| 1. | Consider a fuzzy set A defined on the interval X = [0, 10] of integers by the membership Junction
μA(x) = x / (x+2) Then the α cut corresponding to α = 0.5 will be |
| a. | {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} |
| b. | {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} |
| c. | {2, 3, 4, 5, 6, 7, 8, 9, 10} |
| d. | None of the above |
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Answer: (c).{2, 3, 4, 5, 6, 7, 8, 9, 10}
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| 2. | If A and B are two fuzzy sets with membership functions:
μa(χ) ={0.2,0.5.,0.6,0.1,0.9} μb (χ)= {0.1,0.5,0.2,0.7,0.8} then the value of μa ∩ μb will be |
| a. | {0.2,0.5,0.6,0.7,0.9} |
| b. | {0.2, 0.5,0.2, 0.1,0.8} |
| c. | {0.1, 0.5, 0.6, 0.1,0.8} |
| d. | {0.1, 0.5, 0.2, 0.1,0.8} |
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Answer: (d).{0.1, 0.5, 0.2, 0.1,0.8}
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| 3. | The height h(A) of a fuzzy set A is defined as
h(A) = sup A(x) |
| a. | h(A) = 0 |
| b. | h(A) <0 |
| c. | h(A)=1 |
| d. | h(A)<1 |
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Answer: (c).h(A)=1
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| 4. | A __________ point of a fuzzy set A is a point x ∈ X at which µA(x) = 0.5 |
| a. | Core |
| b. | Support |
| c. | Cross-over |
| d. | α - cut |
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Answer: (c).Cross-over
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| 5. | Suppose the function y and a fuzzy integer number around -4 for x are given as y= (x-3)2 + 2.
Around -4 = {(2, 0.3), (3, 0.6), (4, 1), (5, 0.6), (6, 0.3)} respectively. Then f (Around -4) is given by: |
| a. | {(2, 0.6), (3, 0.3), (6, 1), (11, 0.3)} |
| b. | {(2, 0.6), (3, 1), (6, 1), (11, 0.3)} |
| c. | {(2, 0.6), (3, 1), (6, 0.6), (11, 0.3)} |
| d. | {(2, 0.6), (3, 0.3), (6, 0.6), (11, 0.3)} |
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Answer: (c).{(2, 0.6), (3, 1), (6, 0.6), (11, 0.3)}
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| 6. | Given U = {1,2,3,4,5,6,7}
A = {(3, 0.7), (5, 1), (6, 0.8)} then A will be: (where ~ → complement) |
| a. | {(4, 0.7), (2,1), (1,0.8)} |
| b. | {(4, 0.3.): (5, 0), (6. 0.2) } |
| c. | {(l, 1), (2, 1), (3, 0.3), (4, 1), (6,0.2), (7, 1)} |
| d. | {(3, 0.3), (6.0.2)} |
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Answer: (c).{(l, 1), (2, 1), (3, 0.3), (4, 1), (6,0.2), (7, 1)}
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| 7. | Consider a fuzzy set old as defined below
Old = {(20, 0.1), (30, 0.2), (40, 0.4), (50, 0.6), (60, 0.8), (70, 1), (80, 1)} Then the alpha-cut for alpha = 0.4 for the set old will be |
| a. | {(40,0.4)} |
| b. | {50, 60, 70, 80} |
| c. | {(20, 0.1), (30, 0.2)} |
| d. | {(20, 0), (30, 0), (40, 1), (50,1), (60, 1), (70, 1), (80, 1)} |
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Answer: (d).{(20, 0), (30, 0), (40, 1), (50,1), (60, 1), (70, 1), (80, 1)}
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| 8. | Perceptron learning, Delta learning and LMS learning are learning methods which falls under the category of |
| a. | Error correction learning - learning with a teacher |
| b. | Reinforcement learning - learning with a critic |
| c. | Hebbian learning |
| d. | Competitive learning - learning without a teacher |
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Answer: (a).Error correction learning - learning with a teacher
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| 9. | Let R and S be two fuzzy relations defined as follows. Then, the resulting relation, T, which relates elements of universe x to the elements of universe z using max-min composition is given by:
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| a. | (1) |
| b. | (2) |
| c. | (3) |
| d. | (4) |
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Answer: (c).(3)
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| 10. | What are the following sequence of steps taken in designing a fuzzy logic machine ? |
| a. | Fuzzification → Rule evaluation → Defuzzification |
| b. | Fuzzification → Defuzzification → Rule evaluation |
| c. | Rule evaluation → Fuzzification → Defuzzification |
| d. | Rule evaluation → Defuzzification → Fuzzification |
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Answer: (a).Fuzzification → Rule evaluation → Defuzzification
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