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This particular shape is known as a triangular membership function.
On the other hand, the membership function of medium is a triangular membership function.
Open image in new window Fig. 6 The parameters that define a triangular membership function.
Furthermore, this framework is developed using the fuzzy inference system toolbox of MATLAB, employing specifically the Mamdani algorithm with a triangular membership function.
The values of low and high correspond to a trapezoidal membership function, while other values of the variable use a triangular membership function.
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Figure 3 provides a graphical representation of the triangular membership functions when applied for spectrum fuzzyfication.
For this reason, the value of each moment parameter is characterized by three fuzzy linguistic terms {LOW, MEDIUM, HIGH} subject to a specific range, while three triangular membership functions (7) are selected to describe their behavior, as depicted in Fig. 5. Open image in new window Fig. 5 Inputs/outputs FIS definition.
As shown in Eq. 2, D ij as a fuzzy number can be represented by the triangular membership.
A complete algorithm, using cross-entropy optimization of triangular membership functions, is given and applied to the car-on-the-hill example.
In the proposed model, a previously defined DB constituted by uniform fuzzy partitions with triangular membership functions crossing at height 0.5 is considered.
Triangular membership functions (Figure 1) are often used [30, 31], and a plethora of alternatives exists (e.g., Z-shape, Gaussian, and S-shaped membership functions [32]).
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