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Monotone approximation of aggregation operators using least squares splines

Beliakov, Gleb 2002, Monotone approximation of aggregation operators using least squares splines, International journal of uncertainty, fuzziness, and knowledge-based systems, vol. 10, no. 6, pp. 659-676.

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Title Monotone approximation of aggregation operators using least squares splines
Author(s) Beliakov, Gleb
Journal name International journal of uncertainty, fuzziness, and knowledge-based systems
Volume number 10
Issue number 6
Start page 659
End page 676
Publisher World Scientific
Place of publication Singapore
Publication date 2002
ISSN 0218-4885
Summary The need for monotone approximation of scattered data often arises in many problems of regression, when the monotonicity is semantically important. One such domain is fuzzy set theory, where membership functions and aggregation operators are order preserving. Least squares polynomial splines provide great flexbility when modeling non-linear functions, but may fail to be monotone. Linear restrictions on spline coefficients provide necessary and sufficient conditions for spline monotonicity. The basis for splines is selected in such a way that these restrictions take an especially simple form. The resulting non-negative least squares problem can be solved by a variety of standard proven techniques. Additional interpolation requirements can also be imposed in the same framework. The method is applied to fuzzy systems, where membership functions and aggregation operators are constructed from empirical data.
Notes Electronic version of an article published as International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems Vol. 10, No. 6 (2002) 659-676. DOI: 10.1142/S0218488502001715 © 2002, World Scientific Publishing Company http://www.worldscinet.com/ijufks/ijufks.shtml
Language eng
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
HERDC Research category C1 Refereed article in a scholarly journal
Copyright notice ©2002, World Scientific Publishing Company
Persistent URL http://hdl.handle.net/10536/DRO/DU:30001750

Document type: Journal Article
Collections: School of Information Technology
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