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Once the rules have been composed the solution, as has been seen, is a fuzzy set. However, for most applications (in particular in control) there is a need for a single action or `crisp' solution to emanate from the inferencing process. This will involve the `defuzzification' of the solution set. There are various techniques available. Lee [20] describes the three main approaches as the max criterion, mean of maximum and the centre of area.

The max criterion method finds the point at which the membership function is a maximum.

The mean of maximum takes the mean of those points where the membership function is at a maximum.

The most common method is the centre of area method which finds the centre of gravity of the solution fuzzy sets. For a discrete fuzzy set this is

where is the value from the set that has a membership value . Lee [20] states that ``Unfortunately, there is no systematic procedure for choosing a defuzzification strategy.''. Although the process of reducing the final fuzzy set to a crisp value does seem appropriate for control problems much information is lost by doing this and further work needs to be done on how to use the information available in the solution fuzzy set.

Bob John
Fri Oct 25 14:41:29 BST 1996