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JACIII Vol.16 No.1 pp. 148-153
doi: 10.20965/jaciii.2012.p0148
(2012)

Paper:

Weighted Quasi-Arithmetic Means and the Domain Translations

Yuji Yoshida

Faculty of Economics and Business Administration, University of Kitakyushu, 4-2-1 Kitagata, Kokuraminami, Kitakyushu 802-8577, Japan

Received:
January 15, 2011
Accepted:
October 3, 2011
Published:
January 20, 2012
Keywords:
weighted quasi-arithmetic mean, utility functions, weighting functions, domain translations, indices translation
Abstract

The monotonicity of the weighted quasi-arithmetic means is discussed from the viewpoint of utility functions and weighting functions. Observing the indices given by utility functions and weighting functions, we find that these indices give similarmonotonicity for the weighted quasi-arithmetic means, and this paper investigates the reason using the direct domain translation adapted to the weighted quasi-arithmetic means. Further, general domain translations are introduced and they are discussed in relation to these indices. Some examples are given for the domain translations and as a special case the translation invariance is presented, and a lot of examples with various utility functions and weighting functions are shown, and their indices and the translated forms are derived.

Cite this article as:
Yuji Yoshida, “Weighted Quasi-Arithmetic Means and the Domain Translations,” J. Adv. Comput. Intell. Intell. Inform., Vol.16, No.1, pp. 148-153, 2012.
Data files:
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