Re: Bezdek or Ruspini partition

Martin Ameskamp (ma@informatik.uni-kiel.de)
Wed, 1 May 1996 16:28:33 +0200


In <4m53mr$hp0@laas.laas.fr> lacrose@laas.fr (Veronique Lacrose) writes:
>I have a little problem concerning the definition of
>a fuzzy partition where the membership functions (mbf)
>intersect for a 0.5 membership value.
>In other words, the maximum of a mbf corresponds to the
>minimum of the adjacent ones, that means that the sum of
>the activation degrees of the rules is always equal to 1.

>Well, as far as I know, it is a Bezdek partition. However, in a
>recent workshop, someone told me it was a Ruspini one and
>ask me the reference of this definition. I have read this
>terminology in many articles but I can't find the sources
>of this definition.

Hm, I'm not sure that I understand your question:
Are we talking about fuzzy partitions or fuzzy rules?
I'm sure that both can be used together, but do they have to be?
(Myself, I use both, but quite independently).

As to the name, this question only makes sense if a Ruspini
partition is something different from a Bezdek partition.
There are many concepts that have different names
(Thiessen and Voronoi polygons come to mind).

If you want a reference for Ruspini partitions, try the
following:
E.H. Ruspini, 'A new approach to clustering', Information and Control,
vol 15, 1969, p. 22-32.

Martin