A fuzzy inference system is designed to recommend the speed of a fan of a cooling tower. Three different linguistics variables (2 input and 1 output) are the temperature of the material (x), the humidity of cut (y) and the fan speed (z), respectively. Their membership functions (normalized to a scale of 0 to 10) are given as follows:
μ_low(w) = { w/2, 0 < w ≤ 2; (4-w)/2, 2 < w ≤ 4 }
μ_medium(w) = { (w-2)/3, 2 < w ≤ 5; (8-w)/3, 5 < w ≤ 8 }
μ_high(w) = { (w-6)/2, 6 < w ≤ 8; (10-w)/2, 8 < w ≤ 10 }
The if-then fuzzy rules are given as Table Q4:
Table Q4
Humidity: Low, Medium, High
Temperature Low: L, L, M
Temperature Medium: M, M, H
Temperature High: M, H, H
(e.g. If the temperature is low and the humidity is medium, then fan speed should be medium)
(a) Sketch the membership function of temperature and humidity. (8 marks)
(b) Given the temperature (x) is 3 and the humidity (y) is 7, determine the rules fired and their degree of output functions using the minimum inference method. (12 marks)
(c) Determine the crisp out using the weighted average defuzzification method. Show the equation clearly. (5 marks)