UGC-NET | UGC NET CS 2016 July – III | Question 65

Compute the value of adding the following two fuzzy integers :
A = {(0.3, 1), (0.6, 2), (1, 3), (0.7, 4), (0.2, 5)}
B = {(0.5, 11), (1, 12), (0.5, 13)}
Where fuzzy addition is defined as
μA+B (z) = max x + y = z(min (μA(x), μB(x)))
Then, f (A + B) is equal to
(A) {(0.5, 12), (0.6, 13), (1, 14), (0.7, 15), (0.7, 16), (1, 17), (1, 18)}
(B) {(0.5, 12), (0.6, 13), (1, 14), (1, 15), (1, 16), (1, 17), (1, 18)}
(C) {(0.3, 12), (0.5, 13), (0.5, 14), (1, 15), (0.7, 16), (0.5, 17), (0.2, 18)}
(D) {(0.3, 12), (0.5, 13), (0.6, 14), (1, 15), (0.7, 16), (0.5, 17), (0.2, 18)}


Answer: (D)

Explanation: According to question:
A={(0.3, 1), (0.6, 2), (1, 3), (0.7, 4), (0.2, 5)}
B={(0.5,11), (1, 12), (0.5, 13)}
first add the numbers(x + y = z) and write the min membership value since function is min((μA(x),μB(x)) u will get following 15 terms:
{(0.3, 12), (0.3, 13), (0.3, 14), (0.5, 13), (0.6, 14), (0.5, 15), (0.5, 14), (1, 15), (0.5, 16), (0.5, 15), (0.7, 16), (0.5, 17), (0.2, 16), (0.2, 17), (0.2, 18)
f(A + B) is equal to {(0.3, 12), (0.5, 13), (0.6, 14), (1, 15), (0.7, 16), (0.5, 17), (0.2, 18)}
So, option (D) is correct.

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