Consider a fuzzy logic system that controls a heater in a room. The system takes two inputs: the temperature x and the humidity y. The fuzzy sets for x are Cold and Hot with membership functions μCold(x) and μHot(x), respectively. Similarly, the fuzzy sets for y are Dry and Wet with membership functions μDry(y) and μWet(y), respectively. The output z controls the heater and has Low and High fuzzy sets.The system has two rules:If the room is Cold and Dry, then the heater is set to Low.If the room is Hot and Wet, then the heater is set to High.Now, suppose on a particular day, the membership functions for the inputs are as follows: μCold(x) = 0.4, μHot(x) = 0.6, μDry(y) = 0.5, and μWet(y) = 0.5. Can you compute the rule strengths for the two rules? a. 0.5, 0.5 b. 0.2, 0.3 c. 0.4, 0.5 d. 0.24,0.25
Question
Consider a fuzzy logic system that controls a heater in a room. The system takes two inputs: the temperature x and the humidity y. The fuzzy sets for x are Cold and Hot with membership functions μCold(x) and μHot(x), respectively. Similarly, the fuzzy sets for y are Dry and Wet with membership functions μDry(y) and μWet(y), respectively. The output z controls the heater and has Low and High fuzzy sets.The system has two rules:If the room is Cold and Dry, then the heater is set to Low.If the room is Hot and Wet, then the heater is set to High.Now, suppose on a particular day, the membership functions for the inputs are as follows: μCold(x) = 0.4, μHot(x) = 0.6, μDry(y) = 0.5, and μWet(y) = 0.5. Can you compute the rule strengths for the two rules? a. 0.5, 0.5 b. 0.2, 0.3 c. 0.4, 0.5 d. 0.24,0.25
Solution
The rule strength in a fuzzy logic system is computed by taking the minimum of the membership values of the inputs. This is because the rule is only as strong as its weakest link.
For the first rule, "If the room is Cold and Dry, then the heater is set to Low", the membership values for Cold (x) and Dry (y) are 0.4 and 0.5 respectively. So, the rule strength is min(0.4, 0.5) = 0.4.
For the second rule, "If the room is Hot and Wet, then the heater is set to High", the membership values for Hot (x) and Wet (y) are 0.6 and 0.5 respectively. So, the rule strength is min(0.6, 0.5) = 0.5.
Therefore, the rule strengths for the two rules are 0.4 and 0.5, which corresponds to option c.
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