Stephen P. King (firstname.lastname@example.org)
Fri, 07 May 1999 07:29:55 -0400
[Fwd: Intuitionistic Fuzzy Sets]
Fri, 07 May 1999 07:28:21 -0400
"Stephen P. King" <email@example.com>
fixing the distributivity problem... Remember the set of our precepts
are not necessarily Hausdorff! Thus we have over and under-lap, not
strict disjointness... This seems to be implied by Spencer-Brown... Only
the identity is crisply disjoint...
Re: Intuitionistic Fuzzy Sets
Fri, 7 May 1999 07:43:45 +0200 (MET DST)
Multiple recipients of list <firstname.lastname@example.org>
In traditional fuzzy logic, for every property A and for each element x
universe of discourse, we have a number mA(x) which characterizes to
the element x satisfies the property A. If we want to know to which
extent x has
the property "not A", we just take 1-mA(x).
In some practical situations, this traditional real-value-based approach
For example, we may have good arguments in favor of x having the
property A, and
as good arguments against. In this case, it seems reasonable to assign
mA(x)=m(not A)(x), i.e., the value mA(x)=1/2 describes our knowledge.
For some other preperty B, we may not know anything about B(x). In this
we want to pick a number mB(x), since we have no preferences for B or
not B, it
is also reasonable to select the value mB(x) for which mB(x)=m(not
In both cases, we have the value 1/2, but we would like to be able to
distinguish between the first situation in which 1/2 indicates the equal
of arguments in vfavor of A and not A, and the second situation in which
1/2 means simply that we have no idea at all.
To describe this difference, intuitionistic fuzzy logic describes the
which an object x has a property A by TWO numbers: the value mA(x) and
m(not A)x which describes to which extent x satisfies the property "not
These values must satisfy the inequality mA(x)+m(not A)(x) <=1.
In the above two examples, in the fisrt example, we will have mA(x)=1/2
m(not A)x=1/2, because we do not have serious arguments which support
both A and
not A. In the second example, we do not know anything, so we better take
and m(not B)x=0.
An alternative way of representing an intuitionistic fuzzy set is to say
the "true" (unknown) membership degree can take any value from the
[mA(x),1-m(not A)x]. In this sense, intuitionistic fuzzy sets are
interval-valued fuzzy sets.
> Date: Thu, 6 May 1999 02:25:16 +0200 (MET DST)
> Originator: email@example.com
> From: "Danilo J Castro Jr" <firstname.lastname@example.org>
> To: email@example.com
> I'm new on this group and saw the Bulgarian conference, so please what's
> exactly the diference about this Fuzzy sets and the commom sets.
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