Computing with words and its relationships with fuzzistics

  • Authors:

  • Jerry M. Mendel

  • Affiliations:

  • Signal and Image Processing Institute, Department of Electrical Engineering, University of Southern California, 3740 McClintock Avenue, Los Angeles, CA 90089-2564, United States

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2007

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Abstract

Words mean different things to different people, and so are uncertain. We, therefore, need a fuzzy set model for a word that has the potential to capture their uncertainties. In this paper I propose that an interval type-2 fuzzy set (IT2 FS) be used as a FS model of a word, because it is characterized by its footprint of uncertainty (FOU), and therefore has the potential to capture word uncertainties. Two approaches are presented for collecting data about a word from a group of subjects and then mapping that data into a FOU for that word. The person MF approach, in which each person provides their FOU for a word, is limited to fuzzy set experts because it requires the subject to be knowledgeable about fuzzy sets. The interval end-points approach, in which each person provides the end-points for an interval that they associate with a word on a prescribed scale is not limited to fuzzy set experts. Both approaches map data collected from subjects into a parsimonious parametric model of a FOU, and illustrate the combining of fuzzy sets and statistics-type-2 fuzzistics.