Extracting cover sets from free fuzzy sorting data

Extracting cover sets from free fuzzy sorting data Assignment of items to multiple categories requires suitable statistical methods. The present paper provides a new approach to solve this task. The concept of fuzzy sets is extended to cover sets (sets of overlapping clusters) in a simple manner introducing a vector of item membership sums. The application of the new concept is exemplified by modifying the fuzzy cluster analysis algorithm of Kaufman and Rousseeuw (Finding groups in data: an introduction to cluster analysis, 1990) to cover set cluster analysis appropriately. Wide equivalence of the numerical problems is demonstrated from Lagrange multipliers and Karush-Kuhn-Tucker conditions. Additionally, some extensions are introduced to the algorithm to improve its behavior for suboptimal large or small numbers of clusters. The adapted algorithm in most cases reproduces single sortings for correct numbers of clusters. Two applications to empirical free fuzzy sorting data sets are provided. Limitations of the algorithm are discussed. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

Extracting cover sets from free fuzzy sorting data

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Publisher
Springer Journals
Copyright
Copyright © 2011 by Springer Science+Business Media B.V.
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-011-9497-y
Publisher site
See Article on Publisher Site

Abstract

Assignment of items to multiple categories requires suitable statistical methods. The present paper provides a new approach to solve this task. The concept of fuzzy sets is extended to cover sets (sets of overlapping clusters) in a simple manner introducing a vector of item membership sums. The application of the new concept is exemplified by modifying the fuzzy cluster analysis algorithm of Kaufman and Rousseeuw (Finding groups in data: an introduction to cluster analysis, 1990) to cover set cluster analysis appropriately. Wide equivalence of the numerical problems is demonstrated from Lagrange multipliers and Karush-Kuhn-Tucker conditions. Additionally, some extensions are introduced to the algorithm to improve its behavior for suboptimal large or small numbers of clusters. The adapted algorithm in most cases reproduces single sortings for correct numbers of clusters. Two applications to empirical free fuzzy sorting data sets are provided. Limitations of the algorithm are discussed.

Journal

Quality & QuantitySpringer Journals

Published: Apr 23, 2011

References

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