## NPTEL Introduction To Soft Computing Week 2 Assignment Answers 2024

1. What is the primary difference between crisp propositions and fuzzy propositions?

a. Crisp propositions always return a value between 0 and 1.

b. Fuzzy propositions always return a binary value.

c. Crisp propositions are two-valued, whereas fuzzy propositions can have values between 0 and 1.

d. Fuzzy propositions are two-valued, whereas crisp propositions can have values between 0 and 1.

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2. In the context of fuzzy logic, which operation evaluates the minimum membership value at each point?

a. P ∨ Q

b. P ∧ Q

c. P ⇒ Q

d. P ⇔ Q

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3. Which of the following operations is NOT associated with the T-norm operator?

a. Minimum

b. Algebraic product

c. Union

d. Drastic product

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4. Given the conditional statement “If a student studies hard, then they will pass the exam,” and the observation that “the student did not pass the exam”. What is the valid inference using Modus Tollens?

a. The student did not study hard.

b. The student studied hard.

c. The exam was too difficult.

d. The student will never pass any exam.

Answer :-

5. Given two fuzzy sets:

A ={(a**1,0.3**),(a**2,0.6**),(a**3,0.8**)} , B={(b**1,0.4**),(b**2,0.5**)}

**find** R=(B×A) **?**

Answer :-

6. Which of the following defuzzification methods is not a centroid method?

a. Centre of gravity method (COG)

b. Center of Mass (CoM)

c. Centre of sum method (COS)

d. Center of Area method (CoA)

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7. Consider the two fuzzy sets

Using Zadeh’s notations, the fuzzy set A∪B into λ –cut sets for λ = 0.7 is

a. {0.7, 0.3, 0.6}

b. {0.4, 0.3, 0.6}

c. {0.5, 0.2, 0.6}

d. {0.2, 0.4, 0.6}

Answer :-

8. Which of the following is the correct mathematical expression of the COG method?

Answer :-

9. What is the following sequence of steps taken in designing a fuzzy logic system?

a. Fuzzification → Rule evaluation → Defuzzification

b. Fuzzification → Defuzzification → Rule evaluation

c. Rule evaluation → Fuzzification → Defuzzification

d. Rule evaluation → Defuzzification → Fuzzification

Answer :-

10. A fuzzy conjunction operation denoted as t(x,y) and fuzzy disjunction operator denoted as s(x,Y) from dual pair if they satisfy the condition:

a. t(x,y) = 1 – s(x,y)

b. t(x,y) = s(1-x,1-y)

c. t(x,y) = 1- s(1-x,1-y)

d. t(x,y) = s(1+x,1+y)

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