Abstract
In this paper some connections between a characterization of fuzzy sets and a characterization of fuzzy partitions are explored. We extend the notion of α-level set and sharpness of fuzzy sets to fuzzy partitions. Then we define α-level equivalence and relation of sharpness on the set of all fuzzy partitions of a finite set of objects into k clusters. We define sharpnesshood and complementhood of fuzzy partitions and then we show how to find the complement of a fuzzy partition.
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References
Backer, E. (1978), Cluster Analysis by Optimal Decomposition of Induced Fuzzy Sets, Delftse Universitaire Pers, Delft.
Bezdek, J. (1981) Pattern Recogition with Fuzzy Objective Function Algorithms, Plenum Press, New York.
Bezdek, J., and Harris, J. (1979), Convex Decomposition of Fuzzy Partitions, Journal of Math. Anal, and Applications, 67, 490–512.
De Luca, A., and Termini, S. (1972), A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory, Information and Control, 20, 301–312.
Dubois, D., and Prade, H. (1980), Fuzzy Sets and Systems: Theory and Applications, Academic Press, New York.
Kosko, B. (1992), Neural Networks and Fuzzy Systems, Prentice Hall, Englewood Cliffs.
Zadeh, L.A. (1965), Fuzzy Sets, Information and Control, 8, 338–353.
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© 1993 Springer-Verlag Berlin · Heidelberg
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Bodjanova, S. (1993). Fuzzy Sets and Fuzzy Partitions. In: Opitz, O., Lausen, B., Klar, R. (eds) Information and Classification. Studies in Classification, Data Analysis and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-50974-2_6
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DOI: https://doi.org/10.1007/978-3-642-50974-2_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-56736-3
Online ISBN: 978-3-642-50974-2
eBook Packages: Springer Book Archive