Читать книгу Artificial Intelligence and Quantum Computing for Advanced Wireless Networks - Savo G. Glisic - Страница 66

Let us compute the fuzzy relation for the linguistic model of Figure 4.4. First, we discretize the input and output domains, for instance: X = {0, 1, 2, 3} and Y = {0,25,50,75,100}. The (discrete) membership functions are given in Table 4.1 for both antecedent linguistic terms, and for the consequent terms.

Table 4.1 An example of the (discrete) membership functions for both antecedent linguistic terms, and for the consequent terms.

Antecedent
Domain element
Linguistic term	0	1	2	3
Low	1.0	0.6	0.0	0.0
Moderate	0.0	0.4	1.0	0.4
High	0.0	0.0	0.1	1.0
Consequent
Domain element
Linguistic term	0	25	50	75	100
Low	1.0	1.0	0.6	0.0	0.0
Moderate High	0.0	0.0	0.3	0.9	1.0

The fuzzy relations R_i corresponding to the individual rule can now be computed by using Eq. (4.32). For rule , we have R₁ = Low × Low; for rule , we obtain R₂ = Moderate × High; and finally for rule R₃ = High × Low. The fuzzy relation R, which represents the entire rule base, is the union (element‐wise maximum) of the relations R_i :

Similarly

(4.35)

where from Eq. (4.33) , that is, .