Here is a summary of responses to a request for information on Fuzzy Logic

and its application to motor control.

Many thanks to all who responded.

Cole Galloway

RESPONSES

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

http://www.flll.uni-linz.ac.at/fuzzy/fuzzy.html

http://www.austinlinks.com/Fuzzy/

JIM PATTON

-------

I thought that the following article might be of interest to you. I am

still interested in your work and would appreciate if you could keep me

updated.

Scott Sonnon

Exec. Director

AARMACS, Inc.

Excerpt from Computer Design

April 1992

The Seven Noble Truths Of Fuzzy Logic

by Earl Cox

TRUTH ONE

There Is Nothing Fuzzy About Fuzzy Logic

The idea that fuzzy logic is fuzzy or intrinsically imprecise is

one of the most commonly expressed fables in the fuzzy logic

mythos. This wide-spread belief comes in two flavors, the first

holds that fuzzy logic violates common sense and the well proven

laws of logic, and the second, perhaps inspired by its name,

holds that fuzzy systems produce answers that are somehow

ad-hoc, fuzzy, or vague. The feeling persists that fuzzy logic

systems somehow, through their handling of imprecise and

approximate concepts, produce results that are approximations of

the answer we would get if we had access to a model that worked

on hard facts and crisp information. Nothing could be further

from fact.

There is nothing fuzzy about fuzzy logic, Fuzzy Sets differ from

classical or crisp sets in that they allow partial or gradual

degrees of membership. We can see the difference easily by

looking at the difference between a conventional (or "crisp")

set and a fuzzy set. Thus someone 34 years, eleven months, and

twenty eight days old is not middle aged. In the Fuzzy

representation, however, we see that as a person grows older he

or she acquires a partial membership in the set of Middle Aged

people, with total membership at forty years old.

But there is nothing ambiguous about the fuzzy set itself. If

we know a value from the domain, say an age of 35 years old,

then we can find its exact and unambiguous membership In the

set, say 82%. This precision at the set level allows us to write

fuzzy rules at a rather high level of abstraction. Thus we can

say, if age is middle-aged, then weight is usually quite heavy;

and means that, to the degree that the individual's age is

considered middle aged, their weight should be considered

somewhat heavy. A weight estimating function, following this

(very simple) rule might infer a weight from age through the

following fuzzy implication process.

Much of the discomfort with fuzzy logic stems from the implicit

assumption that a single ``right'' logical system exists and to

the degree that another system deviates from this right and

correct logic it is in error. This ``correct'' logic, of

course, is Aristotelian or Boolean logic. But as a logic of

continuous and partial memberships, Fuzzy Logic has a deep and

impressive pedigree. Using the metaphor of the river, Heraclitus

aptly points out that a continuous reasoning system more

correctly maps nature's logical ambiguities. From his dictum

that all is flux, nothing is stationary, he devcloped a

rudimentary multi-valued logic two hundred years before

Aristotle. Recently, Bart Kosko, one of the most profound

thinkers in fuzzy logic, has shown that Boolean logic is, in

fact, a special case of fuzzy logic.

TRUTH TWO

Fuzzy Logic Is Different from Probability

The difference between probability and fuzzy logic is clear when

we consider the underlying concept that each attempts to model.

Probability is concerned with the undecidability in the outcome

of clearly defined and randomly occurring events, while fuzzy

logic is concerned with the ambiguity or undecidability inherent

in the description of the event itself. Fuzziness is often

expressed as ambiguity rather than imprecision or uncertainty

and remains a characteristic of perception as well as concept.

TRUTH THREE

Designing the Fuzzy Sets is very asy

Not only are fuzzy sets easy to conceptualize and represent, but

they reflect, in a general "one-to-one" mapping, the way experts

actually think about a problem. Experts can quickly sketch out

the approximate shape of a fuzzy set. Later, after we have run

the model or examined the process, the precise characteristics

of the fuzzy vocabulary can be adjusted if necessary.

TRUTH FOUR

Fuzzy Systems are Stable, Easily Tuned,

and can be conventionally Validated

Creating fuzzy sets and building a fuzzy system is faster and

quicker than conventional knowledge-based systems using "crisp"

constructs. These fuzzy systems routinely show a one or two

order of magnitude reduction in rules since fuzzy logic

simultaneously handles all the interlocking degrees of freedom.

Fuzzy systems are very robust since the over-lapping of the

fuzzy regions, representing the continuous domain of each

control and solution variable, contributes to a well-behaved and

predictable system operation. These systems are validated in

the same manner as conventional system. The tuning of fuzzy

systems, however, is usually much simpler since there are fewer

rules; representation if visually centered around fuzzy sets,

and operations act simultaneously on the output areas.

TRUTH FIVE

Fuzzy Systems are Different From

and Complementary to Neural Networks

There is a close relationship between fuzzy logic and neural

systems. A fuzzy system attempts to find a region that

represents the space defined by the intersection, union, or

complement of the fuzzy control variables. This has analogies

to both neural network classifiers and linear programming

models. Yet fuzzy systems approach the problem differently with

a deeper and more robust epistemology. In a fuzzy system, the

classification and bounding process is much more open to the

developer and user with capabilities for explanations, rule and

fuzzy set calibration, performance measurements, and controls

over the way the solution is ultimately derived.

TRUTH SIX

Fuzzy logic "ain't just process control anymore"

Historically we have come to view fuzzy logic as a process

control and signal analysis technique, but fuzzy logic is really

a way of logically representing and analyzing information,

independent of particular applications. The information

management field in particular has, until recently, ignored

fuzzy logic, delaying its introduction into expert system and

decision support technology. Recently, however, new types of

knowledge base construction tools have emerged. Such tools will

make it easier for experts who are not computer experts to

intuitively represent and manipulate information.

TRUTH SEVEN

Fuzzy Logic is a Representation and Reasoning Process

Not the "Magic Bullet" for all AI's current problems - Fuzzy

Logic is a tool for representing imprecise, ambiguous, and vague

information. Its power lies in its ability to perform meaningful

and reasonable operations on concepts that are outside the

definitions available in conventional Boolean logic. We have

used fuzzy logic in such applications as project management,

product pricing models, health care provider fraud detection,

sales forecasting, market share demographic analysis, criminal

identification, capital budgeting, and company acquisition

analysis. Although fuzzy logic is a powerful and versatile tool,

it is not a solution to all problems. Nevertheless, it opens the

door for the modeling of problems that have generally been

extremely difficult or intractable.

Earl Cox, CEO

Metus Systems

White Plains, NY

(914) 238-0647

-----

I suggest the following reference which is by a neuroscientist:

A. Prochazka, ìThe fuzzy logic of visuomotor control,î

Can.J.Physiol.Pharmacol., vol. 74, pp. 456-462, 1996.

The following two articles are also interesting:

Earl Cox, "Fuzzy fundamentals," IEEE spectrum, oct. 1992 pp. 58-61

kevin Self, "Design with fuzzy logic," IEEE spectrum, Nov. 1990, pp. 42-45

Good Lock

Regards

Rahman Davoodi

--------

I am working in fuzzy logic and motor/movement control for about three

years now. The combination has great potential and is fascinating. I have

a couple of suggestions for you.

1. A basic book without formulas is Fuzzy thinking by Bart Kosko

(1993,hyperion publishers). It is a nice introduction to fuzzy logic.

2. Articles about FL and motor control by myself. Also see my website:

http://utwbbwu2.wb.utwente.nl/~jacobs/mysig.htm

Jacobs R & Meijer K (1997) A fuzzy model of skeletal muscle adaptation: A

tool to study surgical, rehabilitation and training procedures. Automedica

(submitted)

Jacobs R.(1997) Control model of human stance using fuzzy logic. Biological

Cybernetics 77:63-70

Jacobs R & Burleigh-Jacobs A (1997) Neural muscular control strategies in

postural coordination. In: Control of posture and movement; neuro-muscular

skeletal interaction and organisational principles. Editors: Winters, J. &

Crago, P., Springer Verlag, New York (In Press)

Jacobs R & Tucker C (1997) Soft computing techniques for evaluation and

control of human performance. In: Control of posture and movement;

neuro-muscular skeletal interaction and organisational principles. Editors:

Winters, J. & Crago, P., Springer Verlag, New York (In Press)

The Winters and Crago book is coming out by the end of this year!!

My address till 1/1/98 is:

Dr. Ron Jacobs

Institute for Biomedical Technology, BMTI-WB/BW

University of Twente

P.O. Box 217, Enschede 7500 AE

The Netherlands

After 1/15/98 my NEW address is:

Intelligent Inference Systems Corp.

333 W Maude Ave., Suite 107

Sunnyvale, CA 94087

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

Contact your local Motorola Semiconductor sales office. They have a

number of good introductory as well as more engineering type

documents and books on the subject. There are also an abundance of

articles and books on the topic at any university engineering

library.

Paul Meadows, M.S.

Senior Scientist

Medical Research Group, LLC

12744 San Fernando Road

Sylmar, California 91342 USA

+1-818-362-8084 Ext. 3021

+1-818-364-2647 FAX

E-Mail: PaulM@medrgrp.com

-------

The basics and beyond very well covered in "CHAOS: the making of a new

science" by

Richard Gleick, who also wrote a terrific bio of Richard Feynman , "GENIUS"

Leonard elbaum

Department of PT

FIU

Miami, FL

-------

There are many web sites concerning Fuzzy Logic. There is also an special

issue of an IEEE

magazine concerning the issue

Jose Haroldo de A. Cavalcante

Engineer

Motion Laboratory - SARAH Hospital

SMHS 501 - cj. A

70.330-150

Brasilia-DF

BRAZIL

------

"A First Course in Fuzzy Logic" by H. T. Nguyen and E. A. Walker, 1996,

published by CRC Press, Boca Raton, Florida , 288

pages, catalog no. 9477. Price: $69.95.

: Ziaul Hasan

: University of Illinois at Chicago (M/C 898)

: 1919 W. Taylor Street, AHP Rm. 447

: Chicago, IL 60612-7251, U.S.A.

: Phone: Voice 312-996-1504, Fax 312-996-4583

: E-mail: zhasan@uic.edu

----------

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

C.Galloway, PT

Dept Physiology/Physiological Sciences Program

University of Arizona 1501 North Campbell Ave., Room 4104 Tucson, AZ 85724

Ph: 520-626-7718 Fax: 520-626-2383 Email: galloway@ccit.arizona.edu

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

To unsubscribe send UNSUBSCRIBE BIOMCH-L to LISTSERV@nic.surfnet.nl

For more information: http://www.kin.ucalgary.ca/isb/biomch-l.html

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

and its application to motor control.

Many thanks to all who responded.

Cole Galloway

RESPONSES

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

http://www.flll.uni-linz.ac.at/fuzzy/fuzzy.html

http://www.austinlinks.com/Fuzzy/

JIM PATTON

-------

I thought that the following article might be of interest to you. I am

still interested in your work and would appreciate if you could keep me

updated.

Scott Sonnon

Exec. Director

AARMACS, Inc.

Excerpt from Computer Design

April 1992

The Seven Noble Truths Of Fuzzy Logic

by Earl Cox

TRUTH ONE

There Is Nothing Fuzzy About Fuzzy Logic

The idea that fuzzy logic is fuzzy or intrinsically imprecise is

one of the most commonly expressed fables in the fuzzy logic

mythos. This wide-spread belief comes in two flavors, the first

holds that fuzzy logic violates common sense and the well proven

laws of logic, and the second, perhaps inspired by its name,

holds that fuzzy systems produce answers that are somehow

ad-hoc, fuzzy, or vague. The feeling persists that fuzzy logic

systems somehow, through their handling of imprecise and

approximate concepts, produce results that are approximations of

the answer we would get if we had access to a model that worked

on hard facts and crisp information. Nothing could be further

from fact.

There is nothing fuzzy about fuzzy logic, Fuzzy Sets differ from

classical or crisp sets in that they allow partial or gradual

degrees of membership. We can see the difference easily by

looking at the difference between a conventional (or "crisp")

set and a fuzzy set. Thus someone 34 years, eleven months, and

twenty eight days old is not middle aged. In the Fuzzy

representation, however, we see that as a person grows older he

or she acquires a partial membership in the set of Middle Aged

people, with total membership at forty years old.

But there is nothing ambiguous about the fuzzy set itself. If

we know a value from the domain, say an age of 35 years old,

then we can find its exact and unambiguous membership In the

set, say 82%. This precision at the set level allows us to write

fuzzy rules at a rather high level of abstraction. Thus we can

say, if age is middle-aged, then weight is usually quite heavy;

and means that, to the degree that the individual's age is

considered middle aged, their weight should be considered

somewhat heavy. A weight estimating function, following this

(very simple) rule might infer a weight from age through the

following fuzzy implication process.

Much of the discomfort with fuzzy logic stems from the implicit

assumption that a single ``right'' logical system exists and to

the degree that another system deviates from this right and

correct logic it is in error. This ``correct'' logic, of

course, is Aristotelian or Boolean logic. But as a logic of

continuous and partial memberships, Fuzzy Logic has a deep and

impressive pedigree. Using the metaphor of the river, Heraclitus

aptly points out that a continuous reasoning system more

correctly maps nature's logical ambiguities. From his dictum

that all is flux, nothing is stationary, he devcloped a

rudimentary multi-valued logic two hundred years before

Aristotle. Recently, Bart Kosko, one of the most profound

thinkers in fuzzy logic, has shown that Boolean logic is, in

fact, a special case of fuzzy logic.

TRUTH TWO

Fuzzy Logic Is Different from Probability

The difference between probability and fuzzy logic is clear when

we consider the underlying concept that each attempts to model.

Probability is concerned with the undecidability in the outcome

of clearly defined and randomly occurring events, while fuzzy

logic is concerned with the ambiguity or undecidability inherent

in the description of the event itself. Fuzziness is often

expressed as ambiguity rather than imprecision or uncertainty

and remains a characteristic of perception as well as concept.

TRUTH THREE

Designing the Fuzzy Sets is very asy

Not only are fuzzy sets easy to conceptualize and represent, but

they reflect, in a general "one-to-one" mapping, the way experts

actually think about a problem. Experts can quickly sketch out

the approximate shape of a fuzzy set. Later, after we have run

the model or examined the process, the precise characteristics

of the fuzzy vocabulary can be adjusted if necessary.

TRUTH FOUR

Fuzzy Systems are Stable, Easily Tuned,

and can be conventionally Validated

Creating fuzzy sets and building a fuzzy system is faster and

quicker than conventional knowledge-based systems using "crisp"

constructs. These fuzzy systems routinely show a one or two

order of magnitude reduction in rules since fuzzy logic

simultaneously handles all the interlocking degrees of freedom.

Fuzzy systems are very robust since the over-lapping of the

fuzzy regions, representing the continuous domain of each

control and solution variable, contributes to a well-behaved and

predictable system operation. These systems are validated in

the same manner as conventional system. The tuning of fuzzy

systems, however, is usually much simpler since there are fewer

rules; representation if visually centered around fuzzy sets,

and operations act simultaneously on the output areas.

TRUTH FIVE

Fuzzy Systems are Different From

and Complementary to Neural Networks

There is a close relationship between fuzzy logic and neural

systems. A fuzzy system attempts to find a region that

represents the space defined by the intersection, union, or

complement of the fuzzy control variables. This has analogies

to both neural network classifiers and linear programming

models. Yet fuzzy systems approach the problem differently with

a deeper and more robust epistemology. In a fuzzy system, the

classification and bounding process is much more open to the

developer and user with capabilities for explanations, rule and

fuzzy set calibration, performance measurements, and controls

over the way the solution is ultimately derived.

TRUTH SIX

Fuzzy logic "ain't just process control anymore"

Historically we have come to view fuzzy logic as a process

control and signal analysis technique, but fuzzy logic is really

a way of logically representing and analyzing information,

independent of particular applications. The information

management field in particular has, until recently, ignored

fuzzy logic, delaying its introduction into expert system and

decision support technology. Recently, however, new types of

knowledge base construction tools have emerged. Such tools will

make it easier for experts who are not computer experts to

intuitively represent and manipulate information.

TRUTH SEVEN

Fuzzy Logic is a Representation and Reasoning Process

Not the "Magic Bullet" for all AI's current problems - Fuzzy

Logic is a tool for representing imprecise, ambiguous, and vague

information. Its power lies in its ability to perform meaningful

and reasonable operations on concepts that are outside the

definitions available in conventional Boolean logic. We have

used fuzzy logic in such applications as project management,

product pricing models, health care provider fraud detection,

sales forecasting, market share demographic analysis, criminal

identification, capital budgeting, and company acquisition

analysis. Although fuzzy logic is a powerful and versatile tool,

it is not a solution to all problems. Nevertheless, it opens the

door for the modeling of problems that have generally been

extremely difficult or intractable.

Earl Cox, CEO

Metus Systems

White Plains, NY

(914) 238-0647

-----

I suggest the following reference which is by a neuroscientist:

A. Prochazka, ìThe fuzzy logic of visuomotor control,î

Can.J.Physiol.Pharmacol., vol. 74, pp. 456-462, 1996.

The following two articles are also interesting:

Earl Cox, "Fuzzy fundamentals," IEEE spectrum, oct. 1992 pp. 58-61

kevin Self, "Design with fuzzy logic," IEEE spectrum, Nov. 1990, pp. 42-45

Good Lock

Regards

Rahman Davoodi

--------

I am working in fuzzy logic and motor/movement control for about three

years now. The combination has great potential and is fascinating. I have

a couple of suggestions for you.

1. A basic book without formulas is Fuzzy thinking by Bart Kosko

(1993,hyperion publishers). It is a nice introduction to fuzzy logic.

2. Articles about FL and motor control by myself. Also see my website:

http://utwbbwu2.wb.utwente.nl/~jacobs/mysig.htm

Jacobs R & Meijer K (1997) A fuzzy model of skeletal muscle adaptation: A

tool to study surgical, rehabilitation and training procedures. Automedica

(submitted)

Jacobs R.(1997) Control model of human stance using fuzzy logic. Biological

Cybernetics 77:63-70

Jacobs R & Burleigh-Jacobs A (1997) Neural muscular control strategies in

postural coordination. In: Control of posture and movement; neuro-muscular

skeletal interaction and organisational principles. Editors: Winters, J. &

Crago, P., Springer Verlag, New York (In Press)

Jacobs R & Tucker C (1997) Soft computing techniques for evaluation and

control of human performance. In: Control of posture and movement;

neuro-muscular skeletal interaction and organisational principles. Editors:

Winters, J. & Crago, P., Springer Verlag, New York (In Press)

The Winters and Crago book is coming out by the end of this year!!

My address till 1/1/98 is:

Dr. Ron Jacobs

Institute for Biomedical Technology, BMTI-WB/BW

University of Twente

P.O. Box 217, Enschede 7500 AE

The Netherlands

After 1/15/98 my NEW address is:

Intelligent Inference Systems Corp.

333 W Maude Ave., Suite 107

Sunnyvale, CA 94087

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

Contact your local Motorola Semiconductor sales office. They have a

number of good introductory as well as more engineering type

documents and books on the subject. There are also an abundance of

articles and books on the topic at any university engineering

library.

Paul Meadows, M.S.

Senior Scientist

Medical Research Group, LLC

12744 San Fernando Road

Sylmar, California 91342 USA

+1-818-362-8084 Ext. 3021

+1-818-364-2647 FAX

E-Mail: PaulM@medrgrp.com

-------

The basics and beyond very well covered in "CHAOS: the making of a new

science" by

Richard Gleick, who also wrote a terrific bio of Richard Feynman , "GENIUS"

Leonard elbaum

Department of PT

FIU

Miami, FL

-------

There are many web sites concerning Fuzzy Logic. There is also an special

issue of an IEEE

magazine concerning the issue

Jose Haroldo de A. Cavalcante

Engineer

Motion Laboratory - SARAH Hospital

SMHS 501 - cj. A

70.330-150

Brasilia-DF

BRAZIL

------

"A First Course in Fuzzy Logic" by H. T. Nguyen and E. A. Walker, 1996,

published by CRC Press, Boca Raton, Florida , 288

pages, catalog no. 9477. Price: $69.95.

: Ziaul Hasan

: University of Illinois at Chicago (M/C 898)

: 1919 W. Taylor Street, AHP Rm. 447

: Chicago, IL 60612-7251, U.S.A.

: Phone: Voice 312-996-1504, Fax 312-996-4583

: E-mail: zhasan@uic.edu

----------

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

C.Galloway, PT

Dept Physiology/Physiological Sciences Program

University of Arizona 1501 North Campbell Ave., Room 4104 Tucson, AZ 85724

Ph: 520-626-7718 Fax: 520-626-2383 Email: galloway@ccit.arizona.edu

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

To unsubscribe send UNSUBSCRIBE BIOMCH-L to LISTSERV@nic.surfnet.nl

For more information: http://www.kin.ucalgary.ca/isb/biomch-l.html

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