Geodesic
Weighted means and weighting functions
Kybernetika, Tome 42 (2006) no. 2, pp. 151-160.

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We present some properties of mixture and generalized mixture operators, with special stress on their monotonicity. We introduce new sufficient conditions for weighting functions to ensure the monotonicity of the corresponding operators. However, mixture operators, generalized mixture operators neither quasi-arithmetic means weighted by a weighting function need not be non- decreasing operators, in general.
Classification : 26E60, 90C29, 91B06
Keywords: mixture operator; generalized mixture operator; monotonicity of the mixture operator; quasi-arithmetic mean; ordinal approach 
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     title = {Weighted means and weighting functions},
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     volume = {42},
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     zbl = {1249.91022},
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Mesiar, Radko; Špirková, Jana. Weighted means and weighting functions. Kybernetika, Tome 42 (2006) no. 2, pp. 151-160. http://geodesic.mathdoc.fr/item/KYB_2006__42_2_a2/