KYBERNETIKA

Kybernetika 42(2):151-160, 2006.

Weighted Means and Weighting Functions

Radko Mesiar and Jana Špirková

Abstract:

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.

Keywords: mixture operator; generalized mixture operator; monotonicity of the mixture operator; quasi-arithmetic mean; ordinal approach;

AMS: 91B06;