UGC-NET | UGC NET CS 2016 July – III | Question 64

Let R and S be two fuzzy relations defined as:

and

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

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

Answer: (D)
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(0.7, 0.9), min(0.5, 0.1))
    = max(0.7 0.1)
    = 0.7
x1z2= max(min(0.7, 0.6), min(0.5, 0.7))
    = max(0.6, 0.5)
    = 0.6
x1z3= max(min(0.7, 0.2), min(0.5, 0.5))
    = max(0.2, 0.5)
    = 0.5
x2z1= max(min(0.8, 0.9), min(0.4, 0.1))
    = max(0.8, 0.1)
    = 0.8
x2z2= max(min(0.8, 0.6), min(0.4, 0.7))
    = max(0.6, 0.4)
    = 0.6
x3z3= max(min(0.8, 0.2), min(0.4, 0.5))
    = max(0.2, 0.4)
    = 0.4

So, option (C) is correct.
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