Weakly monotonic averaging functions

Wilkin,T and Beliakov,G 2015, Weakly monotonic averaging functions, International Journal of Intelligent Systems, vol. 30, no. 2, pp. 144-169, doi: 10.1002/int.21692.

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Title Weakly monotonic averaging functions
Author(s) Wilkin,TORCID iD for Wilkin,T orcid.org/0000-0003-4059-1354
Beliakov,GORCID iD for Beliakov,G orcid.org/0000-0002-9841-5292
Journal name International Journal of Intelligent Systems
Volume number 30
Issue number 2
Start page 144
End page 169
Total pages 26
Publisher John Wiley & Sons
Place of publication NJ, United States
Publication date 2015-02-01
ISSN 0884-8173
Keyword(s) Science & Technology
Computer Science, Artificial Intelligence
Computer Science
Summary Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions. It is also a limiting property that results in many important nonmonotonic averaging functions being excluded from the theoretical framework. This work proposes a definition for weakly monotonic averaging functions, studies some properties of this class of functions, and proves that several families of important nonmonotonic means are actually weakly monotonic averaging functions. Specifically, we provide sufficient conditions for weak monotonicity of the Lehmer mean and generalized mixture operators. We establish weak monotonicity of several robust estimators of location and conditions for weak monotonicity of a large class of penalty-based aggregation functions. These results permit a proof of the weak monotonicity of the class of spatial-tonal filters that include important members such as the bilateral filter and anisotropic diffusion. Our concept of weak monotonicity provides a sound theoretical and practical basis by which (monotonic) aggregation functions and nonmonotonic averaging functions can be related within the same framework, allowing us to bridge the gap between these previously disparate areas of research.
Language eng
DOI 10.1002/int.21692
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
Copyright notice ©2014, John Wiley & Sons
Persistent URL http://hdl.handle.net/10536/DRO/DU:30069344

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