# Re: Fuzzy Logic - why?

Sun, 15 Nov 1998 22:12:55 +0100 (MET)

WSiler <wsiler@aol.com> wrote:
[...]
> [...] the definitions of excluded
> middle for multivalued logics are A AND NOT A = 0, and A OR NOTA = 1. The
> failure of max-min fuzzy logic to obey these laws is why conventional
> fuzzy logic does not obey excluded middle and contradiction.
>
> If the bounded sum and bounded difference operators are used when both
> A and NOT A appear in the same proposition, then these laws are obeyed.
> If A dnd NOT A do not appear in the same proposition, then excluded
> middle and contradiction don't arise, and you can use any multivalued
> logic you please for whatever reason.

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 -- thus I don't think "you can use any multivalued
logic you please for whatever reason."

One work-around is to exclude propositions containing dependent or
correlated variables -- however, such variables are extremely common,
and dependence can often arise in subtle ways. Is there a better way
to patch fuzzy logic so that dependence is handled correctly?

--Robert Dodier

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