How to calculate fuzzy arithmetic?

UGC NET JUNE 2015 Paper III

71.  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)}

Answer : D

Explanation 

In the fuzzy logic symbol ⊗ is used for min property and ⊕ symbol is used for max property. The same hint is given in the question.

below is two fuzzy sets given

A={(1,0.3), (2,0.6), (3,1), (4,0.7), (5,0.2)}

B={(10,0.5), (11,1), (12,0.5)}

based on this fuzzy set first we will find min property  μA(x)⊗μB(y)

how to find min property?

A		B
(1,0.3)	⊗	(10,0.5)	=	(1+10,min(0.3,05)) = 11,0.3
(1,0.3)	⊗	(11,1)	=	(1+11,min(0.3,1)) = 12,0.3
(1,0.3)	⊗	(12,0.5)	=	(1+12,min(0.3,0.5)) = 13,0.3

likewise we find min properties of the set A and set B as following.

(11,0.3),(12,0.3),(13,0.3),

(12,0.5),(13,0.6),(14,0.5),

(13,0.5),(14,1),(15,0.5),

(14,0.5),(15,0.7),(16,0.5),

(15,0.2),(16,0.2),(17,0.2)

now we have to find the max property from the above table.

find (11,0.3) - is there any property with value 11? no so (11,0.3) is max. now check (12,0.3) is there any value of 12 and its fuzzy value larger than 0.3 ? Yes. (12, 0.5) this is max so select (12,0.5) likewise check the value of 13,14,15,16,17. we get the following result.

(11,0.3), (12,0.5), (13,0.6), (14,1), (15,0.7), (16,0.5), (17,0.2) 

this is the answer  D