Extension of bivariate means to weighted means of several arguments by using binary trees

Beliakov, Gleb and Dujmović, Jozo 2016, Extension of bivariate means to weighted means of several arguments by using binary trees, Information sciences, vol. 331, pp. 137-147, doi: 10.1016/j.ins.2015.10.040.

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Title Extension of bivariate means to weighted means of several arguments by using binary trees
Author(s) Beliakov, GlebORCID iD for Beliakov, Gleb orcid.org/0000-0002-9841-5292
Dujmović, Jozo
Journal name Information sciences
Volume number 331
Start page 137
End page 147
Total pages 11
Publisher Elsevier
Place of publication Atlanta, Ga.
Publication date 2016-02-20
ISSN 0020-0255
Keyword(s) aggregation functions
logarithmic mean
identric mean
heronian mean
Summary ABSTRACTAveraging aggregation functions are valuable in building decision making and fuzzy logic systems and in handling uncertainty. Some interesting classes of averages are bivariate and not easily extended to the multivariate case. We propose a generic method for extending bivariate symmetric means to n-variate weighted means by recursively applying the specified bivariate mean in a binary tree construction. We prove that the resulting extension inherits many desirable properties of the base mean and design an efficient numerical algorithm by pruning the binary tree. We show that the proposed method is numerically competitive to the explicit analytical formulas and hence can be used in various computational intelligence systems which rely on aggregation functions.
Language eng
DOI 10.1016/j.ins.2015.10.040
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective 970101 Expanding Knowledge in the Mathematical Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2015, Elsevier
Persistent URL http://hdl.handle.net/10536/DRO/DU:30081996

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