A characterization of arbitrary Ruspini partitions by fuzzy similarity relations

Author

Thiele, Helmut

Author_Institution

Dept. of Comput. Sci. 1, Dortmund Univ., Germany

Volume

1

fYear

1997

fDate

1-5 Jul 1997

Firstpage

131

Abstract

One of the fundamental problems in clustering theory is the mutual definability of clusterings and binary relations establishing bijections between certain classes of clusterings and certain classes of binary relations. Whereas a fuzzy clustering can be generated by a binary fuzzy relation in a standard procedure, the definition of a suitable binary fuzzy relation from a given clustering holds some problems. After describing some different approaches for solving this problem we introduce a new concept in order to construct a binary fuzzy relation starting with a given clustering. This concept, called relation generating function, can be derived from the concepts of a-disjointness and c-covering for clusterings and gives the possibility to define bijections between arbitrary Ruspini (1969) partitions and certain binary fuzzy relations

Keywords

fuzzy set theory; pattern recognition; a-disjointness; arbitrary Ruspini partitions; bijections; binary fuzzy relation; binary relations; c-covering; clustering theory; fuzzy clustering; fuzzy similarity relations; relation generating function; Character generation; Collaboration; Computer science; Fuzzy sets; Power generation;

fLanguage

English

Publisher

ieee

Conference_Titel

Fuzzy Systems, 1997., Proceedings of the Sixth IEEE International Conference on

Conference_Location

Barcelona

Print_ISBN

0-7803-3796-4

Type

conf

DOI

10.1109/FUZZY.1997.616357

Filename

616357