New online fuzzy resource: http://www.type2fuzzylogic.org/

[s***@dmu.ac.uk]

The Centre for Computational Intelligence, De Montfort University, UK,
now has an online resource for type-2 fuzzy logic including news,
conferences, a publications list and so on. This is intended to be a
site for the community and so we allow you to update recent
publications related to type-2 fuzzy logic, add news and conferences
and generally communicate with people working in the field.

The address is:

http://www.type2fuzzylogic.org/

Please register, give us feedback and help us create a great research
resource for the growing community of type-2 fuzzy logic researchers.

Please feel free to link to this resource from relevant pages.

Kind Regards

Simon Coupland

-------------------------------------------------

Research Fellow
Centre for Computational Intelligence
Faculty of Computer Science and Engineering De Montfort University,
Leicester
LE1 9BH,
United Kingdom

Office: Gateway 6.60
Telephone: [phone]
Home page: http://www.cse.dmu.ac.uk/cci/people/simon.html

[Walter Banks]

Could you explain what type 2 fuzzy is, how it distinguishes itself from using conventional fuzzy logic and linguistic variables and how it would alter the results of a conventional approach in a real example (non linear control, financial strategy
planning or fuzzy data bases).

Walter Banks

Post by s***@dmu.ac.uk
The Centre for Computational Intelligence, De Montfort University, UK,
now has an online resource for type-2 fuzzy logic including news,
conferences, a publications list and so on. This is intended to be a
site for the community and so we allow you to update recent
publications related to type-2 fuzzy logic, add news and conferences
and generally communicate with people working in the field.
http://www.type2fuzzylogic.org/
Please register, give us feedback and help us create a great research
resource for the growing community of type-2 fuzzy logic researchers.
Please feel free to link to this resource from relevant pages.
Kind Regards
Simon Coupland
-------------------------------------------------
Research Fellow
Centre for Computational Intelligence
Faculty of Computer Science and Engineering De Montfort University,
Leicester
LE1 9BH,
United Kingdom
Office: Gateway 6.60
Telephone: [phone]
Home page: http://www.cse.dmu.ac.uk/cci/people/simon.html

[s***@dmu.ac.uk]

Hi Walter,

Proponents of type-2 fuzzy logic argue that conventional (type-1) fuzzy
logic cannot model uncertainties that are encountered in real world
problems. Type-1 fuzzy sets have crisp membership functions, consider
for example the fuzzy set Hot. The temperature 40 degrees C may have a
membership grade of 0.7 in HOT. There is no uncertainty about this
value 0.7 HOT. A type-2 version of HOT allows some uncertainty to be
associated with the membership grade i.e. About 0.7 HOT where About 0.7
is a (type-1) fuzzy number between zero and one. A variation of type-2
fuzzy logic is interval fuzzy logic, where About 0.7 Hot is an interval
set between zero and one. These uncertainties are propagated through
the fuzzy system and it is possible to obtain a measure of the
uncertainty that has come through the inferencing process before
defuzzification.

So, does this extra complexity actual help when applying fuzzy methods
to real world problems?

There is mounting evidence that type-2 gives a significant performance
improvement over type-1, see for example:

Hani Hagras (Essex University, UK,
http://cswww.essex.ac.uk/staff/hagras/hani.htm) has demonstrated
interval type-2 robot control outperforms type-1 and is far more robust
in varying (outdoor) conditions.
I have similar work that shows type-2 outperforms both interval type-2
and type-1 in a robot control problem.
Jerry Mendel (University of Southern California,
http://sipi.usc.edu/~mendel/) has shown type-2 can outperform type-1 in
a number of other non control applications.

With my own work I have found that for robot control type-2 fuzzy logic
gives a more consistent performance with less error than type-1. There
is an increased computational cost incurred by when using type-2 rather
than type-1 although recent research has significantly reduced this
problem.

Regards

Simon Coupland

[Walter Banks]

How do you determine the uncertainty linguistic variable's value? ie Hot 0.7 and SureItsHot 0.9 for example
Do you use the crisp uncertainty as a factor?

When a fuzzy rule evaluates a linguistic variable (Hot) that has associated a linguistic variable (SureItsHot) describing the quality of Hot, do you then evaluate the rules differently or do you add more rules that account for the quality terms.

For example how would you change the linguistic declarations and rules for a simple non linear control system with a few rules like the following.

How is type-2 fuzzy logic different from the use of the linguistic variables associated with Error and DeltaError in the following example?


w..


---------------------------------------------------------------------

/* Fuzz-C Fuzzy Logic Preprocessor

Fuzzy PID controller

Copyright 2005 Byte Craft Limited. All rights reserved

Byte Craft Limited
A2-490 Dutton Drive, Waterloo, Ontario N2L 6H7 Canada
VOICE: 1 [phone]
Author: Walter Banks

This program implements a fuzzy PID
(Proportional-Integral-Derivative) controller.

*/

/* for calculating derivative error */
int OldError;

/* external set point */
int Setpoint;

/* Process control that reads the ManVar
and updates control to the process */

int Process(void);

/* proportional error */
LINGUISTIC Error TYPE int MIN -90 MAX 90
{
MEMBER LNegative { -90, -90, -20, 0 }
MEMBER normal { -20, 0, 20 }
MEMBER close { -3, 0, 3 }
MEMBER LPositive { 0, 20, 90, 90 }
}

LINGUISTIC DeltaError TYPE int MIN -90 MAX 90
{
MEMBER Negative { -90, -90, -10, 0 }
MEMBER Positive { 0, 10, 90, 90 }
}

LINGUISTIC SumError TYPE int MIN -90 MAX 90
{
MEMBER LNeg { -90, -90, -5, 0 }
MEMBER LPos { 0, 5, 90, 90 }
}

CONSEQUENCE ManVar TYPE int MIN -20 MAX 20 DEFUZZ cg
{
MEMBER LNegative { -18 }
MEMBER SNegative { -6 }
MEMBER SPositive { 6 }
MEMBER LPositive { 18 }
}

FUZZY pid
{
/* large moves for large proportional errors */
IF Error IS LNegative THEN ManVar IS LPositive
IF Error IS LPositive THEN ManVar IS LNegative

/* small moves for changes in error */
IF Error IS normal AND DeltaError IS Positive
THEN ManVar IS SNegative
IF Error IS normal AND DeltaError IS Negative
THEN ManVar IS SPositive

/* small moves for large sums of accumulated error */
IF Error IS close AND SumError IS LPos
THEN ManVar IS SNegative
IF Error IS close AND SumError IS LNeg
THEN ManVar IS SPositive
}

void main (void)
{
while(1)
{
OldError = Error;
Error = Setpoint - Process();
DeltaError = Error - OldError;
SumError = SumError + Error;
pid();
}
}


=========================================================

Post by s***@dmu.ac.uk
Hi Walter,
Proponents of type-2 fuzzy logic argue that conventional (type-1) fuzzy
logic cannot model uncertainties that are encountered in real world
problems. Type-1 fuzzy sets have crisp membership functions, consider
for example the fuzzy set Hot. The temperature 40 degrees C may have a
membership grade of 0.7 in HOT. There is no uncertainty about this
value 0.7 HOT. A type-2 version of HOT allows some uncertainty to be
associated with the membership grade i.e. About 0.7 HOT where About 0.7
is a (type-1) fuzzy number between zero and one. A variation of type-2
fuzzy logic is interval fuzzy logic, where About 0.7 Hot is an interval
set between zero and one. These uncertainties are propagated through
the fuzzy system and it is possible to obtain a measure of the
uncertainty that has come through the inferencing process before
defuzzification.
So, does this extra complexity actual help when applying fuzzy methods
to real world problems?
There is mounting evidence that type-2 gives a significant performance
Hani Hagras (Essex University, UK,
http://cswww.essex.ac.uk/staff/hagras/hani.htm) has demonstrated
interval type-2 robot control outperforms type-1 and is far more robust
in varying (outdoor) conditions.
I have similar work that shows type-2 outperforms both interval type-2
and type-1 in a robot control problem.
Jerry Mendel (University of Southern California,
http://sipi.usc.edu/~mendel/) has shown type-2 can outperform type-1 in
a number of other non control applications.
With my own work I have found that for robot control type-2 fuzzy logic
gives a more consistent performance with less error than type-1. There
is an increased computational cost incurred by when using type-2 rather
than type-1 although recent research has significantly reduced this
problem.
Regards
Simon Coupland

[d***@gmail.com]

Walter

I am not sure I understand the point or question. Is SureItsHot
applying a hedge to Hot?
or is it a fuzzy set?

Type-2 systems work in the same way as type-1. In other words we have
rules (usually) such as if temp is Hot then fever is High. The variable
are temp and fever and the associated fuzzy sets are Hot and High. The
type-2 approach applies join and meet to work with such rules. These
are analagous to t-norms and t-conorms.I'm not sure what you mean by
linguistic variables in this context.

Look forward to some clarification :)

Bob John
PS Jerry Mendel has a good book on the whole topic

Post by Walter Banks
How do you determine the uncertainty linguistic variable's value? ie Hot 0.7 and SureItsHot 0.9 for example
Do you use the crisp uncertainty as a factor?
When a fuzzy rule evaluates a linguistic variable (Hot) that has associated a linguistic variable (SureItsHot) describing the quality of Hot, do you then evaluate the rules differently or do you add more rules that account for the quality terms.
For example how would you change the linguistic declarations and rules for a simple non linear control system with a few rules like the following.
How is type-2 fuzzy logic different from the use of the linguistic variables associated with Error and DeltaError in the following example?
w..
---------------------------------------------------------------------
/* Fuzz-C Fuzzy Logic Preprocessor
Fuzzy PID controller
Copyright 2005 Byte Craft Limited. All rights reserved
Byte Craft Limited
A2-490 Dutton Drive, Waterloo, Ontario N2L 6H7 Canada
VOICE: 1 [phone]
Author: Walter Banks
This program implements a fuzzy PID
(Proportional-Integral-Derivative) controller.
*/
/* for calculating derivative error */
int OldError;
/* external set point */
int Setpoint;
/* Process control that reads the ManVar
and updates control to the process */
int Process(void);
/* proportional error */
LINGUISTIC Error TYPE int MIN -90 MAX 90
{
MEMBER LNegative { -90, -90, -20, 0 }
MEMBER normal { -20, 0, 20 }
MEMBER close { -3, 0, 3 }
MEMBER LPositive { 0, 20, 90, 90 }
}
LINGUISTIC DeltaError TYPE int MIN -90 MAX 90
{
MEMBER Negative { -90, -90, -10, 0 }
MEMBER Positive { 0, 10, 90, 90 }
}
LINGUISTIC SumError TYPE int MIN -90 MAX 90
{
MEMBER LNeg { -90, -90, -5, 0 }
MEMBER LPos { 0, 5, 90, 90 }
}
CONSEQUENCE ManVar TYPE int MIN -20 MAX 20 DEFUZZ cg
{
MEMBER LNegative { -18 }
MEMBER SNegative { -6 }
MEMBER SPositive { 6 }
MEMBER LPositive { 18 }
}
FUZZY pid
{
/* large moves for large proportional errors */
IF Error IS LNegative THEN ManVar IS LPositive
IF Error IS LPositive THEN ManVar IS LNegative
/* small moves for changes in error */
IF Error IS normal AND DeltaError IS Positive
THEN ManVar IS SNegative
IF Error IS normal AND DeltaError IS Negative
THEN ManVar IS SPositive
/* small moves for large sums of accumulated error */
IF Error IS close AND SumError IS LPos
THEN ManVar IS SNegative
IF Error IS close AND SumError IS LNeg
THEN ManVar IS SPositive
}
void main (void)
{
while(1)
{
OldError = Error;
Error = Setpoint - Process();
DeltaError = Error - OldError;
SumError = SumError + Error;
pid();
}
}
=========================================================

Post by s***@dmu.ac.uk
Hi Walter,
Proponents of type-2 fuzzy logic argue that conventional (type-1) fuzzy
logic cannot model uncertainties that are encountered in real world
problems. Type-1 fuzzy sets have crisp membership functions, consider
for example the fuzzy set Hot. The temperature 40 degrees C may have a
membership grade of 0.7 in HOT. There is no uncertainty about this
value 0.7 HOT. A type-2 version of HOT allows some uncertainty to be
associated with the membership grade i.e. About 0.7 HOT where About 0.7
is a (type-1) fuzzy number between zero and one. A variation of type-2
fuzzy logic is interval fuzzy logic, where About 0.7 Hot is an interval
set between zero and one. These uncertainties are propagated through
the fuzzy system and it is possible to obtain a measure of the
uncertainty that has come through the inferencing process before
defuzzification.
So, does this extra complexity actual help when applying fuzzy methods
to real world problems?
There is mounting evidence that type-2 gives a significant performance
Hani Hagras (Essex University, UK,
http://cswww.essex.ac.uk/staff/hagras/hani.htm) has demonstrated
interval type-2 robot control outperforms type-1 and is far more robust
in varying (outdoor) conditions.
I have similar work that shows type-2 outperforms both interval type-2
and type-1 in a robot control problem.
Jerry Mendel (University of Southern California,
http://sipi.usc.edu/~mendel/) has shown type-2 can outperform type-1 in
a number of other non control applications.
With my own work I have found that for robot control type-2 fuzzy logic
gives a more consistent performance with less error than type-1. There
is an increased computational cost incurred by when using type-2 rather
than type-1 although recent research has significantly reduced this
problem.
Regards
Simon Coupland

[Walter Banks]

Post by d***@gmail.com
Type-2 systems work in the same way as type-1. In other words we have
rules (usually) such as if temp is Hot then fever is High. The variable
are temp and fever and the associated fuzzy sets are Hot and High. The
type-2 approach applies join and meet to work with such rules. These
are analagous to t-norms and t-conorms.I'm not sure what you mean by
linguistic variables in this context.

In teh context just described. The variable "temp" has a crisp value it can have real world units like degrees C for example. The lingustic variables associated withe the crisp variable are Hot and High. All crisp values lingustic variables have a value
from 0 to 1.

I was trying to understand from the desciption how the uncertainy was applied to the lingustic variable definition. Off line I was sent a couple papers that answered this question. Sticking with the Hot theme it says in effect if we take the definition of
Hot from several individuals and define the lingustic variable Hot as a composite against the crisp value temp of these several definitions we will have an overlapping part and at the edges there will be areas where individuals do not agree on the
definition. Combining the uncertainy extremes in a fuzzy function will produce a range of answers some that will be agreed upon by all parties and some that will not have universal acceptance. My understanding from the papers sent to me was the
defuzification was essentially the integration of the results to produce a crisp singleton.

Similar things have regularily regularly happened in practical applications using fuzzy logic.
In the Fuzz-C non linear control example the qualifying the lingustic members associated with Error are defined as follows

LINGUISTIC Error TYPE int MIN -90 MAX 90
{
MEMBER LNegative { -90, -90, -20, 0 }
MEMBER normal { -20, 0, 20 }
MEMBER close { -3, 0, 3 }
MEMBER LPositive { 0, 20, 90, 90 }
}

The linguistic variable close is entirely within the lingustic variable normal. These kind of definitions are often used to define emphasis or refine ranges of options.

Post by d***@gmail.com
Walter
I am not sure I understand the point or question. Is SureItsHot
applying a hedge to Hot?
or is it a fuzzy set?
Type-2 systems work in the same way as type-1. In other words we have
rules (usually) such as if temp is Hot then fever is High. The variable
are temp and fever and the associated fuzzy sets are Hot and High. The
type-2 approach applies join and meet to work with such rules. These
are analagous to t-norms and t-conorms.I'm not sure what you mean by
linguistic variables in this context.
Look forward to some clarification :)
Bob John
PS Jerry Mendel has a good book on the whole topic

Post by Walter Banks
How do you determine the uncertainty linguistic variable's value? ie Hot 0.7 and SureItsHot 0.9 for example
Do you use the crisp uncertainty as a factor?
When a fuzzy rule evaluates a linguistic variable (Hot) that has associated a linguistic variable (SureItsHot) describing the quality of Hot, do you then evaluate the rules differently or do you add more rules that account for the quality terms.
For example how would you change the linguistic declarations and rules for a simple non linear control system with a few rules like the following.
How is type-2 fuzzy logic different from the use of the linguistic variables associated with Error and DeltaError in the following example?
w..
---------------------------------------------------------------------
/* Fuzz-C Fuzzy Logic Preprocessor
Fuzzy PID controller
Copyright 2005 Byte Craft Limited. All rights reserved
Byte Craft Limited
A2-490 Dutton Drive, Waterloo, Ontario N2L 6H7 Canada
VOICE: 1 [phone]
Author: Walter Banks
This program implements a fuzzy PID
(Proportional-Integral-Derivative) controller.
*/
/* for calculating derivative error */
int OldError;
/* external set point */
int Setpoint;
/* Process control that reads the ManVar
and updates control to the process */
int Process(void);
/* proportional error */
LINGUISTIC Error TYPE int MIN -90 MAX 90
{
MEMBER LNegative { -90, -90, -20, 0 }
MEMBER normal { -20, 0, 20 }
MEMBER close { -3, 0, 3 }
MEMBER LPositive { 0, 20, 90, 90 }
}
LINGUISTIC DeltaError TYPE int MIN -90 MAX 90
{
MEMBER Negative { -90, -90, -10, 0 }
MEMBER Positive { 0, 10, 90, 90 }
}
LINGUISTIC SumError TYPE int MIN -90 MAX 90
{
MEMBER LNeg { -90, -90, -5, 0 }
MEMBER LPos { 0, 5, 90, 90 }
}
CONSEQUENCE ManVar TYPE int MIN -20 MAX 20 DEFUZZ cg
{
MEMBER LNegative { -18 }
MEMBER SNegative { -6 }
MEMBER SPositive { 6 }
MEMBER LPositive { 18 }
}
FUZZY pid
{
/* large moves for large proportional errors */
IF Error IS LNegative THEN ManVar IS LPositive
IF Error IS LPositive THEN ManVar IS LNegative
/* small moves for changes in error */
IF Error IS normal AND DeltaError IS Positive
THEN ManVar IS SNegative
IF Error IS normal AND DeltaError IS Negative
THEN ManVar IS SPositive
/* small moves for large sums of accumulated error */
IF Error IS close AND SumError IS LPos
THEN ManVar IS SNegative
IF Error IS close AND SumError IS LNeg
THEN ManVar IS SPositive
}
void main (void)
{
while(1)
{
OldError = Error;
Error = Setpoint - Process();
DeltaError = Error - OldError;
SumError = SumError + Error;
pid();
}
}
=========================================================

Post by s***@dmu.ac.uk
Hi Walter,
Proponents of type-2 fuzzy logic argue that conventional (type-1) fuzzy
logic cannot model uncertainties that are encountered in real world
problems. Type-1 fuzzy sets have crisp membership functions, consider
for example the fuzzy set Hot. The temperature 40 degrees C may have a
membership grade of 0.7 in HOT. There is no uncertainty about this
value 0.7 HOT. A type-2 version of HOT allows some uncertainty to be
associated with the membership grade i.e. About 0.7 HOT where About 0.7
is a (type-1) fuzzy number between zero and one. A variation of type-2
fuzzy logic is interval fuzzy logic, where About 0.7 Hot is an interval
set between zero and one. These uncertainties are propagated through
the fuzzy system and it is possible to obtain a measure of the
uncertainty that has come through the inferencing process before
defuzzification.
So, does this extra complexity actual help when applying fuzzy methods
to real world problems?
There is mounting evidence that type-2 gives a significant performance
Hani Hagras (Essex University, UK,
http://cswww.essex.ac.uk/staff/hagras/hani.htm) has demonstrated
interval type-2 robot control outperforms type-1 and is far more robust
in varying (outdoor) conditions.
I have similar work that shows type-2 outperforms both interval type-2
and type-1 in a robot control problem.
Jerry Mendel (University of Southern California,
http://sipi.usc.edu/~mendel/) has shown type-2 can outperform type-1 in
a number of other non control applications.
With my own work I have found that for robot control type-2 fuzzy logic
gives a more consistent performance with less error than type-1. There
is an increased computational cost incurred by when using type-2 rather
than type-1 although recent research has significantly reduced this
problem.
Regards
Simon Coupland

[Dmitry A. Kazakov]

Post by Walter Banks

Post by d***@gmail.com
Type-2 systems work in the same way as type-1. In other words we have
rules (usually) such as if temp is Hot then fever is High. The variable
are temp and fever and the associated fuzzy sets are Hot and High. The
type-2 approach applies join and meet to work with such rules. These
are analagous to t-norms and t-conorms.I'm not sure what you mean by
linguistic variables in this context.

In teh context just described. The variable "temp" has a crisp value it
can have real world units like degrees C for example. The lingustic
variables associated withe the crisp variable are Hot and High. All crisp
values lingustic variables have a value from 0 to 1.

Linguistic variables Hot and High form a crisp set {Hot, High}. This serves
as the universal set or the domain set.

A fuzzy subset of that universal set is what you are talking about. A
generalization with fuzzy-2 sets is just to consider it being rather
fuzzy-2 subset.

Now when fuzzy-2 is interval sets, then it becomes an intuitionistic fuzzy
set. I.e. you take some "temp" and measure if Hot and High belongs to it.
When "temp" isn't a singleton you automatically come the upper and the
lower bound. I.e.

Hot is in "temp" [L_Hot, U_Hot],
High is in "temp" is [L_High, U_High].

The set {Hot:[L_Hot, U_Hot], High:[L_High, U_High]} is a fuzzy-2 set, a
case of intuitionistic fuzzy set.

Note, though that measurements *aren't* proper sets, either fuzzy-1 or
fuzzy-2 or whatsoever. So the above isn't a fuzzified "temp". Fuzzified
"temp" is "temp" is in Hot, "temp" is in High. [ I discuss it more detailed
in http://www.dmitry-kazakov.de/ada/fuzzy.htm ]

So far the definition of a linguistic variable remains same. It is a
fuzzy-1 subset of the original domain, the set of temperatures. It is of
course possible to generalize this as well, and consider lingustic
variables as fuzzy-2 sets of temperatures. It is difficult to say whether
it would bring something. However if Hot and High are esitmated in some
process, rather than postulated, that could well make then fuzzy-2.

[Walter Banks]

Post by d***@gmail.com
Type-2 systems work in the same way as type-1. In other words we have
rules (usually) such as if temp is Hot then fever is High. The variable
are temp and fever and the associated fuzzy sets are Hot and High. The
type-2 approach applies join and meet to work with such rules. These
are analagous to t-norms and t-conorms.I'm not sure what you mean by
linguistic variables in this context.

In the context just described. The variable "temp" has a crisp value it can have real world units like degrees C for example. The
linguistic variables associated with the crisp variable are Hot and High. All crisp values linguistic variables have a value
from 0 to 1.

I was trying to understand from the description how the uncertainly was applied to the linguistic variable definition. Off line I was
sent a couple papers that answered this question. Sticking with the Hot theme it says in effect if we take the definition of
Hot from several individuals and define the linguistic variable Hot as a composite against the crisp value temp of these several
definitions we will have an overlapping part and at the edges there will be areas where individuals do not agree on the
definition. Combining the uncertainly extremes in a fuzzy function will produce a range of answers some that will be agreed upon by
all parties and some that will not have universal acceptance. My understanding from the papers sent to me was the
defuzification was essentially the integration of the results to produce a crisp singleton.

Similar things have regularly happened in practical applications using fuzzy logic.
In the Fuzz-C non linear control example the qualifying the linguistic members associated with Error are defined as follows

LINGUISTIC Error TYPE int MIN -90 MAX 90
{
MEMBER LNegative { -90, -90, -20, 0 }
MEMBER normal { -20, 0, 20 }
MEMBER close { -3, 0, 3 }
MEMBER LPositive { 0, 20, 90, 90 }
}

The linguistic variable close is entirely within the linguistic variable normal. These kind of definitions are often used to define
emphasis or refine ranges of options.

Post by d***@gmail.com
Walter
I am not sure I understand the point or question. Is SureItsHot
applying a hedge to Hot?
or is it a fuzzy set?
Type-2 systems work in the same way as type-1. In other words we have
rules (usually) such as if temp is Hot then fever is High. The variable
are temp and fever and the associated fuzzy sets are Hot and High. The
type-2 approach applies join and meet to work with such rules. These
are analagous to t-norms and t-conorms.I'm not sure what you mean by
linguistic variables in this context.
Look forward to some clarification :)
Bob John
PS Jerry Mendel has a good book on the whole topic

Post by Walter Banks
How do you determine the uncertainty linguistic variable's value? ie Hot 0.7 and SureItsHot 0.9 for example
Do you use the crisp uncertainty as a factor?
When a fuzzy rule evaluates a linguistic variable (Hot) that has associated a linguistic variable (SureItsHot) describing the quality of Hot, do you then evaluate the rules differently or do you add more rules that account for the quality terms.
For example how would you change the linguistic declarations and rules for a simple non linear control system with a few rules like the following.
How is type-2 fuzzy logic different from the use of the linguistic variables associated with Error and DeltaError in the following example?
w..
---------------------------------------------------------------------
/* Fuzz-C Fuzzy Logic Preprocessor
Fuzzy PID controller
Copyright 2005 Byte Craft Limited. All rights reserved
Byte Craft Limited
A2-490 Dutton Drive, Waterloo, Ontario N2L 6H7 Canada
VOICE: 1 [phone]
Author: Walter Banks
This program implements a fuzzy PID
(Proportional-Integral-Derivative) controller.
*/
/* for calculating derivative error */
int OldError;
/* external set point */
int Setpoint;
/* Process control that reads the ManVar
and updates control to the process */
int Process(void);
/* proportional error */
LINGUISTIC Error TYPE int MIN -90 MAX 90
{
MEMBER LNegative { -90, -90, -20, 0 }
MEMBER normal { -20, 0, 20 }
MEMBER close { -3, 0, 3 }
MEMBER LPositive { 0, 20, 90, 90 }
}
LINGUISTIC DeltaError TYPE int MIN -90 MAX 90
{
MEMBER Negative { -90, -90, -10, 0 }
MEMBER Positive { 0, 10, 90, 90 }
}
LINGUISTIC SumError TYPE int MIN -90 MAX 90
{
MEMBER LNeg { -90, -90, -5, 0 }
MEMBER LPos { 0, 5, 90, 90 }
}
CONSEQUENCE ManVar TYPE int MIN -20 MAX 20 DEFUZZ cg
{
MEMBER LNegative { -18 }
MEMBER SNegative { -6 }
MEMBER SPositive { 6 }
MEMBER LPositive { 18 }
}
FUZZY pid
{
/* large moves for large proportional errors */
IF Error IS LNegative THEN ManVar IS LPositive
IF Error IS LPositive THEN ManVar IS LNegative
/* small moves for changes in error */
IF Error IS normal AND DeltaError IS Positive
THEN ManVar IS SNegative
IF Error IS normal AND DeltaError IS Negative
THEN ManVar IS SPositive
/* small moves for large sums of accumulated error */
IF Error IS close AND SumError IS LPos
THEN ManVar IS SNegative
IF Error IS close AND SumError IS LNeg
THEN ManVar IS SPositive
}
void main (void)
{
while(1)
{
OldError = Error;
Error = Setpoint - Process();
DeltaError = Error - OldError;
SumError = SumError + Error;
pid();
}
}
=========================================================

Post by s***@dmu.ac.uk
Hi Walter,
Proponents of type-2 fuzzy logic argue that conventional (type-1) fuzzy
logic cannot model uncertainties that are encountered in real world
problems. Type-1 fuzzy sets have crisp membership functions, consider
for example the fuzzy set Hot. The temperature 40 degrees C may have a
membership grade of 0.7 in HOT. There is no uncertainty about this
value 0.7 HOT. A type-2 version of HOT allows some uncertainty to be
associated with the membership grade i.e. About 0.7 HOT where About 0.7
is a (type-1) fuzzy number between zero and one. A variation of type-2
fuzzy logic is interval fuzzy logic, where About 0.7 Hot is an interval
set between zero and one. These uncertainties are propagated through
the fuzzy system and it is possible to obtain a measure of the
uncertainty that has come through the inferencing process before
defuzzification.
So, does this extra complexity actual help when applying fuzzy methods
to real world problems?
There is mounting evidence that type-2 gives a significant performance
Hani Hagras (Essex University, UK,
http://cswww.essex.ac.uk/staff/hagras/hani.htm) has demonstrated
interval type-2 robot control outperforms type-1 and is far more robust
in varying (outdoor) conditions.
I have similar work that shows type-2 outperforms both interval type-2
and type-1 in a robot control problem.
Jerry Mendel (University of Southern California,
http://sipi.usc.edu/~mendel/) has shown type-2 can outperform type-1 in
a number of other non control applications.
With my own work I have found that for robot control type-2 fuzzy logic
gives a more consistent performance with less error than type-1. There
is an increased computational cost incurred by when using type-2 rather
than type-1 although recent research has significantly reduced this
problem.
Regards
Simon Coupland

[barbara]

hi all

can any one help me about type 2 fuzzy logic ,to use it like controller

[g***@gmail.com]

Postal Lottery: Turn $6 into $60,000 in 90 days, GUARANTEED

I found this in a news group and decided to try it. A little while
back, I was browsing through newsgroups, just like you are now and
came across a message just like this that said you could make
thousands of dollars within weeks with only an initial investment of
$6.00!!!

So I thought yeah right, this must be a scam!!! But like most of us, I
was curious, so I kept reading. Anyway, it said that you send $1.00 to
each of the 6 names and addresses stated in the message. You then
place your own name and address at the bottom of the list at #6 and
post the message in at least 200 news groups. (There are thousands to
choose from). No catch, that was it.

So after thinking it over, and talking to a few people first. I
thought about trying it. I figured, what have I got to lose except 6
stamps and $6.00, right? So I invested the measly $6.00!!! Guess what?
Within 7 days I started getting money in the mail!!! I was shocked!!!
I figured it would end soon, but the money just kept coming in!!! In
my first week, I had made about $25.00. By the end of the second week,
I had made a total of over $1,000.00!!! In the third week, I had over
$10,000.00 and it is still growing!!! This is now my fourth week and I
have made a total of just over $42,000.00 and it is still coming in
rapidly!!! It's certainly worth $6.00 and 6 stamps!!! I have spent
more than that on the lottery!!!

Let me tell you how this works and most importantly, why it works!!!

Also, make sure you print a copy of this message now. So you can get
the information off of it as you need it. I promise you that if you
follow the directions exactly, that you will start making more money
than you thought possible by doing something so easy!!!

Suggestion: Read this entire message carefully!!! (Print it out or
download it.) Follow the simple directions and watch the money come
in!!! It's easy!!! It's legal!!! Your investment is only $6.00 (plus
postage).

IMPORTANT: This is not a rip-off!!! It is not illegal!!! ? It is
almost entirely risk free and it really works!!! If all of the
following instructions are adhered to, you will receive extraordinary
dividends!!!

Please note: Follow these directions EXACTLY, and $60,000.00 or more
can be yours in 20 to 90 days!!! This program remains successful
because of the honesty and the integrity of the participants!!! Please
continue its success by carefully adhering to the instructions.

You will now become part of the mail order business. In this business
your product is not solid or tangible, it is a service. You are in the
business of developing mailing lists. Many large corporations are
happy to pay big bucks for quality lists. However, the money made from
a mailing list is secondary to the income which is made from people
like you and me asking to be included on your mailing list!!!

Here are the 4 easy steps to success:-

Step 1:- Get 6 separate pieces of paper and write the following on
each piece of paper.

PLEASE PUT ME ON YOUR MAILING LIST

Now get 6 U.S. dollar bills and place ONE inside each of the 6 pieces
of paper so the bills will not be seen through the envelopes (to
prevent mail theft). Next, place one paper in each of the 6 envelopes
and seal them, you should now have 6 sealed envelopes. Each with a
piece of paper stating the above phrase, your name and address, and a
$1.00 bill.

THIS IS ABSOLUTELY LEGAL!!! YOU ARE REQUESTING A LEGITIMATE SERVICE
AND YOU ARE PAYING FOR IT!!!

Like most of us, I was a little skeptical and a little worried about
the legal aspect of it all. So I checked it out with the U.S. Postal
Service and they confirmed that it is indeed legal!!!

Mail the 6 envelopes to the following addresses:-
D. Kumar
Room 2.36 Burkhardt House
Oxford Place, Victoria Park
M14 5RR Manchester
ENGLAND

T. Perce
11505 Headley Avenue
Cleveland, Oh 44111

T. Beckers
Rijksweg 46
6267AH Cadier en Keer
The Netherlands

J. Eddolls
144 Pursey Drive
Bradley Stoke
Bristol
BS32 8DP
United Kingdom

Louis Joseph
1933 Highway 35, #104
Wall, NJ 07719

Jesse Quiroz
2845 Franklin #1001
Mesquite, Texas 75150

Step 2:- Now take the #1 name off the list that you see above, move
the other names up (6 becomes 5, 5 becomes 4, etc.) and add your name
as number 6 on the list.

Step 3:- Change anything you need to, but try to keep this message as
close to what you see as possible. Now, post your amended message to
at least 200 news groups. I think there are close to 24,000 groups!!!
All you need is 200, but remember, the more you post, the more money
you make!!! This is perfectly legal!! If you have any doubts, refer to
Title18 Sec. 1302 & 1341 of the postal lottery laws. Keep a copy of
these steps for yourself and whenever you need money, you can use it
again.

Please remember that this program remains successful because of the
honesty and the integrity of the participants and by their carefully
adhering to the directions!!!

Look at it this way. If you are of integrity, the program will
continue and the money that so many others have received will come
your way!!!

Note: - You may want to retain every name and address sent to you,
either on your computer or hard copy and keep the notes people send
you. This verifies that you are truly providing a service. Also, it
might be a good Idea to wrap the $1 bills in dark paper to reduce the
risk of mail theft.

So, as each post is downloaded and the directions carefully followed,
six members will be reimbursed for their participation as a list
developer with one dollar each. Your name will move up the list
geometrically so that when your name reaches the #1 position, you will
be receiving thousands of dollars in cash!!! What an opportunity for
only $6.00!!! ($1.00 for each of the first six people listed above).

Send it now, add your own name to the list and your in business!!!


DIRECTIONS FOR HOW TO POST TO A NEWS GROUP!!!

Step 1:- You do not need to re-type this entire message to do your own
posting. Simply put your cursor at the beginning of this message and
drag your cursor to the bottom of this message and select copy from
the edit menu. This will copy the entire message into the computer
memory.

Step 2:- Open a blank note pad file and place your cursor at the top
of the blank page. From the edit menu select paste. This will paste a
copy of the message into notepad so that you can add your name to the
list.

Step 3:- Save your new notepad file as a txt file. If you want to do
your posting in a different setting, you'll always have this file to
go back to.

Step 4:- Use Netscape or Internet Explorer and try searching for
various news groups (on-line forums, message boards, chat sites,
discussions, etc.)

Step 5:- Visit these message boards and post this message as a new
message by highlighting the text of this message from your notepad and
selecting paste from the edit menu. Fill in the subject, this will be
the header that everybody sees as they scroll through the list of
postings in a particular group. Click the post message button. You've
done your first one! Congratulations!!! All you have to do is jump to
different news groups and post away, after you get the hang of it, it
will take about 30 seconds for each news group!

REMEMBER, THE MORE NEWS GROUPS YOU POST IN, THE MORE MONEY YOU WILL
MAKE!!! (But you have to post a minimum of 200).

That's it!!! You will begin receiving money from around the world
within days!!! You may eventually want to rent a P.O. Box due to the
large amount of mail you will receive. If you wish to stay anonymous,
you can invent a name to use, as long as the postman will deliver it.

JUST MAKE SURE ALL THE ADDRESSES ARE CORRECT!!!

Now the why part. Out of 200 postings, say you receive only 5 replies
(a very low example). So then you made $5.00 with your name at #6 on
the letter. Now, each of the 5 persons who sent you $1.00 make the
minimum 200 postings, each with your name at #5 and only 5 persons
respond to each of the original 5, that is another $25.00 for you. Now
those 25 each make 200 MINIMUM posts with your name at #4 and only 5
replies each, you will bring in an additional $125.00!!! Now, those
125 persons turn around and post the minimum 200 with your name at #3
and only receive 5 replies each, you will make an additional
$625.00!!! OK, now here is the fun part, each of those 625 persons
post a minimum 200 messages with your name at #2 and they each only
receive 5 replies, that
just made you $3,125.00!!! Those 3,125 persons will all deliver this
message to 200 news groups. If just 5 more reply you will receive
$15,625.00!!! All with an original investment of only $6.00!!! Amazing
isn't it!!!! When your name is no longer on the list, you just take
the latest posting in the news groups and send out another $6.00 to
the names on the list, putting your name at number 6 again.

You must realize that thousands of people all over the world are
joining the internet and reading these messages every day!!! Just like
you are now!!! So, can you afford $6.00 and see if it really works?
I'm glad I did!!! People have said, "what if the plan is played out
and no one sends you the money?" So what!!! What are the chances of
that happening, when there are tons of new honest users and new honest
people who are joining the internet and news groups everyday and are
willing to give it a try? Estimates are at 20,000 to 50,000 new users,
every day!!!

REMEMBER PLAY HONESTLY AND FAIRLY AND THIS WILL REALLY WORK!!!

-- Comments/Feedback (please post your feedback/experiences here) --

Not bad for 1 hr's work....made me around $5320 in roughly 35 days
Anthony M - TX

Hello, I rcvd 269 bucks in the post in 2 weeks.
Dan Miami - FL

I had to wait around 10 days before I had any results - $13,450 as of
3rd Jan 2003 to date (14th Feb 2003).Am gonna re-post it again for
more money!!
Del from Alberta - Canada

Only received around 588 in the post the last 2 months since I
started the program but I'd posted to approx. 100 newsgroups.
James P - Manchester, UK

Cool....didn't expect much out of this "scam" initially but I have pay
my credit card bill
Mustafa - Jordan

For $6,I made $246 in 2 weeks
ROMEO2326 - Little Rock, AR -US of A

Hey, just droppin a line to say that after posting to well over 820
newsgroups on google and my ISP newsgroup server over a period of 4
1/2 months ,Ive raked in $54280 . Mucho dinero baby!!!! Peace
Drew Dallas - TX