Q. The height h(A) of a fuzzy set A is defined as

h(A) = sup A(x)

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Q. A __________ point of a fuzzy set A is a point x ∈ X at which µA(x) = 0.5

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Q. 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:

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Q. Given  U =  {1,2,3,4,5,6,7}
 
             A = {(3, 0.7), (5, 1), (6, 0.8)}
 
then A will be: (where ~ → complement)

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Q. 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

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Q. Perceptron learning, Delta learning and LMS learning are learning methods which falls under the category of

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Q. What are the following sequence of steps taken in designing a fuzzy logic machine ?

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Q. Compute the value of adding the following two fuzzy integers:

A = {(0.3,1), (0.6,2), (1,3), (0.7,4), (0.2,5)}
B = {(0.5,11), (1,12), (0.5,13)}

Where fuzzy addition is defined as

μA+B(z) = maxx+y=z (min(μA(x), μB(x)))
Then, f(A+B) is equal to

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Q. A perceptron has input weights W1 = -3.9 and W2 = 1.1 with threshold value T = 0.3. What output does it give for the input x1 = 1.3 and x2 = 2.2?

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Q. In a single perceptron, the updation rule of weight vector is given by

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Q. The golden ratio ϕ and its conjugate ϕ’ both satisfy the equation

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Q. At any iteration of simplex method, if Δj (Zj – Cj) corresponding to any non-basic variable Xj is obtained as zero, the solution under the test is

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Q. A basic feasible solution to a m-origin, n-destination transportation problem is said to be ................... if the number of positive allocations are less than m + n – 1.

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Q. A fuzzy set A on R is ................. iff A(λx1 + (1 – λ)x2) ≥ min [A(x1), A(x2)] for all x1, x2 ∈ R and all λ ∈ [0, 1], where min denotes the minimum operator.

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Q. 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

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