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Math Help - fuzzy sets

  1. #1
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    fuzzy sets

    Hi Guys,

    I am trying to code a fuzzy set in vb.net and wonder what the function for a such a fuzzy set would look like:



    I have tried f(x)=8 - x^2 but this is just a parabolic function, nothing like on the picture.

    After hours of research I think the only way it can be done is by
    drawing the simple triangular function and adding one after the other to the graph, then determining the degree of membership.

    Fuzzy Sets:

    Fuzzy sets are sets whose elements have degrees of membership. So the input [70 km/h] is to 75% low and 25% medium.

    I just need to calculate the degree of membership for each input e.g. [70 km/h], [60 km/h], [80 km/h].




    Many thanks for any suggestions

    polynaux
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by polynaux View Post
    Hi Guys,

    I am trying to code a fuzzy set in vb.net and wonder what the function for a such a fuzzy set would look like:



    I have tried f(x)=8 - x^2 but this is just a parabolic function, nothing like on the picture.

    After hours of research I think the only way it can be done is by
    drawing the simple triangular function and adding one after the other to the graph, then determining the degree of membership.

    Fuzzy Sets:

    Fuzzy sets are sets whose elements have degrees of membership. So the input [70 km/h] is to 75% low and 25% medium.

    I just need to calculate the degree of membership for each input e.g. [70 km/h], [60 km/h], [80 km/h].




    Many thanks for any suggestions

    polynaux
    Try something like:

    f(x)=\max \left(0, 1-\frac{2|x-l|}{width}\right)

    where l is the location parameter, and width the width of the support of f.

    RonL
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