Question

The consequent membership functions of a five-rule one-input single-output fuzzy reasoning system are specified by TriMF(y,[ai,bi,ci])=max[min((y−ai)/( bi-ai),(ci-y)/(cibi),0] for rule i to 5 such that [a1,b1,c1]=[0,1,2],[a2,b2,c2]=[1,3,5],[a3,b3,c3]=[4,5,6], [a4,b4,c4]=[5,7,9], and [a5,b5,c5]=[8,9,10].

The output weight wi of the rule i for i=1 to 5 are given by w1 is 0.4,w2 is 0.4,w3 is 0.3,w4 is 0.6 , and w5 is 0.5 .
Calculate the defuzzified output of the five-rule one-input single-output fuzzy reasoning system using the fast computation method for defuzzified output as ______Your Answer (rounded to four decimal places)

Answer 1

The defuzzified output of the five-rule one-input single-output fuzzy reasoning system using the fast computation method is 5.3636 when rounded to four decimal places.

Step-by-step explanation:

The question is asking for the defuzzified output of a fuzzy reasoning system using the fast computation method. The given fuzzy reasoning system has five rules with specified triangular membership functions and predefined output weights.

Using the formula for the fast computation method, the defuzzified output Y can be calculated as the sum of the product of each rule's peak output value (bi) and its corresponding output weight (wi), divided by the sum of the output weights. The formula for the defuzzified output Y is given by:

Y = (w1 • b1 + w2 • b2 + w3 • b3 + w4 • b4 + w5 • b5) / (w1 + w2 + w3 + w4 + w5)

Substituting the given values we get:

Y = (0.4 • 1 + 0.4 • 3 + 0.3 • 5 + 0.6 • 7 + 0.5 • 9) / (0.4 + 0.4 + 0.3 + 0.6 + 0.5)

Y = (0.4 + 1.2 + 1.5 + 4.2 + 4.5) / (2.2)

Y = 11.8 / 2.2 = 5.3636

Therefore, the defuzzified output is 5.3636 when rounded to four decimal places.