## NPTEL Introduction To Soft Computing Week 1 Assignment Answers 2024

1. Which of the following is True?

a. Hard computing always requires fuzzy logic.

b. Soft computing is always more computationally expensive.

c. Hard computing is deterministic, while soft computing is probabilistic.

d. Soft computing always provides precise solutions.

Answer :-

2. Which of the following best describes the range of values a fuzzy membership function can take on?

a. (0 ,1)

b. [0 ,1]

c. (0 ,1]

d. (-∞ ,∞)

Answer :-

3. Which of the following statements regarding crisp sets and fuzzy sets is correct?

a. A fuzzy set is a special case of a crisp set.

b. Fuzzy sets are subsets of crisp sets.

c. Crisp and fuzzy sets are distinct concepts with no relationship.

d. A crisp set is a special case of a fuzzy set.

Answer :-

4. A fuzzy set has a non-empty 1-cut (α-cut with α = 1). What can you say about its normality and core?

a. It is guaranteed to be normal, and its core is non-empty.

b. It is normal, but its core could be empty or non-empty.

c. It is definitely not normal, and its core is definitely empty.

d. Normality and the core of fuzzy sets are unrelated to the 1-cut.

Answer :-

5. A Gaussian membership function of x, with two parameters, c and σ, is given by

Answer :-

6. Two fuzzy set A and B are given by A ={(x1, 0.3), (x2, 0.9), (x3, 0.4)}, and B ={(x1, 0.1), (x2, 0.5), (x3, 0.4)} Intersection of these two sets i.e. A⋂B is given by

a. {(x1, 0.3), (x2, 0.5), (x3, 0.4)}

b. {(x1, 0.1), (x2, 0.9), (x3, 0.4)}

c. {(x1, 0.1), (x2, 0.5), (x3, 0.9)}

d. {(x1, 0.1), (x2, 0.5), (x3, 0.4)}

Answer :-

7. If A and B are two fuzzy sets with membership functions

μA(x) = {0.6,0.5,0.1,0.7,0.8}

μB(x) = {0.9,0.2,0.6,0.8,0.5}

Then the value of μ(A∪B)’(x) will be

a. {0.9, 0.5, 0.6, 0.8, 0.8}

b. {0.6, 0.2, 0.1, 0.7, 0.5}

c. {0.1, 0.5, 0.4, 0.2, 0.2}

d. {0.1, 0.5, 0.4, 0.2, 0.3}

Answer :-

8. A ∩ B = B ∩ A This property is called

a. Associativity

b. Distributivity

c. Commutativity

d. Transitivity

Answer :-

9. Two fuzzy relations are given by

**The Max-product composition is**

Answer :-

10. The set of all points x in X in a fuzzy set A is defined as a “core”, if

a. μA(X) = 0

b. μA(X) > 1

c. μA(X) = 1

d. μA(X) < 1

Answer :-