its (0.5,0.9) for union you take the (sup(0.3,0.5),sup(0.7,0.9) and for intersection you take the inf

Dear Shawkat Alkhazaleh Sir, Thank you for your response.

By following this conventional approach, don't we clipping the result partially. 

In the given example we are taking the answer as 

             sup(0.3,0.5),sup(0.7,0.9) = 0.5-0.9 

In this, we are missing the values 0.3-0.5 as a result of union.

Same happens in case of intersection also, we are adding some more value... as we are taking infimum of both values to get the intersection. In this case the ans. will be 0.3-0.7. where as some part of this answer does not belongs to both values.

If we take 

inf(lower ranges) , sup(upper ranges) for union then we will get the ans for given example as (0.3-0.9)

sup(lower ranges) , inf(upper ranges) for intersection will give the ans. (0.5-0.7)

Is it not convincing...?

actually its not convincing in crisp case but in fuzzy case its convincing, let us take the following example

(0,1) union (1,1) by using your formula the ans. is (0,1) which is not correct also for intersection the ans. is (1,1) which is not correct also. this example talking about the border conditions which must be hold in union and intersection

Thank you Sir

Union is equivalent to Max as described by Mr. Shawkat, it makes sense.

Dear All,

Mohanty is right. You are confusing this notion that Union is sup and intersection is inf. For detail consider [0.3, 0.7] as function f: [0,1] into [0,1] where f(x)=1 for x in [0.3,0.7] and f(x)= 0 otherwise. Similarly [0.5, 0.9] define g: [0,1] into [0,1] where g(x)=1 for x in [0.5,0.9] and g(x)= 0 otherwise. Now f and g are fuzzy sets (in fact fuzzy sets of type 1). Take their union and intersection as sup and inf and you will get Mohanty results.

Totally agreed with Ismat Baig

given these two fuzzy sets

A = {(a, 0.2), (b, 0.1), (c, 0.4)}

B = {(a, 0.4), (b, 0.3)}

what is the implication of the difference in the structures of the two fuzzy sets?

Is it possible to find their union and intersection without adjusting B?

{(a, 0.4),(b, 0.3), (c, 0.4)}

Excellent answers

Great, I got it!

Many thanks@Muhammad Saeed

If A=[2*alpha+1, 5-2*alpha]

And B=[2*alpha+2, 6-2*alpha]

Then

A inter. B= min(A,B)= [2*alpha+1, 2*alpha+2]

A union B=max(A,B)=[5-2*alpha, 6-2*alpha]

If it’s wrong, please correct it.