Re: References on the 'shape' of fuzzy sets?

Armin Shmilovici (
Tue, 6 Aug 1996 13:14:52 +0200

> Hi there,
> after reading various papers and books on fuzzy logic control, listening to
> conference presentations, and making the odd experiment myself, I've come to
> the conclusion that the exact 'shape' of a fuzzy set is much less important
> than its overall form, size, and position; meaning that one might as well
> use linear (trapezoidal) functions in cases where these are easier to
> handle or more efficient in computation (I'm sure there are many
> exception!)
> Does anyone know of a publication I could cite that comes to the same
> conclusion? It's hard to know from the title (e.g. from the FSS master
> index) whether a paper does contain a statement of this sort.

Not True --- look

X.J.Zeng and M.G. Singh, "Approximation Accuracy Analysis of
Fuzzy Systems as Functions Approximators", IEEE Trans. FS V. 4 N. 1 February
1996, pp.44-63

The conclusions (as I understand them) are:

1. Product inferencing is more accurate then min inferencing, since it
introduces a second order approximation rather than a first order.

2. The B-spline basis functions, when used as fuzzy sets will provide the most
accuracy (when the other conditions are the same).

3. Under inaccuracies in the data (e.g. noisy observations), the B-splines are
not nessecarily the best to use.

Armin Shmilovici
Tel-Aviv University