10. Fuzzy Classification

  1. Timothy J. Ross

Published Online: 27 DEC 2010

DOI: 10.1002/9781119994374.ch10

Fuzzy Logic with Engineering Applications, Third Edition

Fuzzy Logic with Engineering Applications, Third Edition

How to Cite

Ross, T. J. (2010) Fuzzy Classification, in Fuzzy Logic with Engineering Applications, Third Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119994374.ch10

Author Information

  1. University of New Mexico, USA

Publication History

  1. Published Online: 27 DEC 2010
  2. Published Print: 15 JAN 2010

ISBN Information

Print ISBN: 9780470743768

Online ISBN: 9781119994374



  • cluster analysis;
  • equivalence relations;
  • fuzzy c-means (FCM);
  • fuzzy classification;
  • fuzzy relations;
  • hard c-means (HCM)


This chapter summarizes only two popular methods of classification. The first is classification using equivalence relations. This approach makes use of certain special properties of equivalence relations and the concept of defuzzification known as lambda-cuts on the relations. The second method of classification is a very popular method known as fuzzy c-means (FCM), so named because of its close analog in the crisp world, hard c-means (HCM). This method uses concepts in n-dimensional Euclidean space to determine the geometric closeness of data points by assigning them to various clusters or classes and then determining the distance between the clusters. In the case of fuzzy relations, for all fuzzy equivalence relations, their ?-cuts are equivalent ordinary relations. Hence, to classify data points in the universe using fuzzy relations, we need to find the associated fuzzy equivalence relation.

Controlled Vocabulary Terms

fuzzy logic; pattern clustering