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A topological approach to some cluster methods

  • 8. Uncertainty In Intelligent Systems
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Book cover Uncertainty in Knowledge Bases (IPMU 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 521))

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Abstract

One of the most usual ways of classifying the elements of a set is to cluster them according to some kind of “proximity measure”. Proximity is a topological concept and therefore it is natural to ask for topological structures that lead to cluster methods.

Using this idea, we construct some families of cluster methods starting on from a kind of V D-spaces.

In order to relate the elements of these families, morphisms between cluster methods are defined.

Research partially supported by the DGICYT, project n. PS.87-0108

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References

  1. Alsina, C., Trillas, E. (1978) Introducción a los Espacios Métricos Generalizados. Fund. J. March. Serie Universitaria 49.

    Google Scholar 

  2. Bouchon, B., Cohen, G., Frankl, P. (1982) Metrical properties of fuzzy relations. Problems of Control and Information Theory 11, 389–396.

    Google Scholar 

  3. Defays, D. (1975) Ultramétriques et relations floues. Bull. Societé Royale de Sciences de Liège, 1–2, 104–118.

    Google Scholar 

  4. Jacas, J. (1990) Similarity Relations — The Calculation of Minimal Generating Families, Fuzzy Sets and Systems 35, 151–162.

    Article  Google Scholar 

  5. Jacas, J., Valverde, L. (1987) A Metric Characterization of T-transitive Relations, Proceedings of FISAL-86, Palma de Mallorca 81–89.

    Google Scholar 

  6. Jacas, J., Valverde, L. (1990). On Fuzzy Relations, Metrics and Cluster Analysis in: J.L. Verdegay & M. Delgado Eds., Approximate Reasoning. Tools for Artificial Intelligence (Verlag TÜV, Rheinland) 15R, 96.

    Google Scholar 

  7. Janowitz, H.F., Schweizer, B. (1988) Ordinal amb Percentile Clustering. Technical Report. Dept. of Mathematics and Statistics. Univ. Massachusetts.

    Google Scholar 

  8. Jardine, N., Sibson, R. (1971) Mathematical Taxonomy. Wiley, New York.

    Google Scholar 

  9. Schweizer, B., Sklar, A. (1983) Probabilistic Metric Spaces. North-Holland, New York.

    Google Scholar 

  10. Sneath, P.H.A., Sokal, R.P. (1973) Numberical Taxonomy. W.H. Freeman & Co., San Francisco.

    Google Scholar 

  11. Valverde, L. (1985) On the structure of F-indistinguishability operators. Fuzzy Sets and Systems, 17, 313–328.

    Article  Google Scholar 

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Bernadette Bouchon-Meunier Ronald R. Yager Lotfi A. Zadeh

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© 1991 Springer-Verlag Berlin Heidelberg

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Jacas, J., Recasens, J. (1991). A topological approach to some cluster methods. In: Bouchon-Meunier, B., Yager, R.R., Zadeh, L.A. (eds) Uncertainty in Knowledge Bases. IPMU 1990. Lecture Notes in Computer Science, vol 521. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028134

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  • DOI: https://doi.org/10.1007/BFb0028134

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54346-6

  • Online ISBN: 978-3-540-47580-4

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