ABSTRACT
Figure 21 Membership function /uR(x, y) of the relation R: x is approximately equal to y over the Cartesian product of two continuous sets X and Y.
I t may be interesting to realize that we can interpret this relational matrix as a notation, or model, o f an existing empirical set of IF-THEN rules:
R l : IF (the tomato is) green, T H E N (it is) unripe R2: IF yellow, T H E N semiripe R3: IF red, T H E N ripe
In fact, relations are a convenient tool to model IF -THEN rules. Before plunging into this important part o f FL modeling, let us mention that the relational matrix given above is a crisp one, and not in total agreement wi th our experience. Even tually better interconnection between the fruit color and the state o f the fruit may be given by the fuzzy relational matrix below,
R Unripe Semiripe Ripe Green 1 0.5 0 Yellow 0.3 1 0.4 Red 0 0.2 1
Example 8 Present the fuzzy relational matrix for the relation R that represents the concept o f being very far in geography. Two crisp sets are given as,
X - {Auckland, Tokyo, Belgrade} Y = (Sydney, Athens, Belgrade, Paris, New York}
R: very far Sydney Athens Belgrade Paris New York Auckland 0.2 0.8 0.85 0.90 0.55 Tokyo 0.5 0.5 0.5 0.55 0.4 Belgrade 0.8 0.1 0 0.15 0.5
Hence the relational matrix doesn't necessarily have to be a rectangular one.
