Re: Consistency of fuzzy rules

From: WSiler@aol.com
Date: Wed Oct 31 2001 - 22:07:12 MET

  • Next message: tedd: "fuzzy book"

    In a message dated 10/17/01 2:28:08 AM Central Daylight Time,
    ftrjin@mail.ipm.net writes:

    > >I even would go one step further: rules are never inconsistent.
    > >Inconsistency only arises when rules contradict domain knowledge.
    > >This is irrespective of whether the rules are interpreted as
    > >Mamdani-like rules or as implications.
    >
    > This argument itself is inconsistent. Remind that fuzzy rules are believed
    > to be
    > able to extract knowledge from data. If rules are never inconsistent, how
    > can
    > rules be inconsistent with domain knowledge, which can usually be
    > represented by
    > fuzzy rules? Just an example. From data, you get two rules:
    >
    > R1: If speed is high and distance is short, brake sharply (to stop)
    > R2: If speed is high and distance is short, brake slightly (to stop)
    >
    > These two rules, in my view are inconsistent. (How inconsistent they are
    > depends
    > on the definition of the membership functions and I won't go into further
    > details here). In fact, the second rule is obviously inconsistent to human
    > intuition: If speed is high and distance is short, then one should brake
    > sharply
    >

    Let me take this up one issue at a time.

    >> ...domain knowledge, which can usually be represented by
    fuzzy rules>>

    This is a very common illusion, even in AI circles. Domain knowledge is of
    two kinds: declarative, which can be stored in data bases; and procedural,
    which can be stored in crisp and fuzzy rules. For example, it is fairly easy
    to write rules to interpret a domain knowledge data base (which can results
    in great economy in number of rules). Unfortunately, knowledge of an
    individual as often unreliable. group <dpmain> knowledge is more reliable,
    but is by no means completely so, and is often not codified. Further, each
    individual who writes a fuzzy system uses his own idea of domain knowlege to
    define variables and membership functions, and to write rules.

    In addition, we have data which are input during a program run, and may not
    be very reliable. For example, in an online real-time run where data are
    almost continuously input, we can have noise and artifacts which could result
    in ridiculous conclusions if not detected and allowed for.

    <<In fact, the second rule is obviously inconsistent to human intuition: If
    speed is high and distance is short, then one should brake sharply to stop,
    which is itself a fuzzy rule. (How inconsistent they are depends on the
    definition of the membership functions.) >>

    We make progress! Now inconsistency is no longer binary (Yes/No), but there
    are grades of inconsistency! I agree with this statement. However, if "brake"
    is a linguistic variable, with members only "sharply" and "slightly", and if
    "speed" is also a linguistic variable with members "stop", "very_slow",
    "slow" and "high", it might be that a braking action which is intemediate
    between "sharply" and "slightly" is required. I would think that while this
    condition is unlikely, it is not necessarily an error. However, we are now
    imposing the program-checker's idea of domain knowledge over that of the
    program-writer's idea. In the case of rules and membership functions, this is
    somewhat arrogant and quite error-susceptible. It seems best that a warning
    of possible inconsistency should be issued,

    <<In fact, the second rule is obviously inconsistent to human intuition.>>

    Does "human intuition" qualify for domain knowledge? To some extent, prehaps
    yes, but only a qualified (fuzzy) yes. It is certainly hard to define
    precisely or accurately, and is certainly not completely reliable; it is
    impossible for a single individual to possess all of human intuition.

    So if we qualify the original writer's term "inconsistent rules" to "possibly
    inconsistent rules" I might go along with his ideas, provided that warnings
    instead of error messages were issued, and that I have the option to turn off
    one or more of his criteria during the checking process. Under these
    circumstances, I think ftrjin@mail.ipm.net has made a definite contribution.

    Sincerely,
    William Siler

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    <HTML><FONT FACE=arial,helvetica><FONT SIZE=2>In a message dated 10/17/01 2:28:08 AM Central Daylight Time, ftrjin@mail.ipm.net writes:
    <BR>
    <BR>
    <BR><BLOCKQUOTE TYPE=CITE style="BORDER-LEFT: #0000ff 2px solid; MARGIN-LEFT: 5px; MARGIN-RIGHT: 0px; PADDING-LEFT: 5px">&gt;I even would go one step further: rules are never inconsistent.
    <BR>&gt;Inconsistency only arises when rules contradict domain knowledge.
    <BR>&gt;This is irrespective of whether the rules are interpreted as
    <BR>&gt;Mamdani-like rules or as implications.
    <BR>
    <BR>This argument itself is inconsistent. Remind that fuzzy rules are believed to be
    <BR>able to extract knowledge from data. If rules are never inconsistent, how can
    <BR>rules be inconsistent with domain knowledge, which can usually be represented by
    <BR>fuzzy rules? Just an example. From data, you get two rules:
    <BR>
    <BR>R1: If speed is high and distance is short, brake sharply (to stop)
    <BR>R2: If speed is high and distance is short, brake slightly (to stop)
    <BR>
    <BR>These two rules, in my view are inconsistent. (How inconsistent they are depends
    <BR>on the definition of the membership functions and I won't go into further
    <BR>details here). In fact, the second rule is obviously inconsistent to human
    <BR>intuition: If speed is high and distance is short, then one should brake sharply
    <BR>to stop, which is itself a fuzzy rule. </BLOCKQUOTE>
    <BR>
    <BR>Let me take this up one issue at a time.
    <BR>
    <BR>&gt;&gt; ...domain knowledge, which can usually be represented by
    <BR>fuzzy rules&gt;&gt;
    <BR>
    <BR>This is a very common illusion, even in AI circles. Domain knowledge is of two kinds: <B>declarative</B>, which can be stored in data bases; and <B>procedural</B>, which can be stored in crisp and fuzzy rules. For example, it is fairly easy to write rules to interpret a domain knowledge data base (which can results in great economy in number of rules). Unfortunately, knowledge of an individual as often unreliable. group &lt;dpmain&gt; knowledge is more reliable, but is by no means completely so, and is often not codified. Further, each individual who writes a fuzzy system uses his own idea of domain knowlege to define variables and membership functions, and to write rules.
    <BR>
    <BR>In addition, we have data which are input during a program run, and may not be very reliable. For example, in an online real-time run where data are almost continuously input, we can have noise and artifacts which could result in ridiculous conclusions if not detected and allowed for.
    <BR>
    <BR>&lt;&lt;In fact, the second rule is obviously inconsistent to human intuition: If speed is high and distance is short, then one should brake sharply to stop, which is itself a fuzzy rule. (How inconsistent they are depends on the definition of the membership functions.) &gt;&gt;
    <BR>
    <BR>We make progress! Now inconsistency is no longer binary (Yes/No), but there are grades of inconsistency! I agree with this statement. However, if "brake" is a linguistic variable, with members only "sharply" and "slightly", and if "speed" is also a linguistic variable with members "stop", "very_slow", "slow" and "high", it might be that a braking action which is intemediate between "sharply" and "slightly" is required. I would think that while this condition is unlikely, it is not necessarily an error. However, we are now imposing the program-checker's idea of domain knowledge over that of the program-writer's idea. In the case of rules and membership functions, this is somewhat arrogant and quite error-susceptible. It seems best that a warning of possible inconsistency should be issued,
    <BR>
    <BR>&lt;&lt;In fact, the second rule is obviously inconsistent to human intuition.&gt;&gt;
    <BR>
    <BR>Does "human intuition" qualify for domain knowledge? To some extent, prehaps yes, but only a qualified (fuzzy) yes. It is certainly hard to define precisely or accurately, and is certainly not completely reliable; it is impossible for a single individual to possess all of human intuition.
    <BR>
    <BR>So if we qualify the original writer's term "inconsistent rules" to "possibly inconsistent rules" I might go along with his ideas, provided that warnings instead of error messages were issued, and that I have the option to turn off one or more of his criteria during the checking process. Under these circumstances, I think ftrjin@mail.ipm.net has made a definite contribution.
    <BR>
    <BR>Sincerely,
    <BR>William Siler</FONT></HTML>

    --part1_155.2d683b2.2905907f_boundary--

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