Soft Computing: State of the Art Theory and Novel Applications

Volume 291 of the series Studies in Fuzziness and Soft Computing pp 145-160

Computing with Words Using Weighted Power Mean Aggregation Operators

  • John T. RickardAffiliated withDistributed Infinity, Inc. Email author 
  • , Janet AisbettAffiliated withFaculty of Science and IT, The University of Newcastle
  • , Ronald R. YagerAffiliated withMachine Intelligence Institute, Iona College
  • , Greg GibbonAffiliated withFaculty of Science and IT, The University of Newcastle

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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.


aggregation operators type-2 fuzzy logic computing with words perceptual computing