UGC-NET | UGC NET CS 2017 Jan – III | Question 71

Let R and S be two fuzzy relations defined as :

Then, the resulting relation, T, which relates elements of universe x to the elements of
universe z using max-min composition is given by :

(A) (1)
(B) (2)
(C) (3)
(D) (4)

Answer: (C)
Explanation: Since x is related to y and y is related to z, to relate universe x and universe z we have to compute max-min composition:

x1z1= max(min(0.6, 0.8), min(0.4, 0.0))
    = max(0.6, 0.0)
    = 0.6
x1z2= max(min(0.6, 0.5), min(0.4, 0.6))
    = max(0.5, 0.4)
    = 0.5
x1z3= max(min(0.6, 0.1), min(0.4, 0.4))
    = max(0.1, 0.4)
    = 0.4
x2z1= max(min(0.7, 0.8), min(0.3, 0.0))
    = max(0.7, 0.0)
    = 0.7
x2z2= max(min(0.7, 0.5), min(0.3, 0.6))
    = max(0.5, 0.3)
    = 0.5
x3z3= max(min(0.7, 0.1), min(0.3, 0.4))
    = max(0.1, 0.3)
    = 0.3

So, option (C) is correct.
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