Page 47 - Biomedical Engineering and Design Handbook Volume 1, Fundamentals

24 BIOMEDICAL SYSTEMS ANALYSIS

A B
1 1

Membership 0.5 Severe Moderate Mild Normal Membership 0.5 Severe Moderate Mild Normal

0 0
0 0.2 0.4 0.6 0.8 1 0 10 20 30 40 50

C
1

Membership 0.5 Severe Moderate Mild Normal

0
0 0.2 0.4 0.6 0.8 1
FIGURE 1.14 The membership functions are used to compute the membership values corresponding to the mea-
sured parameters: (a) membership functions for the acceleration magnitude (peak-to-peak value); (b) membership
functions for the peak swallow pressure; and (c) the measured number of attempts to swallow. The variable number of
attempts to swallow n, was transformed by a linear transfer function given by defining a new variable f = (8 − n)/7] and
membership functions defined on the new variable f. [Reproduced with permission from Suryanarayanan et al. (1995).]

The membership values are represented as μ , where i represents the parameter and j represents
i,j
the subset. Corresponding to each parameter a, we have a vector of membership values given by
μ (X) = [μ (x), μ (x), μ (x), μ (x)] (1.62)
a a,1 a,2 a,3 a,4
where a is the parameter, μ a,j is the membership to the jth subset corresponding to parameter a. For
instance, μ a,1 refers to membership value related to severe distortion in the acceleration magnitude, μ a,2
refers to moderate distortion in acceleration magnitude, μ a,3 refers to mild distortion in acceleration
magnitude, and μ a,4 refers to normal acceleration magnitude. Similarly, the elements in μ , μ , μ b,3,
b,1
b,2
and μ refer to severe distortion in the swallow pressure magnitude, moderate distortion in swallow
b,4
pressure magnitude, mild distortion in swallow pressure magnitude, and normal swallow pressure.
For each patient, the measured parameter values are fuzzified to obtain the four membership val-
ues for each of the three parameters. These values are then fed to a rule base R. The function R is
defined as a relation between the parameters defined. A typical relation between input and output
parameters is the IF-THEN rule. The output is given by the rule set R acting upon the membership
values computed for the measured parameters and is represented as
Φ= R . [(μ (x), μ (y), μ (z)] (1.63)
a b c
where subscript a refers to the parameter “acceleration magnitude” and x is the corresponding value,
subscript b refers to the parameter “swallow pressure magnitude” and y is the corresponding value
of this parameter, and subscript c refers to the parameter “number of attempts to swallow” and z is
the corresponding value of this parameter. The rule base can be in the form of a lookup table or in