Clustering of vaguely defined objects

Libor Žák

Archivum Mathematicum (2003)

  • Volume: 039, Issue: 1, page 37-50
  • ISSN: 0044-8753

Abstract

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This paper is concerned with the clustering of objects whose properties cannot be described by exact data. These can only be described by fuzzy sets or by linguistic values of previously defined linguistic variables. To cluster these objects we use a generalization of classic clustering methods in which instead of similarity (dissimilarity) of objects, used fuzzy similarity (fuzzy dissimilarity) to define the clustering of fuzzy objects.

How to cite

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Žák, Libor. "Clustering of vaguely defined objects." Archivum Mathematicum 039.1 (2003): 37-50. <http://eudml.org/doc/249121>.

@article{Žák2003,
abstract = {This paper is concerned with the clustering of objects whose properties cannot be described by exact data. These can only be described by fuzzy sets or by linguistic values of previously defined linguistic variables. To cluster these objects we use a generalization of classic clustering methods in which instead of similarity (dissimilarity) of objects, used fuzzy similarity (fuzzy dissimilarity) to define the clustering of fuzzy objects.},
author = {Žák, Libor},
journal = {Archivum Mathematicum},
keywords = {fuzzy sets; extension principle; clustering methods; fuzzy clustering; fuzzy sets; extension principle; clustering methods; fuzzy clustering},
language = {eng},
number = {1},
pages = {37-50},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Clustering of vaguely defined objects},
url = {http://eudml.org/doc/249121},
volume = {039},
year = {2003},
}

TY - JOUR
AU - Žák, Libor
TI - Clustering of vaguely defined objects
JO - Archivum Mathematicum
PY - 2003
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 039
IS - 1
SP - 37
EP - 50
AB - This paper is concerned with the clustering of objects whose properties cannot be described by exact data. These can only be described by fuzzy sets or by linguistic values of previously defined linguistic variables. To cluster these objects we use a generalization of classic clustering methods in which instead of similarity (dissimilarity) of objects, used fuzzy similarity (fuzzy dissimilarity) to define the clustering of fuzzy objects.
LA - eng
KW - fuzzy sets; extension principle; clustering methods; fuzzy clustering; fuzzy sets; extension principle; clustering methods; fuzzy clustering
UR - http://eudml.org/doc/249121
ER -

References

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  1. Anderberg M. R., Cluster Analysis for Applications, Academic Press, New York, 1973. (1973) Zbl0299.62029MR0326934
  2. Bezdek J. C., Pattern Recognition with Fuzzy Objective Function Alghorithms, Plenium Press, New York, 1981. (1981) MR0631231
  3. Diday, E, Simon J. C., Clustering Analysis, In FU K. S. Digital Pattern Recognition, Springer-Verlag, New York (1980), 47–92. (1980) 
  4. Dubois D., Prade H., Fuzzy Sets and Systems. Theory and Application, Academic Press, New York, 1980. (1980) MR0589341
  5. Karpíšek Z., Pospíšek M., Slavíček K., Properties of Certain Class of Fuzzy Numbers, Proc. Zittau Fuzzy Colloquium, Zittau (2000), 42–52, ISBN 3-00-006723-X. 
  6. Klir G. J., Yuan B., Fuzzy Sets and Fuzzy Logic. Theory and Applications, Prentice Hall PTR, New Jersey, 1995. (1995) Zbl0915.03001MR1329731
  7. Lukasová A.- Šarmanová J., Methods of Clustering Analysis, SNTL Praha, 1985 (in Czech). (1985) 
  8. Moore R. E., Interval Analysis, Prentice-Hall, New Jersey, 1966. (1966) Zbl0176.13301MR0231516
  9. Novák V., Fuzzy Sets and its Applications, SNTL Praha, 1986 (in Czech). (1986) 
  10. Späth H., Cluster Dissection and Analysis, Ellis Horwood, 1985. (1985) Zbl0584.62094
  11. Zadeh L. A., Fuzzy Sets and Their Application to Pattern Classification and Cluster Analysis, In Classification and Clustering, Academic Press, New York, 1977. (1977) MR0483813
  12. Žák L., Fuzzy Clustering, Proc. Fuzzy logika - od metodiky k aplikacím, Hrubá Skála (1998), 81–87, (in Czech). (1998) 
  13. Žák L., Clustering of Fuzzy Objects 1, Proc. Mendel 1999, International Conference on Soft Computing, Brno (1999), 310–317, ISBN 80-214-1131-7. (1999) 
  14. Žák L., Clustering and Fuzzy Objects, Proc. Fuzzy logika - fuzzy logika, neuronové sítě a expertní systémy, Hrubá Skála (1999), 51–58, (in Czech). (1999) 
  15. Žák L., Clustering of Fuzzy Objects 2, . Proc. Mendel 2000, International Conference on Soft Computing, Brno (2000), 310–317, ISBN 80-214-1131-7. 
  16. Žák L., Fuzzy Objects and Fuzzy Clustering, Proc. Zittau Fuzzy Colloquium, Zittau (2000), 293–302, ISBN 3-00-006723-X. 
  17. Žák L., Generalization Fuzzy Clustering for Fuzzy Objects, Proc. Inteligentní systémy pro praxi, Luhačovice (2000), 59–68, ISBN 80-238-6140-9 (in Czech). 
  18. Žák L., Clustering of vaguely defined objects, PhD Thesis, Technical University, Brno, 2002, ISSN 1213-4198 (in Czech). Zbl1122.62319MR1982210

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