Difference, distance and similarity as a basis for fuzzy decision support based on prototypical decision classes

  • Authors:

  • Jon Williams;Nigel Steele

  • Affiliations:

  • Computational Intelligence Group, School of Mathematical and Information Science, Coventry University, Priory Street, Coventry CV1 5FB, UK;Computational Intelligence Group, School of Mathematical and Information Science, Coventry University, Priory Street, Coventry CV1 5FB, UK

  • Venue:
  • Fuzzy Sets and Systems - Special issue: Soft decision analysis
  • Year:
  • 2002

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Abstract

The use of prototypical decision classes as a basis for fuzzy decision support is outlined. It is shown that given certain assumptions about the structure of both numeric and non-numeric linguistic variables Trapezoidal Fuzzy Sets can be used to model linguistic terms. In particular the notion of a fuzzy index is introduced to model sets of linguistic terms for which there is no formal measurement scale. The similarity between prototypes and input cases is measured as a function of the difference or 'distance' between fuzzy sets. The difference measure is itself a fuzzy set to reflect the underlying uncertainties in the original linguistic model. Similarity profiles for different decision classes are output as trapezoidal fuzzy sets. The approach can be applied to the rapid development of decision aids using standard business software.