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(a)Use the fuzzy sets A and B for the following questions:
Given that the value of x is 4,state the membership value of the following
operations.
(i) ~A [1mark ]
0.25 (1)
(ii)A B
[1mark ]
0.25 (1)
(iii)A v B [1mark ]
0.75 (1)
(iv)Provide possible values for “very A ”and “somewhat
A ”[2 marks ]
A possible value for “very ”could
be 0.85 (1); for “somewhat ”it could be 0.5 (1).
(b)A survey gathered the opinions of a representative sample of the
population and determined the following statistics:
100%of the sample agrees that anyone less than 1.4 metre is short
75%of the sample agrees that a person 1.5 metre is short
50%of the sample agrees that a person 1.6 metre is short
25%of the sample agrees that a person 1.7 metre is short
100%of the sample agrees that anyone more than 1.8 metre is not short
100%of the sample agrees that anyone less than 40 kgs is light
75%of the sample agrees that a person 45 kgs is light
50%of the sample agrees that a person 50 kgs is light
25%of the sample agrees that a person 55 kgs is light
100%of the sample agrees that anyone more than 60 kgs is not light
(i)Use the statistics to construct the appropriate fuzzy sets for
height and weight. [4 marks ]
For each graph,(1)for the correct fuzzy set,(1)for the correct numbering
and labelling.
(ii)Given the rule “If a man is short then he is light ”and
the fact that John is 1.7m tall,describe the steps that can be performed
in single inference fuzzy logic.Use the fuzzy graphs to show the working.[6
marks ]
Single rule inference:
1.Fuzzification –finding the membership values for the iniut
fuzzy set (1)
2.Inference –from the membership value, find the output fuzzy
set (1)
3.Defuzzification –from the output fuzzy set, find the final
output value (1)
For the working,(1)for member hip of 0.25,(1)for
the output fuzzy et,(1)for indicating the result.
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