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S12CPUV2 Reference Manual, Rev. 4.0

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The end result of the rule evaluation step is a table of suggested or “raw”

fuzzy outputs in RAM. These values were obtained by plugging current

conditions (fuzzy input values) into the system rules in the knowledge base.

The raw results cannot be supplied directly to the system outputs because

they may be ambiguous. For instance, one raw output can indicate that the

system output should be medium with a degree of truth of 50 percent while,

at the same time, another indicates that the system output should be low

with a degree of truth of 25 percent. The defuzzification step resolves these

ambiguities.

9.2.3 Defuzzification (WAV)

The final step in the fuzzy logic program combines the raw fuzzy outputs into

a composite system output. Unlike the trapezoidal shapes used for inputs,

the CPU12 typically uses singletons for output membership functions. As

with the inputs, the x-axis represents the range of possible values for a

system output. Singleton membership functions consist of the x-axis

position for a label of the system output. Fuzzy outputs correspond to the

y-axis height of the corresponding output membership function.

The WAV instruction calculates the numerator and denominator sums for

weighted average of the fuzzy outputs according to the formula:

Where n is the number of labels of a system output, Si are the singleton

positions from the knowledge base, and Fi are fuzzy outputs from RAM. For

a common fuzzy logic program on the CPU12, n is eight or less (though this

instruction can handle any value to 255) and Si and Fi are 8-bit values. The

final divide is performed with a separate EDIV instruction placed

immediately after the WAV instruction.

Before executing WAV, an accumulator must be loaded with the number of

iterations (n), one index register must be pointed at the list of singleton

positions in the knowledge base, and a second index register must be

pointed at the list of fuzzy outputs in RAM. If the system has more than one

system output, the WAV instruction is executed once for each system

output.

System Output

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