Linguistic weighted power means: Comparison with the linguistic weighted average

We have introduced the linguistic weighted power mean and its computation via a generalization of the Karnick-Mendel algorithm. This new family of aggregation operators admits interval type-2 fuzzy membership functions for both its inputs and its weights to account for imprecise knowledge of these quantities. The simplest member of this family, the linguistic weighted average, is the primary instantiation of a “perceptual computing” engine in Mendel and Wu's recent book by this title. This paper presents a comparison of the linguistic weighted power mean and the linguistic weighted average on one of the examples they describe in detail — the “investment judgment advisor”. Our results illustrate the flexibility and range of logical inference provided by this very versatile aggregation operator for computing with words applications.