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Title: Fuzziness measurement of fuzzy sets and its application in cluster validity analysis
Authors: Gao, X
Li, J
Tao, D 
Li, X
Keywords: Fuzziness measurement
Partition fuzziness
Cluster validity
Partition entropy
Issue Date: 2007
Publisher: Springer
Source: International journal of fuzzy systems, 2007, v. 9, no. 4, p. 188-197 How to cite?
Journal: International journal of fuzzy systems 
Abstract: To measure the fuzziness of fuzzy sets, this paper introduces a distance-based and a fuzzy entropy-based measurements. Then these measurements are generalized to measure the fuzziness of fuzzy partition, namely partition fuzziness. According to the relationship between the validity of fuzzy partition and its partition fuzziness, a family of cluster validity functions is proposed based on the modified partition fuzziness. The new cluster validity functions overcome the increasing tendency of the traditional partition fuzziness with the cluster number, which provides an effective analysis methodology for fuzzy cluster validity. The experimental results with different testing data sets illustrate the effectiveness, reliability, sensitivity and applicability of the proposed cluster validity function.
ISSN: 1562-2479
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