# Re: A challenge: What is an edge?

Subject: Re: A challenge: What is an edge?
From: Paul Victor Birke (nonlinear@home.com)
Date: Sun Apr 16 2000 - 23:21:30 MET DST

"Michelle T. Lin" wrote:

>>snippings<<

> The amorphous facet relates to instances in which an edge is a
> fuzzy set but its membership function does not admit precisiation, and
> there is no internal or external consensus on whether an edge exists
> and, if it exists, how its membership function should be defined. In
> other words, the membership function is a pseudo-function in the sense
> in which I defined it in a recent abstract. In essence, a
> pseudo-function is a function whose meaning cannot be defined in what
> I call the Generalized Constraint Language (GCL) -- a language which
> is maximally expressive.
>
> In this framework, a concept is crisp if its only facet is
> crisp. A concept is fuzzy if has a crisp facet and a fuzzy facet.
> And a concept is amorphic if it has all three facets.

>>snippings<<

For the amorphous portion, could we consider an Ultra Fuzzy Function of
"fatness width" equal to that known or guessed for the amorphous
portion? If you define the inside edge and the outside edge of the
Ultra Fuzzy Function you can have a linear variation of density from
that at the Fuzzy Outside Edge = Ultra Fuzzy Inside Edge = some know
value to that of the Outside Ultra Fuzzy Edge = Beyond Edge Boundary =
some other known value. Within the Ultra Fuzzy function, variation if
obtained by forming a local variable Geometric Mean Fuzzy Function
between the Inside and Outside boundaries of the Ultra Fuzzy function.

Paul

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