Abnormal Membership Function Case 1 - Motorola HC12 Refrence Manual

In 4b, slope_1 is zero if the left side of the trapezoid has infinite slope (vertical). If so,
the result (grade) should be $FF at and to the right of point_1 everywhere within the
trapezoid as far as the left side is concerned. The grade_1 greater than $FF term cor-
responds to the input being to the right of where the left sloping side passes the $FF
cutoff level. If either of these conditions is true, the result (grade) is left at the value it
got from 4a. The "else" condition in 4b corresponds to the input falling on the sloping
portion of the left side of the trapezoid (or possibly outside the trapezoid), so the result
is grade equal grade_1. If the input was outside the trapezoid, flag_d12n would be one
and grade_1 and grade_2 would have been forced to $00 in cycle 3. The else condi-
tion of 4b would set the result to $00.
The following special cases represent abnormal membership function definitions. The
explanations describe how the specific algorithm in the CPU12 resolves these unusual
cases. The results are not all intuitively obvious, but rather fall out from the specific al-
gorithm. Remember, these cases should not occur in a normal system.

9.4.2.1 Abnormal Membership Function Case 1

This membership function is abnormal because the sloping sides cross below the $FF
cutoff level. The flag_d12n signal forces the membership function to evaluate to $00
everywhere except from point_1 to point_2. Within this interval, the tentative values for
grade_1 and grade_2 calculated in cycle 3 fall on the crossed sloping sides. In step
4a, grade gets set to the grade_2 value, but in 4b this is overridden by the grade_1
value, which ends up as the result of the MEM instruction. One way to say this is that
the result follows the left sloping side until the input passes point_2, where the result
goes to $00.
Memory Definition: $60, $80, $04, $04; Point_1, Point_2, Slope_1, Slope_2
Graphical Representation:
P1
Figure 9-6 Abnormal Membership Function Case 1
If point_1 was to the right of point_2, flag_d12n would force the result to be $00 for all
input values. In fact, flag_d12n always limits the region of interest to the space greater
than or equal to point_1 and less than or equal to point_2.
MOTOROLA
9-12
P2
FUZZY LOGIC SUPPORT
How Interpreted:
P1 P2
REFERENCE MANUAL
ABN MEM 1
CPU12