Fuzzy partition models for fitting a set of partitions |
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Authors: | A. D. Gordon M. Vichi |
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Affiliation: | (1) School of Mathematics and Statistics, University of St Andrews, North Haugh, KY16 9SS St Andrews, Scotland;(2) Department of Statistics, Probability and Applied Statistics, La Sapienza University of Rome, P.le A. Moro 5, I-00185 Rome, Italy |
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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.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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Keywords: | classification cluster analysis consensus fuzzy partition membership function three-way data |
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