Distances between fuzzy sets

  • Authors:

  • Azriel Rosenfeld

  • Affiliations:

  • Center for Automation Research, University of Maryland, College Park, MD 20742, USA

  • Venue:
  • Pattern Recognition Letters
  • Year:
  • 1985

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Abstract

Given two fuzzy subsets @m and @n of a metric space S (e.g., the Euclidean plane), we define the 'shortest distance' between @m and @n as a density function on the non-negative reals; our definition is applicable both when @m and @n are discrete-valued and when they are 'smooth' (i.e., differentiable), and it generalizes the definition of shortest distance for crisp sets in a natural way. We also define the mean distance between @m and @n, and show how it relates to the shortest distance. the relationship to earlier definitions of distance between fuzzy sets [1,3] is also discussed.