Ordered Weighted Averages on Intervals and the Sub/Super-Additivity
Faculty of Economics and Business Administration, University of Kitakyushu, 4-2-1 Kitagata, Kokuraminami, Kitakyushu 802-8577, Japan
This paper deals with continuous Ordered Weighted Averages (OWA) on a closed interval and investigates their fundamental properties. In this paper, we focus on OWA with a truncation weight and derive the subadditivity of a top-concentrated average. We then deal with OWA from the bottom and investigate their relations. The subadditivity for OWA with monotone weights is also discussed, then OWA based on probability are demonstrated and value-at-risks are explained as an example.
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