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Construction of k-Lipschitz triangular norms and conorms from empirical data

Beliakov, Gleb and Calvo, Tomasa 2009, Construction of k-Lipschitz triangular norms and conorms from empirical data, IEEE transactions on fuzzy systems, vol. 17, no. 5, pp. 1217-1220.

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Title Construction of k-Lipschitz triangular norms and conorms from empirical data
Formatted title Construction of k-Lipschitz triangular norms and conorms from empirical data

Author(s) Beliakov, Gleb
Calvo, Tomasa
Journal name IEEE transactions on fuzzy systems
Volume number 17
Issue number 5
Start page 1217
End page 1220
Total pages 4
Publisher IEEE
Place of publication Piscataway, N.J.
Publication date 2009-10
ISSN 1063-6706
1941-0034
Keyword(s) aggregation operators
fuzzy sets
k-Lipschitz aggregation functions
triangular norms
Summary This paper examines the practical construction of k-Lipschitz triangular norms and conorms from empirical data. We apply a characterization of such functions based on k-convex additive generators and translate k-convexity of piecewise linear strictly decreasing functions into a simple set of linear inequalities on their coefficients. This is the basis of a simple linear spline-fitting algorithm, which guarantees k-Lipschitz property of the resulting triangular norms and conorms.
Notes 2009 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
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 2009
Copyright notice ©2009, IEEE
Persistent URL http://hdl.handle.net/10536/DRO/DU:30028307

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.