# Re: How is the degree of membership calculated?

WSiler (wsiler@aol.com)
Tue, 28 Apr 1998 16:37:53 +0200 (MET DST)

>Normally one then takes the maximum value over all of the
> memberships for the linguistic set and assigns that to the result.

Sorry, I cannot agree with that. In my experience, one usually wants to do
something after fuzzification. In this case, the input is the value of x. The
output of fuzzification is grades of membership in the fuzzy set say
Temperature composed of Cool, Just_Right, and Warm. If one is (for some
unimaginable reason) controlling simple thermostat with three settings, Cool,
Off and Heat, then what you say might make sense. But using fuzzy math for that
purpose is silly; three simple statements (if x < 65 then Heat, else if x >= 65
and < 72 then Off, else if x >= 72 then Cool) will do the trick perfectly well
without any fuzzy math.

Instead, either the fuzzy set Temperature is piped on to further rules, or
perhaps with a more complex antecedent involving other quantities the result
might be defuzzified for a result.

There are some who, in problems of classification, assume that the
classification with the highest grade of membership is the correct answer. I
emphatically do not agree with this.It is best to take a measure of ambiguity;
if this measure indicates that more than one classification could possibly be
correct, then more rules to resolve the situation should be invoked.

William Siler