Re: fuzzy implication, definition

Paul Bergondy (danb@magicnet.net)
Sun, 21 Jun 1998 16:21:18 +0200 (MET DST)

Will Dwinnell <76743.1740@CompuServe.COM> wrote in article
<uHWwlldm9GA.317@nih2naab.prod2.compuserve.com>...
> Paul Bergondy wrote:
> "I'm curious why the seemingly natural definition of fuzzy
> implication is not used.
>
> That is,
>
> t(p ---> q) := max{1-t(p), t(q)}"
>
> I don't think that would work even for Boolean values. The truth
> of p implying q is based on the extent that the implication
> itself is true, not the individual statement truths. For
> instance, "IF up is down THEN 2+2=4", as an implication, is
> false. Just because the antecedent or (separately) the
> consequent are true, this whole statement does not become true.
>
> --
> Will Dwinnell
>

Actually, the logical implication p--->q is defined in mathematical
logic to be false only when the hypothesis p is true and the conclusion
q is false; that is, to be logically equivalent to the statement (-p or q),

thus, the proposed definition for fuzzy implication would reduce to this
in the Boolean case.

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