Aggregated Mean Ratios of an Interval Induced from Aggregation Operations

This paper deals with quasi-arithmetic means of an interval through utility functions in decision making. The mean values are discussed from the viewpoint of aggregation operators, and they are given as aggregated values of each point in the interval. We investigate the properties of the quasi-arithmetic mean and its translation invariance, and next we demonstrate the decision maker's attitude based on his utility by the quasi-arithmetic mean and the aggregated mean ratio. The dual quasi-arithmetic means are also discussed with dual aggregation operators. Finally, examples of the quasi-arithmetic means and the aggregated mean ratio for various typical utility functions are given to understand the motivation.

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