Two fuzzy sets A and B are represented by the membership functions shown below:

Question

Two fuzzy sets A and B are represented by the membership functions shown below: Sketch the membership functions of the following fuzzy sets/relations: A B. A B. NOT A. A rightarrow B. In (a) and (b) assume that A and B are defined in the same universe X = [0, 8], and in (d) assume that B is defined in another universe Y. Both universes are subsets of the real line R. In case (d) suppose that a crisp reading of A' is observed as x = 5. What is the membership function of the corresponding inference B'? If this inference is defuzzified using the centroid method, what is the crisp action?

Explanation / Answer

a) A U B = maximun(A,B)

b)A intersection B = minimum (A,B)

c)NOT A = total - A

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