July2016 cs Q64

0. Let R and S be two fuzzy relations defined as :
Then, the resulting relation, T, which relates elements of universe x to elements of universe z using max-min composition is given by
and

A
B
C
D

Answer
Comment
Array

Option : 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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