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Math · Advanced Math
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Exercise 8.2. Consider Example 8.1 and determine the y using the indexed center of gravity defuzzifier with α 0.1. Compute the y for the specific values of w1 and w2 in Table 8.1 Attachment Example 8.1. Suppose that the fuzzy set B is the union of the two fuzzy sets shown in Fig. 8.2 with蔧-0 and 12-1. Then the center average defuzzifier gives W2 (8.19) Table 8.1. Comparison of the center of gravity and center average defuzzifiers for Example 8.1. (center of relative error 0.0275 0.0133 0.0428 0.0743 0.0192 0.0342 0.2308 0.1600 0.0476 center 0.9 0.7 0.9 0.5 0.9 0.2 0.6 0.7 0.6 0.5 0.6 0.2 0.3 0.7 0.3 0.5 0.3 0.2 0.4258 0.5457 0.7313 0.3324 0.4460 0.6471 0.1477 0.2155 0.3818 0.4375 0.5385 0.7000 0.3571 0.4545 0.6250 0.1818 0.2500 0.4000 We now compute the y resulting from the center of gravity defuzzifier. First, we notice that the two fuzzy sets interset a hence, ()dy area of the first fuzzy setarea of the second fuzzy set - their intersection uW2 (8.20) From Fig. 8.2 we have yw1(1 -y)dy + yw2ydy 3 (8.21) Dividing (8.21) by (8.20) we obtain the y of the center of gravity defuzzifier. Table 8.1 shows the values of y using these two defuzzifiers for certain values of w and w2. We see that the computation of the center of gravity defuzzifier is much more intensive than that of the center average defuzzifier.

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