Build one multi-layered perceptron neural network, with 3 inputs and 3 outputs, to implement the following function: ! ??# = 5sin (????#) + 20???2 ??2 = 0.3??#??2 + ??67 ??8 = 2cos (0.2??2 ? 2) + ??#??8 ??# ? [?2, 2], ??2 ? [0, 100], and ??8 ? [?5, 3] You should use the MATLAB NN Toolbox to complete this question. In your answer, please clearly provide the following information: a) The NN structure b) The number of training patterns used and how many iterations are required. c) What is the accuracy of your training results. d) Include MATLAB code and output graphs in the assignment e) Print the codes and include in the assignment. (12 marks) 2. Using Hebbian-type of learning rule to obtain a Hopfield network which can memorise the following patterns: [1 1 -1 1 1], [1 -1 1 -1 -1], [1 -1 -1 1 -1] Test the network with the following corrupted patterns to see what are the outputs. Are they the expected outputs? Why? [-1 1 -1 1 1], [1 1 1 -1 -1], [1 -1 -1 -1 -1] You need to include the following in the answer: a) Draw the structure of the Hopfield network b) Clearly indicate the weights and biases in the Hopfield network (5 marks) 3. For a given fuzzy logic controller, we have the following three fuzzy control rules: Rule 1: IF x is A1 OR y is B1, THEN z is C1. Rule 2: IF x is A2 AND y is ?? B 2, THEN z is C2. Rule 3: IF x is A3 AND y is B3, THEN z is C3. Suppose x0 and y0 are the sensor readings for linguistic input variables x and y and the following membership functions for fuzzy predicates A1, A2, A3, B1, B2, B3, C1, C2 and C3