Discussion:
categorical features in (for example) tsk rule systems
(too old to reply)
Christian Setzkorn
2016-12-15 17:41:00 UTC
Permalink
Hi all,

How do you deal with categorical features (e.g. color, gender) in TSK fuzzy rule systems used for regressions. Are they encoded as dummy variables, similar to linear regression. Standard fuzzy sets could then be defined on a dummy variable's domain [0 ... 1].

Any feedback would be very much appreciated. Many thanks in advance.

Best wishes,

Christian
Dmitry A. Kazakov
2016-12-15 17:57:41 UTC
Permalink
Post by Christian Setzkorn
How do you deal with categorical features (e.g. color, gender) in
TSK fuzzy rule systems used for regressions. Are they encoded as dummy
variables, similar to linear regression. Standard fuzzy sets could then
be defined on a dummy variable's domain [0 ... 1].
1. Nominal discrete feature with the enumeration domain: {Red, Blue,
Black, White}.

2. Fuzzified continuous domain, e.g. 3-D color space with fuzzy subsets
defined on it, e.g. Red : Color_Space -> [0,1]. What FCL calls "term".

A fuzzy set over the domain X : {Red, Blue, Black, White} -> [0,1]
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
Christian Setzkorn
2016-12-16 09:01:54 UTC
Permalink
Post by Dmitry A. Kazakov
Post by Christian Setzkorn
How do you deal with categorical features (e.g. color, gender) in
TSK fuzzy rule systems used for regressions. Are they encoded as dummy
variables, similar to linear regression. Standard fuzzy sets could then
be defined on a dummy variable's domain [0 ... 1].
1. Nominal discrete feature with the enumeration domain: {Red, Blue,
Black, White}.
2. Fuzzified continuous domain, e.g. 3-D color space with fuzzy subsets
defined on it, e.g. Red : Color_Space -> [0,1]. What FCL calls "term".
A fuzzy set over the domain X : {Red, Blue, Black, White} -> [0,1]
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
Hi Dmitry,

Just to ensure that I fully understand. So for a nominal variable with 4 levels: X : {Red, Blue, Black, White} an example fuzzy set would be X : {0.1, 0.3, 0.1234, 0.95643}

Is this correct?

Thanks.

Christian
Dmitry A. Kazakov
2016-12-16 10:27:18 UTC
Permalink
Post by Christian Setzkorn
Post by Dmitry A. Kazakov
Post by Christian Setzkorn
How do you deal with categorical features (e.g. color, gender) in
TSK fuzzy rule systems used for regressions. Are they encoded as dummy
variables, similar to linear regression. Standard fuzzy sets could then
be defined on a dummy variable's domain [0 ... 1].
1. Nominal discrete feature with the enumeration domain: {Red, Blue,
Black, White}.
2. Fuzzified continuous domain, e.g. 3-D color space with fuzzy subsets
defined on it, e.g. Red : Color_Space -> [0,1]. What FCL calls "term".
A fuzzy set over the domain X : {Red, Blue, Black, White} -> [0,1]
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
Just to ensure that I fully understand. So for a nominal variable
with 4 levels: X : {Red, Blue, Black, White} an example fuzzy set would be X
: {0.1, 0.3, 0.1234, 0.95643}
Post by Christian Setzkorn
Is this correct?
Yes.

P.S. fuzzy sets must better be normalized when the norm is Possibility,
i.e. reach 1 (fully possible) in at least one point. Assuming that the
domain covers all colors, any observed color must yield a normalized
set. (Depends on the inference framework, of course)
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
Christian Setzkorn
2016-12-17 10:36:29 UTC
Permalink
Post by Christian Setzkorn
Post by Christian Setzkorn
Post by Dmitry A. Kazakov
Post by Christian Setzkorn
How do you deal with categorical features (e.g. color, gender) in
TSK fuzzy rule systems used for regressions. Are they encoded as dummy
variables, similar to linear regression. Standard fuzzy sets could then
be defined on a dummy variable's domain [0 ... 1].
1. Nominal discrete feature with the enumeration domain: {Red, Blue,
Black, White}.
2. Fuzzified continuous domain, e.g. 3-D color space with fuzzy subsets
defined on it, e.g. Red : Color_Space -> [0,1]. What FCL calls "term".
A fuzzy set over the domain X : {Red, Blue, Black, White} -> [0,1]
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
Just to ensure that I fully understand. So for a nominal variable
with 4 levels: X : {Red, Blue, Black, White} an example fuzzy set would be X
: {0.1, 0.3, 0.1234, 0.95643}
Post by Christian Setzkorn
Is this correct?
Yes.
P.S. fuzzy sets must better be normalized when the norm is Possibility,
i.e. reach 1 (fully possible) in at least one point. Assuming that the
domain covers all colors, any observed color must yield a normalized
set. (Depends on the inference framework, of course)
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
Can you please add some relevant links to this so that I can read up on it? Thanks.
Dmitry A. Kazakov
2016-12-17 15:14:22 UTC
Permalink
Post by Christian Setzkorn
Post by Christian Setzkorn
Post by Christian Setzkorn
Post by Dmitry A. Kazakov
Post by Christian Setzkorn
How do you deal with categorical features (e.g. color, gender) in
TSK fuzzy rule systems used for regressions. Are they encoded as dummy
variables, similar to linear regression. Standard fuzzy sets could then
be defined on a dummy variable's domain [0 ... 1].
1. Nominal discrete feature with the enumeration domain: {Red, Blue,
Black, White}.
2. Fuzzified continuous domain, e.g. 3-D color space with fuzzy subsets
defined on it, e.g. Red : Color_Space -> [0,1]. What FCL calls "term".
A fuzzy set over the domain X : {Red, Blue, Black, White} -> [0,1]
Just to ensure that I fully understand. So for a nominal variable
with 4 levels: X : {Red, Blue, Black, White} an example fuzzy set would be X
: {0.1, 0.3, 0.1234, 0.95643}
Post by Christian Setzkorn
Is this correct?
Yes.
P.S. fuzzy sets must better be normalized when the norm is Possibility,
i.e. reach 1 (fully possible) in at least one point. Assuming that the
domain covers all colors, any observed color must yield a normalized
set. (Depends on the inference framework, of course)
Can you please add some relevant links to this so that I can read up on it? Thanks.
On Possibility theory? It is Dubois and Prade.

On inference there is a lot of publications, but it really depends on
the system you are going to use, and the type of sets involved. Bare
fuzzy sets, intuitionistic sets, fuzzy-2 sets etc.
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
Christian Setzkorn
2016-12-20 09:02:52 UTC
Permalink
Post by Dmitry A. Kazakov
Post by Christian Setzkorn
Post by Christian Setzkorn
Post by Christian Setzkorn
Post by Dmitry A. Kazakov
Post by Christian Setzkorn
How do you deal with categorical features (e.g. color, gender) in
TSK fuzzy rule systems used for regressions. Are they encoded as dummy
variables, similar to linear regression. Standard fuzzy sets could then
be defined on a dummy variable's domain [0 ... 1].
1. Nominal discrete feature with the enumeration domain: {Red, Blue,
Black, White}.
2. Fuzzified continuous domain, e.g. 3-D color space with fuzzy subsets
defined on it, e.g. Red : Color_Space -> [0,1]. What FCL calls "term".
A fuzzy set over the domain X : {Red, Blue, Black, White} -> [0,1]
Just to ensure that I fully understand. So for a nominal variable
with 4 levels: X : {Red, Blue, Black, White} an example fuzzy set would be X
: {0.1, 0.3, 0.1234, 0.95643}
Post by Christian Setzkorn
Is this correct?
Yes.
P.S. fuzzy sets must better be normalized when the norm is Possibility,
i.e. reach 1 (fully possible) in at least one point. Assuming that the
domain covers all colors, any observed color must yield a normalized
set. (Depends on the inference framework, of course)
Can you please add some relevant links to this so that I can read up on it? Thanks.
On Possibility theory? It is Dubois and Prade.
On inference there is a lot of publications, but it really depends on
the system you are going to use, and the type of sets involved. Bare
fuzzy sets, intuitionistic sets, fuzzy-2 sets etc.
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
Hi,

The TSK system is intended to be used for regression. So the output is just continuous. Hence, I do not care about 'theological' debates fuzzy sets vs. probabilities etc. I was just wondering how nominal variables are handled in these situations. At the moment I gather that you recommend to use:

{Red, Blue, Black, White} -> [0,1]

Meaning that each category can have a value between 0 and 1. I also think that these values do not have to be normalized (i.e. add up to one). is this correct?

Thanks.

Christian
Dmitry A. Kazakov
2016-12-20 11:02:53 UTC
Permalink
Post by Christian Setzkorn
The TSK system is intended to be used for regression. So the output
is just continuous. Hence, I do not care about 'theological' debates fuzzy
sets vs. probabilities etc.
It is the meaning of the calculations done. The "theology" of regression
is linear approximation in square mean norm. If the norm is different,
regression becomes numerology.
Post by Christian Setzkorn
I was just wondering how nominal variables
are handled in these situations.
It is a meaningless question before attaching a good deal of "theology".
There are various approaches to substitute a continuous system for a
discrete one and back. With fuzzy sets it is called [de]fuzzification.
But without "theology" any method and any result is as good as any
other. Write the outcome 4.12 be done with it...
Post by Christian Setzkorn
At the moment I gather that you
{Red, Blue, Black, White} -> [0,1]
Meaning that each category can have a value between 0 and 1. I also
think that these values do not have to be normalized (i.e. add up to
one). is this correct?
Then it is not a fuzzy set, but a probabilistic set. Probability is
additive. Though you cannot say that the sum of probabilities is 1,
because for that the events (colors in your case) must be independent
and cover all of the color body.
--
Regards,
Dmitry A. Kazakov
http://www.dmitry-kazakov.de
Loading...