Re: Request: empirical determination of membership-functions

Vicen Torra (
Tue, 18 Jun 1996 16:38:16 +0200


On Fri, 14 Jun 1996, Andre Ramos wrote:

> Hi,
> One approach I've seen for engineering parameters is to let the engineer
> define the points to which he/she feels the relation between the given
> parameter/memebership value are appropriate. Then, a spline is fitted to
> the points and the membership function is formed based on the the spline.
> See the paper:
> J.E. Chen and K.N. Otto, Constructing membership functions using
> interpolation and measurement theory, Fuzzy Set and Systems 73(1995), pp.
> 313-327

I have recently implemented the above method, and although the
guidelines are very interesting I have found several errors in the
formula given. Also, the cases included in the algorithm are not
In my implementation, as the problem to which it was oriented was
slightly different, the extreme conditions were changed. The authors
require that in the extreme points the derivative is zero (although in
the last figure this is not always shown), I have changed that condition
to have a smooth curve in the extremes.
I have described the modified algorithm in a paper submitted to Fuzzy
Sets and Systems. If you are interested in it, I can send you a preprint.

> Hope this helps a bit,
Also, hope this helps

Vicenc Torra,
Dept. Enginyeria Informatica, Universitat Rovira i Virgili
Carretera de Salou, s/n, 43006 Tarragona, Catalunya, Spain
phone: 34-77-55-96-81, fax: 34-77-55-97-10