The Boolean shape is a special case in fuzzy logic, and it essentially mimics the way most data classification algorithms work: it either 'IS' or it 'AIN'T.' The Boolean shape does have uses, however. In Fuzzy Logic one can make the decision shapes overlap as needed. A Boolean set could certainly be set up as a 'watchdog' that could be used to force a decision should the decision algorithm have a flaw. For instance, let's say that your data is speed in MPH, from 1 - 100. You decide that 0-15 is SLOW and taper it to 25mph using a trapezoidal set. The MEDIUM SLOW set may start at 15mph and ramp up to another trapezoidal decision shape's linear area at 35mph. The Boolean MEDIUM_WATCH would take effect at 15.1 mph to say, 55 mph. Now let's assume that for whatever reason that a data point is read that is 50% SLOW membership (20 mph) and ALSO 50% MEDIUM membership. Your decision algorithm, depending on it's robustness, could miss this data. The Boolean set, however, acts as a watchdog such that in the event of an equality of overlapping set membership, the Boolean set can be used to make the decision. It would not normally be consulted, but when it is, it would work well.
