03-08-2012, 01:52 PM
DEFUZZIFICATION
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Defuzzification is a mapping process from a space of fuzzy control actions defined over an output universe of discourse into a space of crisp (nonfuzzy) control actions.
Defuzzification is a process of converting output fuzzy variable into a unique number .
Defuzzification process has the capability to reduce a fuzzy set into a crisp single-valued quantity or into a crisp set; to convert a fuzzy matrix into a crisp matrix; or to convert a fuzzy number into a crisp number.
CENTER OF SUMS
This method employs the algebraic sum of the individual fuzzy subsets instead of their unions. The calculations here are very fast but the main drawback is that the intersecting areas are added twice. The defuzzified value x* is given by
CENTER OF LARGEST AREA
This method can be adopted when the output consists of at least two convex fuzzy subsets which are not overlapping. The output in this case is biased towards a side of one membership function. When output fuzzy set has at least two convex regions then the center-of-gravity of the convex fuzzy subregion having the largest area is used to obtain the defuzzified value x*. This value is given by
SUMMARY
Defuzzification process is essential because some engineering applications need exact values for performing the operation.
Example: If speed of a motor has to be varied, we cannot instruct to raise it “slightly”, “high”, etc., using linguistic variables; rather, it should be specified as raise it by 200 rpm or so, i.e., a specific amount of raise should be mentioned.
The method of defuzzification should be assessed on the basis of the output in the context of data available.