Psychometrika

, Volume 66, Issue 2, pp 229–247

Fuzzy partition models for fitting a set of partitions

Articles

DOI: 10.1007/BF02294837

Cite this article as:
Gordon, A.D. & Vichi, M. Psychometrika (2001) 66: 229. doi:10.1007/BF02294837

Abstract

Methodology is described for fitting a fuzzy consensus partition to a set of partitions of the same set of objects. Three models defining median partitions are described: two of them are obtained from a least-squares fit of a set of membership functions, and the third (proposed by Pittau and Vichi) is acquired from a least-squares fit of a set of joint membership functions. The models are illustrated by application to both a set of hard partitions and a set of fuzzy partitions and comparisons are made between them and an alternative approach to obtaining a consensus fuzzy partition proposed by Sato and Sato; a discussion is given of some interesting differences in the results.

Key words

classification cluster analysis consensus fuzzy partition membership function three-way data 

Copyright information

© The Psychometric Society 2001

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of St Andrews, North HaughSt AndrewsScotland
  2. 2.Department of Statistics, Probability and Applied Statistics‘La Sapienza’ University of RomeRomeItaly

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