# Calculating the extension principle

Geraldo =?iso-8859-1?Q?Xex=E9o?= (xexeo@cos.ufrj.br)
Wed, 3 Mar 1999 03:29:33 +0100 (MET)

In a paper that is cited in many books, "Rating and Ranking of Multiple
Aspect Alternatives Using Fuzzy Sets" Baas and Kwakernaak, Automatica
(13)pp47-58, written in 1977, there is a approach to calculating a
weighted average of fuzzy ratings with fuzzy weigths.

Since this paper is from the earlier days, it uses the extension
principle without naming it and later provide a shortcut method to
calculate it. Basically, it provides some interesting points and prove
that they are the solution for max(min(mi(x)) given f(x)=Y.

There are any further works in general algorithms to calculate the
fuzzy extension of a function?

Is Maximize(Minimum(mi(x1),mi(x2),...)) the only way?

There is a constructive numerical solution?

Thanks,
Jerry

```--
Geraldo Xexéo, D.Sc. (DCC/IM/UFRJ e PESC/COPPE/UFRJ)
mailto:xexeo@cos.ufrj.br http://www.cos.ufrj.br/~xexeo
ICQ#:12662368 Tel. 590 2552 R 236
"Se você acha a Educação cara, experimente a ignorância." C.W. Elliot

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