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Fuzzy Logic
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Example 2: Representing Age

Problem 2-1. Fuzzy sets can be used to represent fuzzy concepts. Let U be a reasonable age interval of human beings.

U = {0, 1, 2, 3, ... , 100}

Solution 2-1. This interval can be interpreted with fuzzy sets by setting the universal space for age to range from 0 to 100.

SetOptions[FuzzySet, UniversalSpace -> {0, 100}] ;

Problem 2-2. Assume that the concept of "young" is represented by a fuzzy set Young, whose membership function is given by the following fuzzy set.

Young = FuzzyTrapezoid[0, 0, 25, 40] ;

The concept of "old" can also be represented by a fuzzy set, Old, whose membership function could be defined in the following way.

Old = FuzzyTrapezoid[50, 65, 100, 100] ;

We define the concept of middle-aged to be neither young nor old. We do this by using fuzzy operators from Fuzzy Logic.

Solution 2-2. We can find a fuzzy set to represent the concept of middle-aged by taking the intersection of the complements of our Young and Old fuzzy sets.

MiddleAged = Intersection[Complement[Young], Complement[Old]] ;

We can now see a graphical interpretation of our age descriptors by using the FuzzyPlot command.

FuzzyPlot[Young, MiddleAged, Old, PlotJoined -> True] ;


From the graph, you can see that the intersection of "not young" and "not old" gives a reasonable definition for the concept of "middle-aged."

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