Question

A crisp set A defined over X={1,2,3,5,7} is A={1,3,7}. What would be it’s equivalent fuzzy set?

Answer 1

Answer:

Consider the two crisp sets A and B as given below. A ={ 1, 2, 3, 4}

B = {3, 5, 7 }.

Then, A × B = {(1, 3),(1, 5),(1, 7),(2, 3),(2, 5),(2, 7),(3, 3),(3, 5),

(3, 7),(4, 3),(4, 5),(4, 7)}

Let us define a relation R as R = {(a, b)|b = a + 1,(a, b) ∈ A × B}

Then, R = {(2, 3),(4, 5)} in this case.

We can represent the relation R in a matrix form as follows.

R =









3 5 7

1 0 0 0

2 1 0 0

3 0 0 0

4 0 1 0







