3.3 Multiplication of fuzzy numbers

The generalized product x1* x2* of two fuzzy numbers with corresponding characterizing functions ξ1(·) and ξ2(·) is defined by using the extension principle to the function f : 2 → with f (x, y) = x · y, after combining x1* and x2* by the minimum t-norm.

The characterizing function ξx1* x2*(·) of the x1* x1* is given by

Remark 3.5:

Using Theorem 3.1 the δ-cuts of the product x1* x2* can be calculated:

It can be proved that the following is valid:

It should be noted that the product of trapezoidal fuzzy numbers is not trapezoidal.

In Figure 3.3 an example ...

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