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The difference between the probable and the fuzzy

Discussion in 'Electronic Basics' started by Immortalist, Aug 21, 2008.

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  1. Immortalist

    Immortalist Guest

    At this juncture it is important to point out the distinction between
    fuzzy systems and probability. Both operate over the same numeric
    range, and at first glance both have similar values: 0.0 representing
    False (or non-membership), and 1.0 representing True (or membership).

    However, there is a distinction to be made between the two statements:
    The probabilistic approach yields the natural-language statement,
    "There is an 80% chance that Jane is old," while the fuzzy terminology
    corresponds to "Jane's degree of membership within the set of old
    people is 0.80." The semantic difference is significant: the first
    view supposes that Jane is or is not old (still caught in the Law of
    the Excluded Middle); it is just that we only have an 80% chance of
    knowing which set she is in. By contrast, fuzzy terminology supposes
    that Jane is "more or less" old, or some other term corresponding to
    the value of 0.80. There are more very technical ways to show how
    comparing probibility with fuzzy degrees of truth and falsehood don't
    match.

    Natural language abounds with vague and imprecise concepts, such as
    "Sally is tall," or "It is very hot today." Such statements are
    difficult to translate into more precise language without losing some
    of their semantic value: for example, the statement "Sally's height is
    152 cm." does not explicitly state that she is tall, and the statement
    "Sally's height is 1.2 standard deviations about the mean height for
    women of her age in her culture" is fraught with difficulties: would a
    woman 1.1999999 standard deviations above the mean be tall? Which
    culture does Sally belong to, and how is membership in it defined?

    While it might be argued that such vagueness is an obstacle to clarity
    of meaning, only the most staunch traditionalists would hold that
    there is no loss of richness of meaning when statements such as "Sally
    is tall" are discarded from a language. Yet this is just what happens
    when one tries to translate human language into classic logic.

    "To what degree is something true or false?"

    )) There are two types of thinking:
    )) Approximate and Exact.

    Exact is just a "degree of truth" equal to 100%. Approximate is a
    degree of truth between 1% and 99%. Therefore there is only one type
    of thinking: Fuzzy Think!

    )) Approximate always trumps Exact.

    Unlike traditional or classical logic, which attempts to categorize
    information into binary patterns such as black / white, true / false,
    yes / no, or all / nothing, Fuzzy Logic pays attention to the
    "excluded middle" and tries to account for the "grays", the partially
    true and partially false situations which make up 99.9% of human
    reasoning in everyday life. It builds upon the assumption that
    everything consists of degrees on a sliding scale-whether it be truth,
    age, beauty, wealth, color, race, or anything else that is effected by
    the dynamic nature of human behavior and perception. The question
    Zadeh always insists upon asking is, "To what degree is something true
    or false?"

    Zadeh looks around him in the real world which he finds pervaded by
    concepts which do not have sharply defined boundaries, where
    information is often incomplete or sometimes unreliable. In fact, he
    would classify most words as having fuzzy meanings-virtually every
    adjective or adverb in ordinary speech. These concepts become clear if
    seen in transition from membership to non-membership in gradual,
    rather than abrupt, increments.

    In quest for precision, scientists have generally attempted to
    manipulate the real world into artificial mathematical models that
    make no provision for gradation. They have tried to describe the laws
    governing the incredibly complex behavior of humans, both singly and
    in groups, in mathematical terms similar to those employed in the
    analysis of inanimate systems, which, in Zadeh's view, has been, and
    will continue to be, a misdirected effort.

    Because the human mind can't handle so many isolated separate ideas at
    one time, it tends to bundle similarly-related objects into categories
    in such a way as to reduce the complexity of the information
    processing task. It is this incredible capacity of the human mind to
    manipulate these fuzzy or unsharp categories that distinguishes human
    intelligence from the machine intelligence of current generation
    computers.

    Because Fuzzy Logic provides the tools to classify information into
    broad, coarse categorizations or groupings, it has infinite
    possibilities for application which have proven to be much cheaper,
    simpler and more effective than other systems in handling complex
    information. Fuzzy Logic has extremely broad implications for many
    fields not just electrical engineering and computer technology which
    have been fairly quick to incorporate its theoretical principles.
    Numerous consumer goods especially household products and electronic
    equipment-microwaves, cameras, and camcorders already incorporate
    Fuzzy Logic into their design. So have computer control systems such
    as the famous subway of Sendai, Japan, or numerous complex diagnostic
    and monitoring biomedical systems which are starting to be used in
    hospitals.

    But other fields such as the social sciences-economy, finance,
    psychology, sociology, politics, religion, ethics, law, medicine,
    geography, folklore, anthropology that deal with the complexity of
    human behavior-are just beginning to explore the infinite
    possibilities of Fuzzy Logic.

    Zadeh was not the first to think about "shades of gray". Philosophers
    such as Plato indicated that there was a third region (beyond "true"
    and "false") where opposites "tumbled about". Hegel, Marx, Engels and
    Lukasiewicz, among others, also dealt with middle regions. But it was
    Zadeh who first developed the general theory and laid the foundation
    for what Fuzzy Logic is today.

    For a well-researched, very readable, popular description of Lotfi
    Zadeh and the development of the field of Fuzzy Logic, refer to Daniel
    McNeill and Paul Freiberger's award winning book, Fuzzy Logic: The
    Revolutionary Computer Technology that is Changing our World, 1993.
    For a technical introduction to the field, see Zadeh's Fuzzy Sets and
    Applications: Selected Papers. Edited by Yager, Ovchnikov, Tong, and
    Nguyen. New York: Wiley, 1987.

    http://www.google.com/search?h­l=en&q=Zadeh+fuzzy+logic

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

    Now remembering that in fuzzy logic the truth of any statement is a
    matter of degree, how will these truth tables be altered? The input
    values can be real numbers between 0 and 1. What function will
    preserve the results of the AND truth table (for example) and also
    extend to all real numbers between 0 and 1?

    One answer is the min operation. That is, resolve the statement A AND
    B, where A and B are limited to the range (0,1), by using the function
    min(A,B). Using the same reasoning, we can replace the OR operation
    with the max function, so that A OR B becomes equivalent to max(A,B).
    Finally, the operation NOT A becomes equivalent to the operation .
    Notice how the truth table above is completely unchanged by this
    substitution.

    http://www-rohan.sdsu.edu/doc/­matlab/toolbox/fuzzy/fuzzytu4.­html

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

    You want to replace the truth table with the degree table below it?

    "Tomorrow will be a very important day for you. It is your birthday.
    We are going to invite your two best friends from your preschool.
    Alice and Barbara are coming to your party."

    Notice that in Western logic this last statement is just true or
    false. There are no shades of gray. The result is the same (false) if
    either Alice or Barbara do not come for some reason (lines 2 and 3),
    and if both Alice and Barbara don't come (line 4).

    A B A · B
    T T T
    T F F
    F T F
    F F F


    A B Result


    0 0 0
    15 15 .08
    30 30 .16
    45 45 .25
    60 60 .33
    75 75 .41
    90 90 .50
    105 105 .58
    120 120 .66
    135 135 .75
    150 150 .83
    165 165 .91
    180 180 1.0


    Notice that when we say that Alice or Barbara "attends" the little
    girl's party that this is potentially a fuzzy concept. Suppose the
    mothers of Alice and Barbara tell the little girl's mother that they
    will be very busy that day and are not sure they can make it, but they
    are pretty sure they can stop by for at least a little while. So you
    see from the little girl's point of view "attends" is not a black and
    white (true or false) event. What if one girl comes for only fifteen
    minutes and the other comes for the full time? Or some other
    variation of times? This will make a big difference from the little
    girl's perspective for how much truth is in the statement "Alice and
    Barbara are coming to your party."

    So, here is how a fuzzy logic truth table might look. If we assume
    the party is three hours long and we break the party up into 15-minute
    segments, we would have a table that looked like this.

    ...adding degrees-of-truth-reasoning to the very foundations of logic
    has a drastic effect on all the other rules of logic. All the rules we
    have learned become applicable to only extreme cases -- cases of
    complete truth or complete falsehood. Even deductive validity and
    invalidity become more like the distinction we made in Chapter 3
    between "strong inductive" and "weak inductive" arguments. A fuzzy
    valid argument can "blend into" an invalid deductive argument.

    The huge issue all this raises is, "What is the status of logic?" The
    fancy way philosophers ask the question is, "What is the ontological
    status of logic and mathematics?" Are they just rules we make up like
    that of a game (e.g.. basketball)? Are they simply part of a cultural
    view of reality? Or, are they some kind of absolutes that the universe
    obeys, like the law of gravity? Are they simply rules used by the
    human mind? Are they rules in the mind of God?

    http://www.hcc.hawaii.edu/~pin­e/Phil110/chapt12sup2.htm

    # A OR B = MAX(m(A(x)), m(B(x)))
    # A AND B = MIN(m(A(x)), m(B(x)))
    # A' (NOT A) = 1 - mA(x)


    http://www.generation5.org/con­tent/1999/fuzzyintro.asp
     
  2. Why?, they are both disappointingly vague.

    "Do, or do not, there is no try" - Yoda.
    Yoda was obviously a digital guy.

    I think I'll go have some chocolate.

    Dave.
     
  3. Immortalist

    Immortalist Guest

     
  4. You appear to be seriously in need of a date.
    Try here:
    http://www.match.com

    Some advice might help you on your way:


    Dave.
     
  5. Here is an old out of print book on fuzzy,
    my book "Fuzzy Logic A Practical Approach".
    http://www.fuzzysys.com/books/FLLib/FUZZYPDF/FUZZYLOG.PDF
    and the old demo programs from the book :
    http://www.fuzzysys.com/books/FLLib/PC/PRACTAPP/PRACTAPP.zip
    you must unzip it and run install.exe.

    and here is the typo list for the book :
    http://www.fuzzysys.com/typolist.html

    The products mentioned are no longer for sale.
    If you have any problems accessing these items,
    let me know.

    --
    Frederick Martin McNeill
    Poway, California, United States of America

    ******************************************
    "I never cease being dumbfounded by the unbelievable things people believe."
    - Leo Rosten
    ******************************************
     
  6. ZerkonX

    ZerkonX Guest

    More like: Wrong Think! Why, OH WHY can't this number tyranny be broken,
    overthrown and put in it's place once and for all. Physics awaken! You
    guys know somewhere deep down or up shallow this is fuzzy true, more or
    less, to some degree, sorta, kinda. Your science has been pointing that
    way now for years.

    There are not two "types" of thinking. This is a self-serving position.
    'Types' demands numerical amounts. 1-99 and 0/1 (100%) are the same
    thing, a numerical concept into which all must be classified, by force if
    need be. It's one way to think about thinking and only that.
    Beware, heresy ahead.

    Data/information retention is a primitive and base function. It is not
    complex. It does not indicate real intelligence unless intelligence is to
    be defined only as such. Real human work, thought, comes in the
    processing of information and here quantity does not ensure quality.

    A person who can recall and only recall a library of information would
    not be able to function at any level. Another who was able to only
    vaguely recall a small amount of information but who draws generalities
    applicable and constructive to situations detached from the retained
    information demonstrates human intelligence.

    There is still a huge fuzzy growing on what information retention is AND
    what information is usable or used information. Using computer "memory"
    addresses, or the old 'warehouse boxes model' seems to be more metaphors
    gone wild and wrong.

    Each person as thinker defines their own 'type' of thinking. Logic
    satisfies first the thinker. Then only if there is a need, other thinkers.

    A shift moves now from thought to the communication of thought.
    Communication becomes a standard type, an accepted methodology. So
    thought goes to communication which is formed into acceptable
    methodology. Now, here, the methodology, forgetting it's lowly place in
    line, turns around to define thought in it's own image!

    What's next? Computers telling us what to do?!?
     
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