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New results in fuzzy clustering based on the concept of indistinguishability relation
September 1988 (vol. 10 no. 5)
pp. 754,755,756,757
The issue of validity in clustering is considered and a definition of fuzzy r-cluster that extends E. Ruspini's definition (1982) is proposed. This definition is based on an indistinguishability relation based on the concept of t-norm. The fuzzy r-cluster's metrical properties are studied through the dual concept of t-conorm that leads to G-pseudometrics. From the concept of G-pseudometric, fuzzy r-clusters and fuzzy cluster coverages are defined. The authors propose a measure of cluster validity based on the concept of fuzzy coverage. The basic idea of the approach presented is that the smaller the difference between the degrees of membership and the degrees of indistinguishability, the better the clustering.<>

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Index Terms:
pattern recognition,fuzzy set theory,dual concept,pattern recognition,fuzzy set theory,G-pseudometrics concept,fuzzy clustering,indistinguishability relation,Prototypes,Graph theory,Length measurement,Fuzzy sets,Contracts,Clustering algorithms,Partitioning algorithms
Citation:
"New results in fuzzy clustering based on the concept of indistinguishability relation," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 5, pp. 754,755,756,757, Sept. 1988, doi:10.1109/34.6788
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