Fuzzy Geometry and Topology

robertl1@home.com
Tue, 24 Mar 1998 02:17:41 +0100 (MET)

Hello all,

I am looking at an application that might be approached using what I will call
"Fuzzy" geometry. So I am wondering if such a subject exists? And do you have
links to its literature?

I will explain. Fuzzy sets were introduced by Lofti Zadeh as an extension of
the idea of sets. Membership in the set was not so hard core as in
conventional sets. One has distribution functions and all of that. Talks of
possibilities etc. So a fuzzy logic gets developed on top of fuzzy sets. It is
all quite rigorous, etc.

So I ran across this geometry problem that looked like it could be handled
best with a fuzzy approach to geometry. If for instance one starts with simple
geometry based on point sets and their connections in simple spaces then it
would seem straightforward to construct a fuzzy geometry based on fuzzy sets.
Given mathematicians proclivity for generalization this would seem a natural
industry for their talents.

Has this been done yet? Can you provide me with some references?

Also repeat this question for a Fuzzy Topology.

TIA,

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