Date May 31, 2017
Deposit Date Apr 26, 2016
Publicly Available Date Jun 1, 2016
Journal IEEE Transactions on Fuzzy Systems
Print ISSN 1063-6706
Electronic ISSN 1941-0034
Publisher Institute of Electrical and Electronics Engineers
Peer Reviewed Peer Reviewed
Volume 25
Issue 3
Public URL
Publisher URL
Copyright Statement Copyright information regarding this work can be found at the following address:


T2alpha FINAL.pdf (320 Kb)

Copyright Statement
Copyright information regarding this work can be found at the following address:

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