Computing with Words Using Weighted Power Mean Aggregation Operators

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Weighted power means are a flexible and powerful family of aggregation functions. The simplest member of this family, the weighted arithmetic mean, previously has been adapted for interval type-2 fuzzy scores and weights. This operator has been termed a “linguistic weighted average,” and has been a primary instantiation of a “perceptual computer” in recent literature. We present an algorithm for computing weighted power means of arbitrary power for type-1 or interval type-2 fuzzy inputs and weights, which we call “linguistic weighted power means.” We compare the linguistic weighted power mean and the linguistic weighted average on an “investment judgment advisor” example. Our results illustrate the flexibility and range of logical inference provided by this very versatile aggregation operator for computing with words applications.