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On Lipschitz properties of generated aggregation functions

Beliakov, Gleb, Calvo, Tomasa and James, Simon 2010, On Lipschitz properties of generated aggregation functions, Fuzzy sets and systems, vol. 161, no. 10, pp. 1437-1447.

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Title On Lipschitz properties of generated aggregation functions
Author(s) Beliakov, Gleb
Calvo, Tomasa
James, Simon
Journal name Fuzzy sets and systems
Volume number 161
Issue number 10
Start page 1437
End page 1447
Total pages 11
Publisher Elsevier
Place of publication Amsterdam, Netherlands
Publication date 2010-05
ISSN 0165-0114
1872-6801
Keyword(s) aggregation functions
generated aggregation functions
k-Lipschitz aggregation functions
triangular norms
quasi-arithmetic means
uninorms
nullnorms
stability
Summary This article discusses Lipschitz properties of generated aggregation functions. Such generated functions include triangular norms and conorms, quasi-arithmetic means, uninorms, nullnorms and continuous generated functions with a neutral element. The Lipschitz property guarantees stability of aggregation operations with respect to input inaccuracies, and is important for applications. We provide verifiable sufficient conditions to determine when a generated aggregation function holds the k-Lipschitz property, and calculate the Lipschitz constants of power means. We also establish sufficient conditions which guarantee that a generated aggregation function is not Lipschitz. We found the only 1-Lipschitz generated function with a neutral element e ∈]0, 1[.
Notes Reproduced with the specific permission of the copyright owner.
Language eng
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
HERDC collection year 2010
Copyright notice ©2009, Elsevier B.V.
Persistent URL http://hdl.handle.net/10536/DRO/DU:30028315

Document type: Journal Article
Collections: School of Information Technology
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Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.