# Re: Fuzzy Logic - why?

WSiler (wsiler@aol.com)
Sun, 15 Nov 1998 22:54:17 +0100 (MET)

>I see a difficulty here -- suppose that we need to know "A and not B",
>or "A or not B" where B is not the same as A but it is dependent or
>correlated with A.
>
>(E.g., A = "temperature sensor 1 is very high", B = "temperature sensor 2
>is very high" -- where the sensors are measuring the same process, so
>they're meant to be redundant.)
>
>Then "A and not B" ought to be close to false and "A or not B" ought to
>be close to true, but that's not what you get if you use ordinary
>min-max operators --
>
As it happens, in the case you cite max-min works just fine. The reason is that
A and B are measuring almost the same thing, so they are highly positively
associated.

However, if A and B were strongly negatively associated, max-min wouldn't work
well. In this situation bounded sum ans difference would work well, with a AND
b = max(0, 1 - (a + b)) and a OR b = min(1, a+b).

But this kind of reasoning is only appropriate if we have PRIOR associations.
In the case of two sensors measuring pretty much the same thing on a process,
we would have reasonably reliable prior associations. We're up against the same
thing that plagues Bayes' theorem - what are the priors? Mostly we don't know,
and max-min is a good default.

William Siler

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