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Fuzzy Partition Models for Fitting a Set of Partitions

Published online by Cambridge University Press:  01 January 2025

A. D. Gordon  and
M. Vichi
A. D. Gordon*
Affiliation:
University of St Andrews
M. Vichi*
Affiliation:
‘La Sapienza’ University of Rome
*
Requests for reprints should be sent to A.D. Gordon, School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews KY16 9SS, SCOTLAND. E-Mail: adg@st-andrews.ac.uk
M. Vichi, Department of Statistics, Probability and Applied Statistics, 'La Sapienza' University of Rome, Rle A. Moro 5, 1-00185 Rome, ITALY. E-Mail: vichi@dmqte.unich.it
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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.

Keywords

classificationcluster analysisconsensus fuzzy partitionmembership functionthree-way data
Type
Articles
Information
Psychometrika , Volume 66 , Issue 2 , June 2001 , pp. 229 - 247
Copyright
Copyright © 2001 The Psychometric Society

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Footnotes

We are grateful to Dr. M.G. Pittau for carrying out the analyses of the macroeconomic data using the method of Sato and Sato (1994).

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