Fuzzy-logic

Question 1
Let A and B be two fuzzy integers defined as :
A = {(1, 0.3), (2, 0.6), (3, 1), (4, 0.7), (5, 0.2)}
B = {(10, 0.5), (11, 1), (12, 0.5)}
Using fuzzy arithmetic operation given by
A
{(11, 0.8), ,(13, 1), (15, 1)}
B
{(11, 0.3), ,(12, 0.5), (13, 1), (14, 1), (15, 1), (16, 0.5), (17, 0.2)}
C
{(11, 0.3), ,(12, 0.5), (13, 0.6), (14, 1), (15, 1), (16, 0.5), (17, 0.2)}
D
{(11, 0.3), ,(12, 0.5), (13, 0.6), (14, 1), (15, 0.7), (16, 0.5), (17, 0.2)}
Engineering-MathematicsFuzzy-logicUGC NET CS 2015 June Paper-3
Question 1 Explanation: 

Step 2: Now from Step 1 select distinct elements and if two elements are same then select the one having maximum membership.
μ A+B (2) = { (11, 0 .3) (12, 0 .5) (13, 0 .6) (14, 1 ) (15, 0 .7) (16, 0 .5) (17, 0 .2)}
⟶ Hence option (D) is the correct answer.
Question 2
Suppose the function y and a fuzzy integer number around - 4 for x are given as y = (x - 3)​ 2​ + 2.
Around - 4 = {(2, 0.3), (3, 0.6), (4, 1), (5, 0.6), (6, 0.3)} respectively. Then f (Around - 4) is given by:
A
{(2, 0.6), (3, 0.3), (6, 1), (11, 0.3)}
B
{(2, 0.6), (3, 1), (6, 1), (11, 0.3)}
C
{(2, 0.6), (3, 1), (6, 0.6), (11, 0.3)}
D
{(2, 0.6), (3, 0.3), (6, 0.6), (11, 0.3)}
Engineering-MathematicsFuzzy-logicUGC NET CS 2015 June Paper-3
Question 2 Explanation: 

⟶ Take highest membership i.e., ‘1’.
So Around -4 for y is
{(3, 1 ) (2, 0 .6) (6, 0 .6) (11, 0 .3)}
⟶ Hence option (C) is the correct answer.
There are 2 questions to complete.

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