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  • Fuzzy logic and motor control summary

    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, The fuzzy logic of visuomotor control,
    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

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