**Stephen P. King** (*stephenk1@home.com*)

*Fri, 07 May 1999 07:29:55 -0400*

**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Next message:**Hitoshi Kitada: "[time 285] Re: [time 279] Re: [time 278] Re: [time 276] [Fwd: Fisher information]"**Previous message:**Hitoshi Kitada: "[time 283] correction on numbering"

Subject:

[Fwd: Intuitionistic Fuzzy Sets]

Date:

Fri, 07 May 1999 07:28:21 -0400

From:

"Stephen P. King" <stephenk1@home.com>

Organization:

OutLaw Scientific

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...

Subject:

Re: Intuitionistic Fuzzy Sets

Date:

Fri, 7 May 1999 07:43:45 +0200 (MET DST)

From:

vladik <vladik@cs.utep.edu>

To:

Multiple recipients of list <fuzzy-mail@dbai.tuwien.ac.at>

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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