On optimal averages
type: Item
instance of: scholarly article
title: On optimal averages
zbMATH Open document ID: 0798.28010
DOI: 10.1007/BF01874945
published in: Acta Mathematica Hungarica
publication date: 1994-11-06T00:00:00Z
review text: By an optimal measure we mean a set function defined on a \(\sigma\)- algebra into the interval \([0,1]\), suitably normalized, which is continuous from above and maps finite unions into finite maxima. As a natural consequence we introduced on the set of measurable functions the so-called optimal average which is a positively homogeneous, monotone increasing, subadditive and finite maximum preserving functional. This nonlinear functional seems to parallel in many ways the Lebesgue integral (or mathematical expectation): in the theory of Lebesgue integral, a good deal of fundamental theorems have each a counterpart in the theory of optimal average.
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 556297
zbMATH Keywords: optimal measure
zbMATH Keywords: optimal average
zbMATH Keywords: maximum preserving functional
author: Nutefe Kwami Agbeko
MaRDI profile type: Publication
cites work: Q3918790
cites work: Q3679426
cites work: Properties of measures of information in evidence and possibility theories
cites work: A possibility measure is not a fuzzy measure
cites work: Fuzzy sets as a basis for a theory of possibility
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description: scientific article; zbMATH DE number 556297