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
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 ...