Proximity-Based Measures

  • Valerie V. Cross
  • Thomas A. Sudkamp
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 93)


Tversky [221] noted that “most theoretical and empirical analyses of similarity assume that objects can be adequately represented as points in some coordinate space and that dissimilarity behaves like a distance function.” While Tversky’s observation concerned objects as crisp values, the notion of proximity defining similarity can also be used to assess the similarity of fuzzy sets. For fuzzy sets, the distance is not between points but rather between membership functions. In this chapter we consider three methods for producing metric based similarity measures.


Membership Function Fuzzy Number Hausdorff Distance Jaccard Index Symmetric Difference 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Valerie V. Cross
    • 1
  • Thomas A. Sudkamp
    • 2
  1. 1.Department of Computer Science and EngineeringUniversity of South CarolinaColumbiaUSA
  2. 2.Department of Computer ScienceWright State UniversityDaytonUSA

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