UGC NET CSE | June 2016 | Part 3 | Question: 65

Question

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

$\mu_{A+B} (z) = max_{x+y=z} (min (\mu_A(x), \mu_b(x)))$

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 1

μA+B(z)=max x+y=z(min(μA(x),μB(x)))

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 follwing 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)}

now write all distinct elements with max membership (written in bold)  value since max is there in the question

ANS WILL BE D     {(0.3, 12), (0.5, 13), (0.6, 14), (1, 15), (0.7, 16), (0.5, 17), (0.2, 18)}

Comments

Thanks a lot for explanation

---

Hello Sanjay ..can u explain it properly specially second half

---

It has been taken like,

with 12, there is only (0.3, 12)
with 13, there are (0.3,13) (0.5,13). thus max is (0.5,13)

with 14, there are (0.3,14) (0.6,14) (0.5,14). thus max is (0.6,14)

this continues for all the terms. 

Last we will get,
{(0.3, 12), (0.5, 13), (0.6, 14), (1, 15), (0.7, 16), (0.5, 17), (0.2, 18)}