Re: fuzzy logic

[phrp@bigcat.fhsu.edu (Roger Pruitt)]

All of the responses that have been given to Ludwig's question about
fuzzy logic are good. In brief, it the the kind of logic that is applied
when there are no clearly defined alternatives. As an example, you are
driving down the street and the green light turns yellow. Do you stop,
do you speed up, or do you keep going hoping that you can successfully
get through the intersection without the light turning red?

Roger Pruitt

Miguel A. Santos wrote:
> > What is fuzzy logic?
> If you don't have any idea, then I think this post will
> give 2 cents. Otherwise,  if you know the basics, it won't add
> nothing more:
>
> Our usual algebra, and the deduction schemes therein, is
> based, among others, on the axiom of 'no contradiction'. That
> is,
>
>         p or -p     (-p stands for 'no-p')
>
> is a tautology in the Logic of Propositions, which implies
> we are working with a bi-valued logic. Any sentence is a proposition
> iif it can be asigned a truth value which will be either 'true' or 'false'.
>
> A natural generalization of this scheme was proposed long ago
> by Lukasiewicz. He set up  a discrete n-valued logic were any
> proposition could be assigned the truth value
>
>         Pk = (k-1)/(n-1)    k=1,...,n
>
> This, of course, will change our usual connectivities, that is, the
> logic operators: AND, OR, IF-THEN, IIF-THEN, NOT. For instance,
>
>         p AND q = min(p,q)
>         p ->  q = min(1,1+q-p)
>         p <-> q = 1 - abs(p-q)
>
> A step further in this process of generalizing our classical Logic,
> is making the truth value a continuos parameter.Then you get a
> continous-valued-logic. Roughly, this is what is called ''Fuzzy Logic'.
> It will make it possible to deal with reasoning schemes like:
>
>         Usually, antic furniture is difficult to find
>         What is difficult to find is expensive
>         ----------------------------------------------
>         Usually, antic furniture is expensive
>
> This involves, fuzzy quantifiers like 'usually' and also
> fuzzy predicates like: 'antic', 'difficult' and 'expensive'.
>
> How can we sistematically decide about the correctness of this
> reasonig ? For there is no agreement upon what these expressions mean:
> wveryone will understand something slightly different. Well,
> Fuzzy Logic provides us with a way.
>
> Unfortunately, I don't remember the details, so I can't tell you,
> at this moment, much more.
>
> Regards,
> M.A.Santos
> msantos@etse.urv.es