Hi

Plz refer this page...

https://www.csie.ntu.edu.tw/~sylee/courses/FuzzyJ/Docs/FuzzySet.html

If the membership function is equal to 1, you can use:

Common area = 1/2 * (c - d) / (c - b + e - d).

For more details please see the attachment.

Hi Bardia,

The intersection (common area) of two fuzzy sets, symbolized by A∧B, is similar to the classical intersection of two sets as shown in the Venn diagram. The fuzzy intersection is defined as the min operation on the membership functions as x traverses the universe of discourse:

μA∧B(x1, x2) = min(μA(x1), μB(x2))

In fuzzy rules, where the If–Then statements are connected with the words “And, Or,” we take that “And” is the min operator. In linguistic terms, the fuzzy intersection is governed by the rule with “And” connective:

If x1 is μA(x) And x2 is μB(x), Then y is output.

The area of intersection, however, is determined by the shapes and sizes of the fuzzy membership functions.

Dear all,

Hello

I greatly appreciate your valuable answers. They are very helpful.

Nevertheless, let me ask my question from different point of view:

In an ordinary fuzzy diagram, that you are not sure about the severity of uncertainties, what is the recommended range for "dc" (please refer to the picture in the question).

Should it be equal to, for example, 20% of the average of "ac" and "df" (in the same picture)?

Is there any references which discuss about this issue?

Hi Bardia,

There is no general rule for the determination of the type of membership functions (MFs) and it mainly depends on your specific problem. Ideally, if you have the data, you can probably derive the appropriate shape of the MF from the probability distribution of data.

Otherwise, the general consensus is that symmetrical and equal-in-size MFs should be selected and positioned such that the cross-point of adjacent MFs is at degree 0.5 in the preliminary design. The shapes can be tuned later to suit your needs. See the example in the figure.

http://fooplot.com/#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