answer:The degree of membership of a fuzzy set is a value between 0 and 1 that represents the degree to which an element belongs to that set. In this case, we need to determine the degree of membership of the speed 50 mph in the "medium" set. The "medium" speed set consists of speeds greater than 30 mph and less than or equal to 70 mph. Since 50 mph satisfies both conditions, it fully belongs to the "medium" speed set. Therefore, the degree of membership of the speed 50 mph in the "medium" set is 1.,Using the fuzzy logic system and the given rules, the degree of membership of the speed in the "medium" set can be calculated as follows: For a speed of 50 mph: 1. It is not less than or equal to 30 mph, so it does not belong to the "low" speed set. 2. It is greater than 30 mph, so it can belong to either the "medium" or "high" speed set. 3. It is less than or equal to 70 mph, so it belongs to the "medium" speed set. Since the crisp value of 50 mph belongs to the "medium" speed set, the degree of membership of the speed in the "medium" set is 1.,Since the car's speed is 50 mph, it falls within the "medium" speed set, which is defined as speeds greater than 30 mph and less than or equal to 70 mph. In this case, the degree of membership of the speed in the "medium" set is 1, as it fully belongs to this set.

answer:To find the membership values of the complement of A (denoted as Ac), we will use the formula: µAc(x) = 1 - µA(x) Now, we can calculate the membership values for each element in Ac: µAc(1) = 1 - µA(1) = 1 - 0.2 = 0.8 µAc(2) = 1 - µA(2) = 1 - 0.6 = 0.4 µAc(3) = 1 - µA(3) = 1 - 0.9 = 0.1 µAc(4) = 1 - µA(4) = 1 - 0.7 = 0.3 So, the membership values for Ac are: µAc(1) = 0.8 µAc(2) = 0.4 µAc(3) = 0.1 µAc(4) = 0.3,To find the membership values for the complement of A (Ac), we need to subtract the membership values of A from 1 since the sum of the membership values for a fuzzy set and its complement should always be equal to 1. µAc(x) = 1 - µA(x) Now, let's calculate the membership values for Ac for each element in the universe of discourse X: µAc(1) = 1 - µA(1) = 1 - 0.2 = 0.8 µAc(2) = 1 - µA(2) = 1 - 0.6 = 0.4 µAc(3) = 1 - µA(3) = 1 - 0.9 = 0.1 µAc(4) = 1 - µA(4) = 1 - 0.7 = 0.3 So, the membership values for the complement of A (Ac) are: µAc(1) = 0.8 µAc(2) = 0.4 µAc(3) = 0.1 µAc(4) = 0.3, The complement of a fuzzy set A, denoted by Ac, is defined as the set of all elements in the universe of discourse that do not belong to A. The membership function of the complement Ac is given by: µAc(x) = 1 - µA(x) for every x in X. So, for the given fuzzy set A with the membership function µA, we have: µAc(1) = 1 - µA(1) = 1 - 0.2 = 0.8 µAc(2) = 1 - µA(2) = 1 - 0.6 = 0.4 µAc(3) = 1 - µA(3) = 1 - 0.9 = 0.1 µAc(4) = 1 - µA(4) = 1 - 0.7 = 0.3 Therefore, the membership values of the complement of A for each element are: µAc(1) = 0.8 µAc(2) = 0.4 µAc(3) = 0.1 µAc(4) = 0.3

answer:First, we need to find the price of the item after the 20% discount. The original price is 50, so the discount is: 20% of 50 = 0.20 * 50 = 10 Now, subtract the discount from the original price to find the new price: 50 - 10 = 40 Now that we have the new price, we can find the degree of membership for the item in the fuzzy set "Cheap" using the given membership function: μ(x) = 1/2 - 1/2t In this case, x is the new price (40) and t is the original price (50). Plug these values into the membership function: μ(40) = 1/2 - 1/2(50) μ(40) = 1/2 - 1/100 μ(40) = 50/100 - 1/100 μ(40) = 49/100 So, the degree of membership for the item in the fuzzy set "Cheap" after the sale is 49/100 or 0.49.,First, we need to find the discounted price of the item after the 20% markdown. If the original price is 50, then: Discounted price = Original price - (0.2 * Original price) Discounted price = 50 - (0.2 * 50) Discounted price = 50 - 10 = 40 Now we can find the degree of membership for the item in the fuzzy set "Cheap" after the sale. We need to find the value of t (the absolute price of the item) for the new discounted price of 40. Since 0 ≤ x ≤ t, we can find the corresponding x-value for the given membership function: x = 1/2t - 1/2 x = 1/2(40) - 1/2 x = 20 - 1/2 x = 20 - 10 = 10 Now, we can find the degree of membership µ(x): µ(x) = 1/2 - 1/2t µ(x) = 1/2 - 1/2(40) µ(x) = 1/2 - 20 µ(x) = -10 However, the degree of membership should lie between 0 and 1, but the calculated value is negative. This indicates that the given membership function is not suitable for this particular problem or that the problem statement may be incorrect. Please clarify or provide additional information for further assistance., The degree of membership of an element in a fuzzy set is determined by its membership function. In this case, the membership function of the fuzzy set "Cheap" is given by: μ(x) = 1/2 - 1/2t, where t is the absolute price of the item. Since the original price of the item is 50, the degree of membership of the item in the fuzzy set "Cheap" after the 20% markdown can be found by first calculating the new price: New price = Original price - (Original price × Markdown percentage) New price = 50 - (50 × 0.20) = 50 - 10 = 40 Now, we can use the membership function to determine the degree of membership: t = 40 (new price) μ(x) = 1/2 - 1/2t μ(x) = 1/2 - 1/2 × 40 μ(x) = 1/2 - 20 μ(x) = -19.50 (This value is negative because the membership function is not properly scaled for the given universe. However, since we only care about the magnitude of the membership value and not its sign, the degree of membership remains positive.) To correct the scale, divide the membership function by the maximum membership value (in this case, the maximum value of t is 50 since the original price is 50, and the minimum value of t is 0): Degree of membership = |μ(x)| / (Maximum possible value of μ(x)) Degree of membership = abs(-19.50) / abs((1/2 - 1/2 × 50) / 50) Degree of membership = 19.50 / (25) Degree of membership ≈ 0.78 Hence, the degree of membership of the item in the fuzzy set "Cheap" after the sale is approximately 0.78.

answer:To determine the degree of satisfaction using fuzzy logic, we need to define the fuzzy sets for the satisfaction levels. Let's assume the following fuzzy sets for the satisfaction levels: 1. Very Satisfied (VS): 8 to 10 2. Satisfied (S): 6 to 8 3. Neutral (N): 4 to 6 4. Dissatisfied (D): 2 to 4 5. Very Dissatisfied (VD): 0 to 2 The customer rated the meal as 7.5. We can see that this rating falls in the overlapping region of the Satisfied (S) and Very Satisfied (VS) fuzzy sets. To determine the degree of satisfaction, we will calculate the membership values for these two fuzzy sets. For the Satisfied (S) fuzzy set, we can use a linear decreasing function from 8 to 6: Membership value of S (µS) = (8 - 7.5) / (8 - 6) = 0.5 / 2 = 0.25 For the Very Satisfied (VS) fuzzy set, we can use a linear increasing function from 8 to 10: Membership value of VS (µVS) = (7.5 - 8) / (10 - 8) = -0.5 / 2 = -0.25 (since the value is negative, the membership value is 0) So, the degree of satisfaction for the customer is: - 25% Satisfied (S) - 0% Very Satisfied (VS) The customer is 25% satisfied with the meal, which indicates a moderate level of satisfaction., In fuzzy logic, we can't provide an exact answer since it deals with uncertain and vague concepts. However, I can tell you how to interpret the customer's satisfaction level using fuzzy sets. The customer rated the meal as 7.5, which falls under the "satisfied" category in most fuzzy logic applications. The "very satisfied" category typically starts from around 8 or 9, depending on the specific definition of the membership function used. To represent this mathematically, you would need to define a membership function for each category (very satisfied, satisfied, neutral, dissatisfied, very dissatisfied). For example, a possible membership function for the "satisfied" category could be: μ_Satisfied(x) = { 0 if x < 5, (x - 5) / (8 - 5) if 5 <= x < 8, 1 if x >= 8, } Using this membership function, we can calculate the degree of membership for the customer's rating of 7.5 as follows: μ_Satisfied(7.5) = (7.5 - 5) / (8 - 5) = 0.5 So, according to this interpretation, the customer has a degree of satisfaction of 0.5, meaning they are moderately satisfied with the meal.,To determine the degree of satisfaction using fuzzy logic, we need to create fuzzy sets for each satisfaction level. Here are some possible fuzzy sets for the satisfaction levels: 1. Very Satisfied (VS): (0, 3 2. Satisfied (S): (3, 7 3. Neutral (N): (7, 8 4. Dissatisfied (D): (8, 10 5. Very Dissatisfied (VD): (10, 11 Now let's define a membership function for each fuzzy set: 1. VS(x): x > 3 2. S(x): 3 ≤ x ≤ 7 3. N(x): 7 < x ≤ 8 4. D(x): 8 < x ≤ 10 5. VD(x): x > 10 Since the customer rated the meal as 7.5, we want to find the degree of satisfaction by integrating each membership function over the domain: VF(7.5) = VS * d(x) + S * d(x) + N * d(x) + D * d(x) + VD * d(x) where d(x) is the width of the overlapping interval (difference between the upper and lower limits) for each fuzzy set at x=7.5. 1. VS: 0 since x is 7.5 and the upper limit for VS is 3. 2. S: d(x) = 7.5 - 3 = 4.5 3. N: d(x) = 8 - 7.5 = 0.5 4. D: d(x) = 10 - 8 = 2 5. VD: 0 since x is 7.5 and the upper limit for VD is 11. Now we can calculate the values for each membership function and sum them up: VS: 0 S: 4.5 * S(7.5) = 4.5 N: 0.5 * N(7.5) = 0.5 D: 2 * D(7.5) = 0 (since the customer is not in the D range)