Quasi-arithmetic means and ratios of an interval induced from weighted aggregation operations

In this paper we deal with weighted quasi-arithmetic means of an interval using utility functions in decision making. The mean values are discussed from the viewpoint of weighted aggregation operators, and they are given as weighted aggregated values of each point in the interval. The properties of the weighted quasi-arithmetic mean and its translation invariance are investigated. For the application in economics, we demonstrate the decision maker’s attitude based on his utility by the weighted quasi-arithmetic mean and the aggregated mean ratio. Several examples of the weighted quasi-arithmetic mean and the aggregated mean ratio for various typical utility functions are shown to understand our motivation and for the applications in decision making.

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