he room temperature x in Fahrenheit (F) is converted to y in Celsius (C) through the function y = f(x) = 5(x-32)/9. Let a fuzzy set B1 (in Fahrenheit) be defined by B1 = 0.15/76 + 0.42/78 + 0.78/80 + 1.0/82 + 1.0/84 What is the induced fuzzy set of B1 in terms of the extension principle? B2 =
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- The room temperature x in Fahrenheit is converted to y in Celsius through the function y = f(x) = 5(x-32)/9. Let a fuzzy set B1 (in Fahrenheit) be defined by B1 = 0.15/76 + 0.42/78 + 0.78/80 + 1.0/82 + 1.0/84 What is the induced fuzzy set of B1 in terms of the extension principle? B2 = ?Fuzzy databases make use of fuzzy set theory. In this theory, any subset ? of a universe ? is represented by a characteristic function ?? that maps ? to _________________. For every element ? ∈ ?, the value ??(?) is interpreted as the degree of confidence that ? ∈ ?. the set {0,1} the interval 0,1 the set ℜ of all real numbers the set ℤ of all integersPlease answer the following question in depth with full detail. Consider the 8-puzzle that we discussed in class. Suppose we define a new heuristic function h3 which is the average of h1 and h2, and another heuristic function h4 which is the sum of h1 and h2. That is, for every state s ∈ S: h3(s) =h1(s) + h2(s) 2 h4(s) =h1(s) + h2(s) where h1 and h2 are defined as “the number of misplaced tiles”, and “the sum of the distances of the tiles from their goal positions”, respectively. Are h3 and h4 admissible? If admissible, compare their dominance with respect to h1 and h2, if not, provide a counterexample, i.e. a puzzle configuration where dominance does not hold.
- Given an abstraction of the City Tube Map where each node represents the city’s attraction, plan the trip for the tourist to visit. Start from node 1 that is their hotel, a group of tourists wants to visit all places. However, due to the time limitation, they can only visit each attraction once. To find the best order of places to visit, genetic algorithm can be used to derive the best possible solutions.(control variates) Reproduce the class example of estimating int 0 ^ 1 2 dz 1+x by the MC approach using 100 uniform random variables and after that by using a control variate with function g(U) = 1 + U as suggested in class. Compare the results.Given the sets A={1,2,a,d,f} and B={a,b,c,d,e,f}. The cardinality of A – B is
- If sets A={10,20,30,40} B ={30,40,50,60} C= {50,60,70} U = {10,20,30,40,50,60,70}What is the cardinality of A? DO NOT FORGET TO ENCLOSE YOUR ANSWERS IN A BRACKET { } IF IT IS A SET.2. Given a Sample Space S = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, Event A = {1, 3, 4, 7, 9}, and Event B = {3, 7, 9, 11, 12, 13} Find the probability P(A|B). State your answer as a value with one digit after the decimal point.5. Let R = {1, 3, π, 4, 1, 9, 10}, S = {{1}, 3, 9, 10}, T = {1, 3, π}, and U = {{1, 3, π}, 1}. Which of thefollowing are true? For those that are not, why not? (d) 1 ⊆ U(e) {1} ⊆ T(f) {1} ⊆ S(g) {1} ∈ S
- 1.suppose fuzzy set A is described by ua(x)=bell(x;a,b,c).show that the classical fuzzy component of A is described as ua(x)=bell(x;a,-b,c) 2. Find the level set A(alpha) and its width for a fuzzy set A defined by uA(x)= trapezoid(x;a,b,c,d).When a temperature gauge surpasses a threshold, your local nuclear power station sounds an alarm. Core temperature is gauged. Consider the Boolean variables A (alarm sounds), FA (faulty alarm), and FG (faulty gauge) and the multivalued nodes G (gauge reading) and T (real core temperature). Since the gauge is more likely to fail at high core temperatures, draw a Bayesian network for this domain.Let the Universal set be {daisy, rose, lily, buttercup, dandelion, tulip, daffodil, clematis, bluebell, pansy, foxglove} Consider the sets G = (rose, lily, tulip, daffodil, clematis, pansy, foxglove} W = {daisy, buttercup, dandelion, daffodil, bluebell, foxglove} B = {bluebell, foxglove, clematis} What is (B n W) U G? {} {daisy, rose, lily, buttercup, dandelion, tulip, daffodil, clematis, bluebell, pan foxglove} • (daisy, daffodil, foxglove} • (bluebell, foxglove, rose, lily, tulip, daffodil, clematis, pansy}