An early expression of fuzzy sets?

From: Zunt@aol.com
Date: Wed Feb 28 2001 - 21:09:59 MET

  • Next message: Masoud Nikravesh: "BISC: CFP"

    Howdy all,

    In 1923, Max Freyd of the University of Pennsylvania wrote about the "Graphic
    Rating Scale" (GRS) in the Journal of Educational Psychology. Upon
    reflection, I think that the scale he describes is closely related to a fuzzy
    set, but before I expend a lot more energy on the topic I figured I'd toss
    the idea to my friends on this list to see what they make of it. I'd greatly
    appreciate any comments--this all has a bearing on the dissertation I'm
    trying to cough up.

    Freyd (1923) listed several forms of rating scales, including these two
    (where, for the sake of example, the variable of interest happens to be
    self-consciousness):

    "8. Draw a line to represent the range of self-consciousness, and have judges
    indicate each man's self-consciousness by making a cross along this line,"

    and

    "9. A large number of phrases descriptive of varying degrees of
    self-consciousness may be collected, and arranged in order as in the examples
    cited from Plant and Downey. These phrases may be numbered from 1 to 5, or
    from 1 to 10, depending on the number of phrases. The judges may indicate
    their rating by checking the phrase which corresponds most closely to their
    estimate of the man's self-consciousness."

    [both quotations from p.88]

    Freyd (1923) identified the GRS as the combination of those two scales.

    Now it seems to me that the line in Freyd's (1923) method #8 should be
    familiar to everyone on this list as the continuum along which fuzzy granules
    are perched. And the phrases that he's writing about in his method #9 look
    to me like the granules themselves. So the GRS--as a combination of those
    two methods--winds up looking to me just like the typical x-axis of a fuzzy
    set, and the y-axis we typically draw (where the membership values range from
    0 to 1) can be inferred properly from context.

    Am I making sense here? Does anyone know of a paper where this connection
    has been established nicely?

    Freyd (1923) wrote that the GRS was not his invention, but it came into use
    by unnamed researchers at the Scott Company. In particular, he cited "The
    Scott Co. Laboratory. _Bulletins on the Graphic Rating Scale_," and pegged
    their date at 1920. (It was kind of him to mention this, because he's the
    one who gets credit nowadays for developing the scale; some consider it to be
    one of the many significant developments in the field of psychology.) He went
    on to say that the GRS's "...only original feature is the combination of the
    methods of rating on a line and by checking descriptive terms, both of which
    were in prior existence...."

    By the way, Freyd (1923) didn't say who actually came up with the "rating on
    a line" business. One of my friends on another list is searching very hard
    on his own account for the answer to that question, so if anyone here can
    provide a reference, I'd be delighted to pass it along.

    Thanks in advance for your attention and replies...

    Regards,

    Bob Briggs
    Westport, MA

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