3. For a given fuzzy logic controller, we have the following three fuzzy control rules: Rule 1: IF x is A3 AND y is B₁, THEN z is C₂. Rule 2:

IF x is A₂ AND y is B3, THEN z is NOT C3. Rule 3: IF x is A₁ OR y is B2, THEN z is C₁. Suppose the following membership functions for fuzzy predicates A₁, A2, A3, B₁, B2, B3, C1, C2 and C3 are given: HA₂ (x) = HB₂ (y) = 5+x 5 1 10-x 5 3+z H₁₂ (2) = 1 3-Z Note: • -5≤x≤0 0≤x≤5, HA₂ (x) = 5 ≤ x ≤ 10 1≤ y ≤ 5 5≤ y ≤7 HB₂ (Y) = 7 12-y -3 ≤z≤-1 -1 ≤z≤+1, Mc₂ (2) = 1≤z≤ 3 -E 2≤x≤5 5≤x≤9' 1≤ y ≤8 8≤ y ≤ 12' HA₂ (X)= - | - 10 1≤z≤4 4≤257' H²₂ (2) = 14-X y-8 Ha₂(y)= 15-y 2-5 11-z 6 ≤ x ≤ 10 10 ≤ x ≤ 14' MATLAB Fuzzy Logic Toolbox can be used to confirm the results. You are NOT required to submit the Fuzzy Logic Toolbox codes. 8 ≤ y ≤ 12 12 ≤ y ≤ 15' Assume discrete universes for x, y and z. If at time t₁, the sensor reading values are x(t₁) = 3.5 and y(t₁) = 6.5, manually calculate the final control output. Clearly state assumptions and procedures that you made in solving this problem. 5≤z≤7 7≤z≤9 9 ≤z≤ 11 (10 marks)