Re: Intuitionistic Fuzzy Sets

vladik (vladik@cs.utep.edu)
Fri, 7 May 1999 07:50:54 +0200 (MET DST)

In traditional fuzzy logic, for every property A and for each element x from the
universe of discourse, we have a number mA(x) which characterizes to what extent
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 is not
completely adequate.

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 the value
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 case, if
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 B)(x), i.e.,
mB(x).

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 weight
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 degree to
which an object x has a property A by TWO numbers: the value mA(x) and the value
m(not A)x which describes to which extent x satisfies the property "not A".
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 and
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 mB(x)=0
and m(not B)x=0.

An alternative way of representing an intuitionistic fuzzy set is to say that
the "true" (unknown) membership degree can take any value from the interval
[mA(x),1-m(not A)x]. In this sense, intuitionistic fuzzy sets are related to
interval-valued fuzzy sets.

> Date: Thu, 6 May 1999 02:25:16 +0200 (MET DST)
> Originator: fuzzy-mail@dbai.tuwien.ac.at
> From: "Danilo J Castro Jr" <danilo@iee.efei.br>
> To: nafips-l@sphinx.gsu.edu

> 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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